IU Average move How The Script Works :
1. This script calculate the average movement of the price in a user defined custom session and plot the data in a table from on top left corner of the chart.
2. The script takes highest and lowest value of that custom session and store their difference into an array.
3. Then the script average the array thus gets the average price.
4. Addition to that the script converter the price pip change into percentage in order to calculate the value in percentage form.
5. This script is pure price action based the script only take price value and doesn't take any indicator for calculation.
6. The script works on every type of market.
7. If the session is invalid it returns nothing
8. The background color, text color and transparency is changeable.
How User Can Benefit From This Script:
1. User can understand the volatility of any session that he/she wish to trade.
2. It can be helpful for understanding the average price moment of any tradeble asset.
3. It will give the average price movement both in percentage and points bases.
4. By understanding the volatility user can adjust his stop loss or take profit with respect his risk management.
Statistics
Quadratic & Linear Time Series Regression [SS]Hey everyone,
Releasing the Quadratic/Linear Time Series regression indicator.
About the indicator:
Most of you will be familiar with the conventional linear regression trend boxes (see below):
This is an awesome feature in Tradingview and there are quite a few indicators that follow this same principle.
However, because of the exponential and cyclical nature of stocks, linear regression tends to not be the best fit for stock time series data. From my experience, stocks tend to fit better with quadratic (or curvlinear) regression, which there really isn't a lot of resources for.
To put it into perspective, let's take SPX on the 1 month timeframe and plot a linear regression trend from 1930 till now:
You can see that its not really a great fit because of the exponential growth that SPX has endured since the 1930s. However, if we take a quadratic approach to the time series data, this is what we get:
This is a quadratic time series version, extended by up to 3 standard deviations. You can see that it is a bit more fitting.
Quadratic regression can also be helpful for looking at cycle patterns. For example, if we wanted to plot out how the S&P has performed from its COVID crash till now, this is how it would look using a linear regression approach:
But this is how it would look using the quadratic approach:
So which is better?
Both linear regression and quadratic regression are pivotal and important tools for traders. Sometimes, linear regression is more appropriate and others quadratic regression is more appropriate.
In general, if you are long dating your analysis and you want to see the trajectory of a ticker further back (over the course of say, 10 or 15 years), quadratic regression is likely going to be better for most stocks.
If you are looking for short term trades and short term trend assessments, linear regression is going to be the most appropriate.
The indicator will do both and it will fit the linear regression model to the data, which is different from other linreg indicators. Most will only find the start of the strongest trend and draw from there, this will fit the model to whatever period of time you wish, it just may not be that significant.
But, to keep it easy, the indicator will actually tell you which model will work better for the data you are selecting. You can see it in the example in the main chart, and here:
Here we see that the indicator indicates a better fit on the quadratic model.
And SPY during its recent uptrend:
For that, let's take a look at the Quadratic Vs the Linear, to see how they compare:
Quadratic:
Linear:
Functions:
You will see that you have 2 optional tables. The statistics table which shows you:
The R Squared to assess for Variance.
The Correlation to assess for the strength of the trend.
The Confidence interval which is set at a default of 1.96 but can be toggled to adjust for the confidence reading in the settings menu. (The confidence interval gives us a range of values that is likely to contain the true value of the coefficient with a certain level of confidence).
The strongest relationship (quadratic or linear).
Then there is the range table, which shows you the anticipated price ranges based on the distance in standard deviations from the mean.
The range table will also display to you how often a ticker has spent in each corresponding range, whether that be within the anticipated range, within 1 SD, 2 SD or 3 SD.
You can select up to 3 additional standard deviations to plot on the chart and you can manually select the 3 standard deviations you want to plot. Whether that be 1, 2, 3, or 1.5, 2.5 or 3.5, or any combination, you just enter the standard deviations in the settings menu and the indicator will adjust the price targets and plotted bands according to your preferences. It will also count the amount of time the ticker spent in that range based on your own selected standard deviation inputs.
Tips on Use:
This works best on the larger timeframes (1 hour and up), with RTH enabled.
The max lookback is 5,000 candles.
If you want to ascertain a longer term trend (over years to months), its best to adjust your chart timeframe to the weekly and/or monthly perspective.
And that's the indicator! Hopefully you all find it helpful.
Let me know your questions and suggestions below!
Safe trades to all!
[dharmatech] Area Under Yield Curve : USThis indicator displays the area under the U.S. Treasury Securities yield curve.
If you compare this to SP:SPX , you'll see that there are large periods where they are inversely related. Other times, they track together. When the move together, watch out for the expected and eventual divergence.
By default, this indicator will show up in a separate pane. If you move it to an existing pane (e.g. along side SP:SPX ) you'll need to move it to a different price scale.
The area under the yield curve is a quick way to see if the overall yield curve moved up or down. Generally speaking, increasing yields isn't good for markets, unless there is some other stimulus going on simultaneously.
The following treasury securities are used in this calculation:
FRED:DGS1MO (1 month)
FRED:DGS3MO (3 month)
FRED:DGS6MO (6 month)
FRED:DGS1 (1 year)
FRED:DGS2 (2 year)
FRED:DGS3 (3 year)
FRED:DGS5 (5 year)
FRED:DGS7 (7 year)
FRED:DGS10 (10 year)
FRED:DGS20 (20 year)
FRED:DGS30 (30 year)
Tops & Bottoms - Time of Day Report█ OVERVIEW
The indicator tracks and reports the percentage of occurrence of daily tops and bottoms by the time of the day.
█ CONCEPTS
At certain times during the trading day, the market reverses and marks the high or low of the day. Tops and bottoms are vital when entering a trade, as they will decide if you are catching the train or being straight offside. They are equally crucial when exiting a position, as they will determine if you are closing at the optimal price or seeing your unrealized profits vanish.
This indicator is before all for educational purposes. It aims to make the knowledge available to all traders, facilitate understanding of the various markets, and ultimately get to know your trading pairs by heart.
Tops and bottoms percentage of occurrence on EURGBP (London time).
Up days versus down days on EURUSD (London time).
█ FEATURES
Selectable time zones
Present the column chart in your local time zone (or other market participants).
Configurable time range filter
Select the period to report from.
Day type filter
Analyze all days, or filter only up days or down days.
█ HOW TO USE
Plot the indicator and visit the 1-hour or 30-minute timeframe.
█ NOTES
Timeframe choice
The 1-hour timeframe produces a higher number of days sampled. Prefer the usage of the 30-minute timeframe when your market starts at 9:30 AM.
Daylight Saving Time (DST)
The exchange time and geographical time zone options may observe Daylight Saving Time, unlike UTC+0.
Monte Carlo Simulation - Your Strategy [Kioseff Trading]Hello!
This script “Monte Carlo Simulation - Your Strategy” uses Monte Carlo simulations for your inputted strategy returns or the asset on your chart!
Features
Monte Carlo Simulation: Performs Monte Carlo simulation to generate multiple future paths.
Asset Price or Strategy: Can simulate either future asset prices based on historical log returns or a specific trading strategy's future performance.
User-Defined Input: Allows you to input your own historical returns for simulation.
Statistical Methods: Offers two simulation methods—Gaussian (Normal) distribution and Bootstrapping.
Graphical Display: Provides options for graphical representation, including line plots and histograms.
Cumulative Probability Target: Enables setting a user-defined cumulative probability target to quantify simulation results.
Adjustable Parameters: Offers numerous user-adjustable settings like number of simulations, forecast length, and more.
Historical Data Points: Option to specify the amount of historical data to be used in the simulation (price).
Custom Binning: Allows you to select the binning method for histograms, with options like Sturges, Rice, and Square Root.
Best/Worst Case: Allows you to show only the best case / worst case outcome (range) for all simulations!
Scatterplot: allows you to show up to 1000 potential outcomes for a specified trade number (or bars forward price endpoint) using a scatter plot.
The image above shows the primary components of the indicator!
The image above shows the best/worst case outcome feature in action!
The image above shows a "fun feature" where 1000 simulated end points for a 15-bar price trajectory are shown as a scatter plot!
How To Perform a Monte Carlo Simulation On Your Strategy
Really, you can input any data into the indicator it will perform a Monte Carlo Simulation on it :D
The following instructions show how to export your strategy results from TradingView to an Excel File, copy the data, and input it into the indicator.
However , you are not limited to following this method!
Wherever your strategy results are stored, simply copy and paste them into the indicator text area in the settings and simulations will begin.
Returns Should Follow This Format
1
3
-3
2
-5
The numbers are presented as a single column. No commas or separators used.
The numbers above are in sequential order. A return of "1" for the first trade and a return of "-5" for the last trade. Your strategy returns will likely be in sequential order already so don't worry too much about this (:
How To Perform a Monte Carlo Simulation On Your TradingView Strategy With Excel Data
Export your strategy returns to an excel file using TradingView
Navigate to your downloads folder to column G "Profit"
Click the column and press CTRL + SPACE to highlight the entire column
Press CTRL + C to copy the entire column
Open this indicator's settings and paste the returns into the text area
The image above illustrates the process!
Notes on Inputting Returns
*Must input your returns without a separate as a vertical list
*The initial text area can only hold so many return values. If your list of trades is large you can input additional returns into two additional text areas at the bottom of the indicator settings.
That should be it; thank you for checking this out!
Xeeder - US Government Bonds AnalysisXeeder - US Government Bonds Analysis (USBA)
The "Xeeder - US Government Bonds Analysis" (USBA) is a comprehensive tool designed to assist traders in analyzing the spread, historical volatility, and correlation between two different U.S. Government Bonds. This indicator is crucial for understanding the relative performance and risk factors between two bond assets.
Details of the Indicator:
Bond Input Settings: This feature allows traders to select two different U.S. Government Bonds from a dropdown list. The bonds range from 1-month to 30-year maturities.
Timeframe Settings: Traders can choose the timeframe for the analysis, such as Daily, Weekly, etc.
Moving Average (MA) Settings: The indicator offers various types of moving averages like SMA, EMA, WMA, etc., for calculating the spread's moving average. Traders can also specify the length of the moving average.
Spread Calculation: The indicator calculates the spread between the selected bonds and plots it on the chart.
Historical Volatility: The indicator calculates and plots the historical volatility of the spread, which is useful for risk assessment.
Correlation Coefficient: This feature calculates the correlation between the two selected bonds over a specified period.
How to Use the Indicator:
Select Bonds: Choose two U.S. Government Bonds from the dropdown list that you are interested in analyzing.
Choose Timeframe: Select the timeframe that aligns with your trading or investment strategy.
Configure MA Settings: Adjust the type and length of the moving average according to your needs.
Analyze Plots: Observe the plotted spread, its moving average, historical volatility, and correlation coefficient to gain insights into the bonds' relative performance and risk factors.
Interpret Data: Use the plotted data to make informed decisions about bond trading or hedging strategies.
Example of Usage:
As a trader focused on swing trading and strategy development, you can use the USBA indicator to:
Select Bonds: Choose bonds that you believe will show significant spread changes based on your macroeconomic and geopolitical analysis.
Adjust Settings: Configure the MA settings to suit your trading strategy.
Analysis and Comparison: Examine the spread, historical volatility, and correlation to identify potential trading opportunities or hedging strategies.
Content Creation: Use the insights gained to write compelling articles on bond market trends, risks, and opportunities, enriching your financial journalism portfolio.
Remember, the USBA indicator is a versatile tool that provides a multi-faceted analysis of U.S. Government Bonds. Always consider your broader trading strategy and market conditions when using this tool.
Seasonal Trend by LogReturnSeasonal trend in terms of stocks refers to typical and recurring patterns in stock prices that happen at a specific time of the year. There are many theories and beliefs regarding seasonal trends in the financial markets, and some traders use these patterns to guide their investment decisions.
This indicator calculates the trend by "Daily" logarithmic returns of the past years.
So, you should use this indicator with a "Daily" mainchart.
Note: If you select more years in the past than data is available, the line turns red.
Statistical Package for the Trading Sciences [SS]
This is SPTS.
It stands for Statistical Package for the Trading Sciences.
Its a play on SPSS (Statistical Package for the Social Sciences) by IBM (software that, prior to Pinescript, I would use on a daily basis for trading).
Let's preface this indicator first:
This isn't so much an indicator as it is a project. A passion project really.
This has been in the works for months and I still feel like its incomplete. But the plan here is to continue to add functionality to it and actually have the Pinecoding and Tradingview community contribute to it.
As a math based trader, I relied on Excel, SPSS and R constantly to plan my trades. Since learning a functional amount of Pinescript and coding a lot of what I do and what I relied on SPSS, Excel and R for, I use it perhaps maybe a few times a week.
This indicator, or package, has some of the key things I used Excel and SPSS for on a daily and weekly basis. This also adds a lot of, I would say, fairly complex math functionality to Pinescript. Because this is adding functionality not necessarily native to Pinescript, I have placed most, if not all, of the functionality into actual exportable functions. I have also set it up as a kind of library, with explanations and tips on how other coders can take these functions and implement them into other scripts.
The hope here is that other coders will take it, build upon it, improve it and hopefully share additional functionality that can be added into this package. Hence why I call it a project. Okay, let's get into an overview:
Current Functions of SPTS:
SPTS currently has the following functionality (further explanations will be offered below):
Ability to Perform a One-Tailed, Two-Tailed and Paired Sample T-Test, with corresponding P value.
Standard Pearson Correlation (with functionality to be able to calculate the Pearson Correlation between 2 arrays).
Quadratic (or Curvlinear) correlation assessments.
R squared Assessments.
Standard Linear Regression.
Multiple Regression of 2 independent variables.
Tests of Normality (with Kurtosis and Skewness) and recognition of up to 7 Different Distributions.
ARIMA Modeller (Sort of, more details below)
Okay, so let's go over each of them!
T-Tests
So traditionally, most correlation assessments on Pinescript are done with a generic Pearson Correlation using the "ta.correlation" argument. However, this is not always the best test to be used for correlations and determine effects. One approach to correlation assessments used frequently in economics is the T-Test assessment.
The t-test is a statistical hypothesis test used to determine if there is a significant difference between the means of two groups. It assesses whether the sample means are likely to have come from populations with the same mean. The test produces a t-statistic, which is then compared to a critical value from the t-distribution to determine statistical significance. Lower p-values indicate stronger evidence against the null hypothesis of equal means.
A significant t-test result, indicating the rejection of the null hypothesis, suggests that there is statistical evidence to support that there is a significant difference between the means of the two groups being compared. In practical terms, it means that the observed difference in sample means is unlikely to have occurred by random chance alone. Researchers typically interpret this as evidence that there is a real, meaningful difference between the groups being studied.
Some uses of the T-Test in finance include:
Risk Assessment: The t-test can be used to compare the risk profiles of different financial assets or portfolios. It helps investors assess whether the differences in returns or volatility are statistically significant.
Pairs Trading: Traders often apply the t-test when engaging in pairs trading, a strategy that involves trading two correlated securities. It helps determine when the price spread between the two assets is statistically significant and may revert to the mean.
Volatility Analysis: Traders and risk managers use t-tests to compare the volatility of different assets or portfolios, assessing whether one is significantly more or less volatile than another.
Market Efficiency Tests: Financial researchers use t-tests to test the Efficient Market Hypothesis by assessing whether stock price movements follow a random walk or if there are statistically significant deviations from it.
Value at Risk (VaR) Calculation: Risk managers use t-tests to calculate VaR, a measure of potential losses in a portfolio. It helps assess whether a portfolio's value is likely to fall below a certain threshold.
There are many other applications, but these are a few of the highlights. SPTS permits 3 different types of T-Test analyses, these being the One Tailed T-Test (if you want to test a single direction), two tailed T-Test (if you are unsure of which direction is significant) and a paired sample t-test.
Which T is the Right T?
Generally, a one-tailed t-test is used to determine if a sample mean is significantly greater than or less than a specified population mean, whereas a two-tailed t-test assesses if the sample mean is significantly different (either greater or less) from the population mean. In contrast, a paired sample t-test compares two sets of paired observations (e.g., before and after treatment) to assess if there's a significant difference in their means, typically used when the data points in each pair are related or dependent.
So which do you use? Well, it depends on what you want to know. As a general rule a one tailed t-test is sufficient and will help you pinpoint directionality of the relationship (that one ticker or economic indicator has a significant affect on another in a linear way).
A two tailed is more broad and looks for significance in either direction.
A paired sample t-test usually looks at identical groups to see if one group has a statistically different outcome. This is usually used in clinical trials to compare treatment interventions in identical groups. It's use in finance is somewhat limited, but it is invaluable when you want to compare equities that track the same thing (for example SPX vs SPY vs ES1!) or you want to test a hypothesis about an index and a leveraged share (for example, the relationship between FNGU and, say, MSFT or NVDA).
Statistical Significance
In general, with a t-test you would need to reference a T-Table to determine the statistical significance of the degree of Freedom and the T-Statistic.
However, because I wanted Pinescript to full fledge replace SPSS and Excel, I went ahead and threw the T-Table into an array, so that Pinescript can make the determination itself of the actual P value for a t-test, no cross referencing required :-).
Left tail (Significant):
Both tails (Significant):
Distributed throughout (insignificant):
As you can see in the images above, the t-test will also display a bell-curve analysis of where the significance falls (left tail, both tails or insignificant, distributed throughout).
That said, I have not included this function for the paired sample t-test because that is a bit more nuanced. But for the one and two tailed assessments, the indicator will provide you the P value.
Pearson Correlation Assessment
I don't think I need to go into too much detail on this one.
I have put in functionality to quickly calculate the Pearson Correlation of two array's, which is not currently possible with the "ta.correlation" function.
Quadratic (Curvlinear) Correlation
Not everything in life is linear, sometimes things are curved!
The Pearson Correlation is great for linear assessments, but tends to under-estimate the degree of the relationship in curved relationships. There currently is no native function to t-test for quadratic/curvlinear relationships, so I went ahead and created one.
You can see an example of how Quadratic and Pearson Correlations vary when you look at CME_MINI:ES1! against AMEX:DIA for the past 10 ish months:
Pearson Correlation:
Quadratic Correlation:
One or the other is not always the best, so it is important to check both!
R-Squared Assessments:
The R-squared value, or the square of the Pearson correlation coefficient (r), is used to measure the proportion of variance in one variable that can be explained by the linear relationship with another variable. It represents the goodness-of-fit of a linear regression model with a single predictor variable.
R-Squared is offered in 3 separate forms within this indicator. First, there is the generic R squared which is taking the square root of a Pearson Correlation assessment to assess the variance.
The next is the R-Squared which is calculated from an actual linear regression model done within the indicator.
The first is the R-Squared which is calculated from a multiple regression model done within the indicator.
Regardless of which R-Squared value you are using, the meaning is the same. R-Square assesses the variance between the variables under assessment and can offer an insight into the goodness of fit and the ability of the model to account for the degree of variance.
Here is the R Squared assessment of the SPX against the US Money Supply:
Standard Linear Regression
The indicator contains the ability to do a standard linear regression model. You can convert one ticker or economic indicator into a stock, ticker or other economic indicator. The indicator will provide you with all of the expected information from a linear regression model, including the coefficients, intercept, error assessments, correlation and R2 value.
Here is AAPL and MSFT as an example:
Multiple Regression
Oh man, this was something I really wanted in Pinescript, and now we have it!
I have created a function for multiple regression, which, if you export the function, will permit you to perform multiple regression on any variables available in Pinescript!
Using this functionality in the indicator, you will need to select 2, dependent variables and a single independent variable.
Here is an example of multiple regression for NASDAQ:AAPL using NASDAQ:MSFT and NASDAQ:NVDA :
And an example of SPX using the US Money Supply (M2) and AMEX:GLD :
Tests of Normality:
Many indicators perform a lot of functions on the assumption of normality, yet there are no indicators that actually test that assumption!
So, I have inputted a function to assess for normality. It uses the Kurtosis and Skewness to determine up to 7 different distribution types and it will explain the implication of the distribution. Here is an example of SP:SPX on the Monthly Perspective since 2010:
And NYSE:BA since the 60s:
And NVDA since 2015:
ARIMA Modeller
Okay, so let me disclose, this isn't a full fledge ARIMA modeller. I took some shortcuts.
True ARIMA modelling would involve decomposing the seasonality from the trend. I omitted this step for simplicity sake. Instead, you can select between using an EMA or SMA based approach, and it will perform an autogressive type analysis on the EMA or SMA.
I have tested it on lookback with results provided by SPSS and this actually works better than SPSS' ARIMA function. So I am actually kind of impressed.
You will need to input your parameters for the ARIMA model, I usually would do a 14, 21 and 50 day EMA of the close price, and it will forecast out that range over the length of the EMA.
So for example, if you select the EMA 50 on the daily, it will plot out the forecast for the next 50 days based on an autoregressive model created on the EMA 50. Here is how it looks on AMEX:SPY :
You can also elect to plot the upper and lower confidence bands:
Closing Remarks
So that is the indicator/package.
I do hope to continue expanding its functionality, but as of now, it does already have quite a lot of functionality.
I really hope you enjoy it and find it helpful. This. Has. Taken. AGES! No joke. Between referencing my old statistics textbooks, trying to remember how to calculate some of these things, and wanting to throw my computer against the wall because of errors in the code, this was a task, that's for sure. So I really hope you find some usefulness in it all and enjoy the ability to be able to do functions that previously could really only be done in external software.
As always, leave your comments, suggestions and feedback below!
Take care!
Correlation Coefficient based on Log ReturnsMeasuring correlations based on log returns, rather than raw prices or simple returns, offers several advantages:
- stationarity: Log returns are more stationary, resulting in more meaningful and reliable results
- volatility: Log returns give a consistent measure of relative changes of assets with different volatility
Log returns are time-additive and often more stationary than simple returns, making them statistically more reliable for analyses in financial contexts. Additionally, they provide a consistent measure of relative price changes and align more closely with the assumptions of many statistical models, including normal distribution.
K's Reversal Indicator IIIK's Reversal Indicator III is based on the concept of autocorrelation of returns. The main theory is that extreme autocorrelation (trending) that coincide with a technical signals such as one from the RSI, may result in a powerful short-term signal that can be exploited.
The indicator is calculated as follows:
1. Calculate the price differential (returns) as the current price minus the previous price.
2. the correlation between the current return and the return from 14 periods ago using a lookback of 14 periods.
3. Calculate a 14-period RSI on the close prices.
To generate the signals, use the following rules:
* A bullish signal is generated whenever the correlation is above 0.60 while the RSI is below 40.
* A bearish signal is generated whenever the correlation is above 0.60 while the RSI is above 60.
Position Cost DistributionThe Position Cost Distribution indicator (also known as the Market Position Overview, Chip Distribution, or CYQ Algorithm) provides an estimate of how shares are distributed across different price levels. Visually, it resembles the Volume Profile indicator, though they rely on distinct computational approaches.
🟠 Principle
The Position Cost Distribution algorithm is based on the principle that a security's total shares outstanding usually remains constant, except under conditions like stock splits, reverse splits, or new share issuance. It views all trading activity as simply exchanging share positions between holders at different price points.
By analyzing daily trade volume and the prior day's distribution, the algorithm infers the resulting share distribution after each day. By tracking these inferred transpositions over time, the indicator builds up an aggregate view of the estimated share concentration at each price level. This provides insights into potential buying and selling pressure zones that could form support or resistance areas.
Together with the Volume Profile, the Position Cost Distribution gives traders multiple lenses for examining market structure from both a volume and positional standpoint. Both can help identify meaningful technical price levels.
🟠 Algorithm
The algorithm initializes by allocating all shares to the price range encompassed by the first bar displayed on the chart. Preferably, the chart window should include the stock's IPO date, allowing the model to distribute shares specifically to the IPO price.
For subsequent trading sessions, the indicator performs the following calculations:
1. The daily turnover ratio is calculated by dividing the bar's trading volume by total outstanding shares.
2. For each price level (bucket), the number of shares is reduced by the turnover amount to represent shares transferring from existing holders.
3. The bar's total volume is then added to buckets corresponding to that period's price range.
Currently, the model assumes each share has an equal probability of being exchanged, regardless of how long ago it was acquired or at what price. Potential optimizations could incorporate factors like making shares held longer face a smaller chance of transfer compared to more recently purchased shares.
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中文介绍：该指标为“筹码分布”的一个 TradingView 实现 :)
WIPFunctionLyaponovLibrary "WIPFunctionLyaponov"
Lyapunov exponents are mathematical measures used to describe the behavior of a system over
time. They are named after Russian mathematician Alexei Lyapunov, who first introduced the concept in the
late 19th century. The exponent is defined as the rate at which a particular function or variable changes
over time, and can be positive, negative, or zero.
Positive exponents indicate that a system tends to grow or expand over time, while negative exponents
indicate that a system tends to shrink or decay. Zero exponents indicate that the system does not change
significantly over time. Lyapunov exponents are used in various fields of science and engineering, including
physics, economics, and biology, to study the long-term behavior of complex systems.
~ generated description from vicuna13b
---
To calculate the Lyapunov Exponent (LE) of a given Time Series, we need to follow these steps:
1. Firstly, you should have access to your data in some format like CSV or Excel file. If not, then you can collect it manually using tools such as stopwatches and measuring tapes.
2. Once the data is collected, clean it up by removing any outliers that may skew results. This step involves checking for inconsistencies within your dataset (e.g., extremely large or small values) and either discarding them entirely or replacing with more reasonable estimates based on surrounding values.
3. Next, you need to determine the dimension of your time series data. In most cases, this will be equal to the number of variables being measured in each observation period (e.g., temperature, humidity, wind speed).
4. Now that we have a clean dataset with known dimensions, we can calculate the LE for our Time Series using the following formula:
λ = log(||M^T * M - I||)/log(||v||)
where:
λ (Lyapunov Exponent) is the quantity that will be calculated.
||...|| denotes an Euclidean norm of a vector or matrix, which essentially means taking the square root of the sum of squares for each element in the vector/matrix.
M represents our Jacobian Matrix whose elements are given by:
J_ij = (∂fj / ∂xj) where fj is the jth variable and xj is the ith component of the initial condition vector x(t). In other words, each element in this matrix represents how much a small change in one variable affects another.
I denotes an identity matrix whose elements are all equal to 1 (or any constant value if you prefer). This term essentially acts as a baseline for comparison purposes since we want our Jacobian Matrix M^T * M to be close to it when the system is stable and far away from it when the system is unstable.
v represents an arbitrary vector whose Euclidean norm ||v|| will serve as a scaling factor in our calculation. The choice of this particular vector does not matter since we are only interested in its magnitude (i.e., length) for purposes of normalization. However, if you want to ensure that your results are accurate and consistent across different datasets or scenarios, it is recommended to use the same initial condition vector x(t) as used earlier when calculating our Jacobian Matrix M.
5. Finally, once we have calculated λ using the formula above, we can interpret its value in terms of stability/instability for our Time Series data:
- If λ < 0, then this indicates that the system is stable (i.e., nearby trajectories will converge towards each other over time).
- On the other hand, if λ > 0, then this implies that the system is unstable (i.e., nearby trajectories will diverge away from one another over time).
~ generated description from airoboros33b
---
Reference:
en.wikipedia.org
www.collimator.ai
blog.abhranil.net
www.researchgate.net
physics.stackexchange.com
---
This is a work in progress, it may contain errors so use with caution.
If you find flaws or suggest something new, please leave a comment bellow.
_measure_function(i)
helper function to get the name of distance function by a index (0 -> 13).\
Functions: SSD, Euclidean, Manhattan, Minkowski, Chebyshev, Correlation, Cosine, Camberra, MAE, MSE, Lorentzian, Intersection, Penrose Shape, Meehl.
Parameters:
i (int)
_test(L)
Helper function to test the output exponents state system and outputs description into a string.
Parameters:
L (float )
estimate(X, initial_distance, distance_function)
Estimate the Lyaponov Exponents for multiple series in a row matrix.
Parameters:
X (map)
initial_distance (float) : Initial distance limit.
distance_function (string) : Name of the distance function to be used, default:`ssd`.
Returns: List of Lyaponov exponents.
max(L)
Maximal Lyaponov Exponent.
Parameters:
L (float ) : List of Lyapunov exponents.
Returns: Highest exponent.
Median of Means Estimator Median of Means (MoM) is a measure of central tendency like mean (average) and median. However, it could be a better and robust estimator of central tendency when the data is not normal, asymmetric, have fat tails (like stock price data) and have outliers. The MoM can be used as a robust trend following tool and in other derived indicators.
Median of means (MoM) is calculated as follows, the MoM estimator shuffles the "n" data points and then splits them into k groups of m data points (n= k*m). It then computes the Arithmetic Mean of each group (k). Finally, it calculate the median over the resulting k Arithmetic Means. This technique diminishes the effect that outliers have on the final estimation by splitting the data and only considering the median of the resulting sub-estimations. This preserves the overall trend despite the data shuffle.
Below is an example to illustrate the advantages of MoM
Set A Set B Set C
3 4 4
3 4 4
3 5 5
3 5 5
4 5 5
4 5 5
5 5 5
5 5 5
6 6 8
6 6 8
7 7 10
7 7 15
8 8 40
9 9 50
10 100 100
Median 5 5 5
Mean 5.5 12.1 17.9
MoM 5.7 6.0 17.3
For all three sets the median is the same, though set A and B are the same except for one outlier in set B (100) it skews the mean but the median is resilient. However, in set C the group has several high values despite that the median is not responsive and still give 5 as the central tendency of the group, but the median of means is a value of 17.3 which is very close to the group mean 17.9. In all three cases (set A, B and C) the MoM provides a better snapshot of the central tendency of the group. Note: The MoM is dependent on the way we split the data initially and the value might slightly vary when the randomization is done sevral time and the resulting value can give the confidence interval of the MoM estimator.
Cumulative Distribution of a Dataset [SS]This is the Cumulative Distribution of a Dataset indicator that also calculates the Kurtosis and Skewness for a selected dataset and determines the normality and distribution type.
What it does, in pragmatic terms?
In the most simplest terms, it calculates the cumulative distribution function (or CDF) of user-defined dataset.
The cumulative distribution function (CDF) is a concept used in statistics and probability to describe how the probability of a random variable taking on a certain value or less is distributed across the entire range of possible values. In simpler terms, you can conceptualize the CDF as this:
Imagine you have a list of data, such as test scores of students in a class. The CDF helps you answer questions like, "What's the probability that a randomly chosen student scored 80 or less on the test?"
Or in our case, say we are in a strong up or downtrend on a stock. The CDF can help us answer questions like "Based on this current xyz trend, what is the probability that a ticker will fall above X price or below Y price".
Within the indicator, you can manually assess a price of interest. Let's say, for NVDA, we want to know the probability NVDA goes above or below $450. We can enter $450 into the indicator and get this result:
Other functions:
Kurtosis and Skewness Functions:
In addition to calculating and plotting the CDF, we can also plot the kurtosis & Skewness.
This can help you look for outlier periods where the distribution of your dataset changed. It can potentially alert you to when a stock is behaving abnormally and when it is more stable and evenly distributed.
Tests of normality
The indicator will use the kurtosis and skewness to determine the normality of the dataset. The indicator is programmed to recognize up to 7 different distribution types and alert you to them and the implications they have in your overall assessment.
e.g. #1 AMC during short squeeze:
e.g. #2: BA during the COVID crash:
Plotting the standardized Z-Score of the Distribution Dataset
You can also standardize the dataset by converting it into Z-Score format:
Plot the raw, CDF results
Two values are plotting, the green and the red. The green represents the probability of a ticker going higher than the current value. The red represents the probability of a ticker going lower than the current value.
Limitations
There are some limitations of the indicator which I think are important to point out. They are:
The indicator cannot tell you timelines, it can only tell you the general probability that data within the dataset will fall above or below a certain value.
The indicator cannot take into account projected periods of consolidation. It is possible a ticker can remain in a consolidation phase for a very long time. This would have the effect of stabilizing the probability in one direction (if there was a lot of downside room, it can normalize the data out so that the extent of the downside probability is mitigated). Thus, its important to use judgement and other methods to assess the likelihood that a stock will pullback or continue up, based on the overall probability.
The indicator is only looking at an individual dataset.
Using this indicator, you have to omit a large amount of data and look at solely a confined dataset. In a way, this actually improves the accuracy, but can also be misleading, depending on the size and strength of the dataset being chosen. It is important to balance your choice of dataset time with such things as:
a) The strength of the uptrend or downtrend.
b) The length of the uptrend or downtrend.
c) The overall performance of the stock leading into the dataset time period
And that is the indicator in a nutshell.
Hopefully you find it helpful and interesting. Feel free to leave questions, comments and suggestions below.
Safe trades everyone and take care!
Returns Model by TenozenHey there! I've been diving into the book "Paul Wilmott on Quantitative Finance," and I stumbled upon this cool model for calculating and modeling returns. Basically, it helps us figure out how much a price has changed over a set number of periods—I like to use 20 periods as a default. Once we get that rate of change value, we crunch some numbers to find the standard deviation and mean using all the historical data we have. That's the foundation of this model.
Now, let's talk about how to use it. This model shows us how returns and price behavior are connected. When returns hang out in the +1 to +2 standard deviation range, it usually means returns are about to drop, and vice versa. Often, this leads to corresponding price moves. But here's the thing: sometimes prices don't do what we expect. Why? It's because there's another hidden factor at play—I like to call it "power."
This "power" isn't something we can see directly, but it's there. Basically, when returns are within that standard deviation range, the market faces resistance when trying to move in its preferred direction, whether bullish or bearish. The strength of this "power" determines if the market will snap back to the average or go for a wild ride. It can show up as small price wiggles, big price jumps, or lightning-fast moves. By understanding this "power," we can get a better handle on what the market might do next and avoid getting blindsided. In the meantime, I couldn't explain "power" yet, but In the future, when I've learned enough, I'd love to share the model with you guys!
So... I'm planning to explore and share more models from this book as I learn, even if those pesky math formulas can be tough to crack. I hope you find this indicator as helpful as I do, and if you've got any suggestions or feedback, please feel free to share! Ciao!
TTP PNR filterPNR filter uses the "percentile nearest rank" method to produce signals from any source including oscillator indicators and price bars.
Features:
* Length - how many candles back in time to use for calculating PNR
* % low and high - what range of the spread of values captured will form the PNR band. Use 99&100 to create a band on the 1% highest percentile or 0&1 to create a band in the lowest percentile. It accepts float numbers so you can find very rare occurrences.
* src - by default it will use the close price but PNR filter can be used with any source. It's particularly useful when working with oscillators like RSI, MACD, ADX, etc.
* Signal direction - The indicator will print 1 when the selected conditions are met. Once the PNR band is plotted you can chose from cross over, cross under, above and below conditions to trigger a signal.
* Signal source - the band consists in a % low and % high, this option allows you to pick which band will be used with the "signal direction" parameter.
Example configuration:
1) Select 200 as the length
2) Select % low 0 and % high 1
3) Add RSI to the chart and select it as the source parameter
4) Select signal direction cross over
5) Select signal source % high which corresponds to the 1% band
In this setup you are finding values of RSI that in the past 200 candles have been that low only 1% of the time. With each new candle the calculation window will move as well leaving the oldest candle out.
lib_profileLibrary "lib_profile"
a library with functions to calculate a volume profile for either a set of candles within the current chart, or a single candle from its lower timeframe security data. All you need is to feed the
method delete(this)
deletes this bucket's plot from the chart
Namespace types: Bucket
Parameters:
this (Bucket)
method delete(this)
Namespace types: Profile
Parameters:
this (Profile)
method delete(this)
Namespace types: Bucket
Parameters:
this (Bucket )
method delete(this)
Namespace types: Profile
Parameters:
this (Profile )
method update(this, top, bottom, value, fraction)
updates this bucket's data
Namespace types: Bucket
Parameters:
this (Bucket)
top (float)
bottom (float)
value (float)
fraction (float)
method update(this, tops, bottoms, values)
update this Profile's data (recalculates the whole profile and applies the result to this object) TODO optimisation to calculate this incremental to improve performance in realtime on high resolution
Namespace types: Profile
Parameters:
this (Profile)
tops (float ) : array of range top/high values (either from ltf or chart candles using history() function
bottoms (float ) : array of range bottom/low values (either from ltf or chart candles using history() function
values (float ) : array of range volume/1 values (either from ltf or chart candles using history() function (1s can be used for analysing candles in bucket/price range over time)
method tostring(this)
allows debug print of a bucket
Namespace types: Bucket
Parameters:
this (Bucket)
method draw(this, start_t, start_i, end_t, end_i, args, line_color)
allows drawing a line in a Profile, representing this bucket and it's value + it's value's fraction of the Profile total value
Namespace types: Bucket
Parameters:
this (Bucket)
start_t (int) : the time x coordinate of the line's left end (depends on the Profile box)
start_i (int) : the bar_index x coordinate of the line's left end (depends on the Profile box)
end_t (int) : the time x coordinate of the line's right end (depends on the Profile box)
end_i (int) : the bar_index x coordinate of the line's right end (depends on the Profile box)
args (LineArgs type from robbatt/lib_plot_objects/24) : the default arguments for the line style
line_color (color) : the color override for POC/VAH/VAL lines
method draw(this, forced_width)
draw all components of this Profile (Box, Background, Bucket lines, POC/VAH/VAL overlay levels and labels)
Namespace types: Profile
Parameters:
this (Profile)
forced_width (int) : allows to force width of the Profile Box, overrides the ProfileArgs.default_size and ProfileArgs.extend arguments (default: na)
method init(this)
Namespace types: ProfileArgs
Parameters:
this (ProfileArgs)
method init(this)
Namespace types: Profile
Parameters:
this (Profile)
profile(tops, bottoms, values, resolution, vah_pc, val_pc, bucket_buffer)
split a chart/parent bar into 'resolution' sections, figure out in which section the most volume/time was spent, by analysing a given set of (intra)bars' top/bottom/volume values. Then return price center of the bin with the highest volume, essentially marking the point of control / highest volume (poc) in the chart/parent bar.
Parameters:
tops (float ) : array of range top/high values (either from ltf or chart candles using history() function
bottoms (float ) : array of range bottom/low values (either from ltf or chart candles using history() function
values (float ) : array of range volume/1 values (either from ltf or chart candles using history() function (1s can be used for analysing candles in bucket/price range over time)
resolution (int) : amount of buckets/price ranges to sort the candle data into (analyse how much volume / time was spent in a certain bucket/price range) (default: 25)
vah_pc (float) : a threshold percentage (of values' total) for the top end of the value area (default: 80)
val_pc (float) : a threshold percentage (of values' total) for the bottom end of the value area (default: 20)
bucket_buffer (Bucket ) : optional buffer of empty Buckets to fill, if omitted a new one is created and returned. The buffer length must match the resolution
Returns: poc (price level), vah (price level), val (price level), poc_index (idx in buckets), vah_index (idx in buckets), val_index (idx in buckets), buckets (filled buffer or new)
create_profile(start_idx, tops, bottoms, values, resolution, vah_pc, val_pc, args)
split a chart/parent bar into 'resolution' sections, figure out in which section the most volume/time was spent, by analysing a given set of (intra)bars' top/bottom/volume values. Then return price center of the bin with the highest volume, essentially marking the point of control / highest volume (poc) in the chart/parent bar.
Parameters:
start_idx (int) : the bar_index at which the Profile should start drawing
tops (float ) : array of range top/high values (either from ltf or chart candles using history() function
bottoms (float ) : array of range bottom/low values (either from ltf or chart candles using history() function
values (float ) : array of range volume/1 values (either from ltf or chart candles using history() function (1s can be used for analysing candles in bucket/price range over time)
resolution (int) : amount of buckets/price ranges to sort the candle data into (analyse how much volume / time was spent in a certain bucket/price range) (default: 25)
vah_pc (float) : a threshold percentage (of values' total) for the top end of the value area (default: 80)
val_pc (float) : a threshold percentage (of values' total) for the bottom end of the value area (default: 20)
args (ProfileArgs)
Returns: poc (price level), vah (price level), val (price level), poc_index (idx in buckets), vah_index (idx in buckets), val_index (idx in buckets), buckets (filled buffer or new)
history(src, len, offset)
allows fetching an array of values from the history series with offset from current candle
Parameters:
src (int)
len (int)
offset (int)
history(src, len, offset)
allows fetching an array of values from the history series with offset from current candle
Parameters:
src (float)
len (int)
offset (int)
history(src, len, offset)
allows fetching an array of values from the history series with offset from current candle
Parameters:
src (bool)
len (int)
offset (int)
history(src, len, offset)
allows fetching an array of values from the history series with offset from current candle
Parameters:
src (string)
len (int)
offset (int)
Bucket
Fields:
idx (series int) : the index of this Bucket within the Profile starting with 0 for the lowest Bucket at the bottom of the Profile
value (series float) : the value of this Bucket, can be volume or time, for using time pass and array of 1s to the update function
top (series float) : the top of this Bucket's price range (for calculation)
btm (series float) : the bottom of this Bucket's price range (for calculation)
center (series float) : the center of this Bucket's price range (for plotting)
fraction (series float) : the fraction this Bucket's value is compared to the total of the Profile
plot_bucket_line (Line type from robbatt/lib_plot_objects/24) : the line that resembles this bucket and it's valeu in the Profile
ProfileArgs
Fields:
show_poc (series bool) : whether to plot a POC line across the Profile Box (default: true)
show_profile (series bool) : whether to plot a line for each Bucket in the Profile Box, indicating the value per Bucket (Price range), e.g. volume that occured in a certain time and price range (default: false)
show_va (series bool) : whether to plot a VAH/VAL line across the Profile Box (default: false)
show_va_fill (series bool) : whether to fill the 'value' area between VAH/VAL line (default: false)
show_background (series bool) : whether to fill the Profile Box with a background color (default: false)
show_labels (series bool) : whether to add labels to the right end of the POC/VAH/VAL line (default: false)
show_price_levels (series bool) : whether add price values to the labels to the right end of the POC/VAH/VAL line (default: false)
extend (series bool) : whether extend the Profile Box to the current candle (default: false)
default_size (series int) : the default min. width of the Profile Box (default: 30)
args_poc_line (LineArgs type from robbatt/lib_plot_objects/24) : arguments for the poc line plot
args_va_line (LineArgs type from robbatt/lib_plot_objects/24) : arguments for the va line plot
args_poc_label (LabelArgs type from robbatt/lib_plot_objects/24) : arguments for the poc label plot
args_va_label (LabelArgs type from robbatt/lib_plot_objects/24) : arguments for the va label plot
args_profile_line (LineArgs type from robbatt/lib_plot_objects/24) : arguments for the Bucket line plots
args_profile_bg (BoxArgs type from robbatt/lib_plot_objects/24)
va_fill_color (series color) : color for the va area fill plot
Profile
Fields:
start (series int) : left x coordinate for the Profile Box
end (series int) : right x coordinate for the Profile Box
resolution (series int) : the amount of buckets/price ranges the Profile will dissect the data into
vah_threshold_pc (series float) : the percentage of the total data value to mark the upper threshold for the main value area
val_threshold_pc (series float) : the percentage of the total data value to mark the lower threshold for the main value area
args (ProfileArgs) : the style arguments for the Profile Box
h (series float) : the highest price of the data
l (series float) : the lowest price of the data
total (series float) : the total data value (e.g. volume of all candles, or just one each to analyse candle distribution over time)
buckets (Bucket ) : the Bucket objects holding the data for each price range bucket
poc_bucket_index (series int) : the Bucket index in buckets, that holds the poc Bucket
vah_bucket_index (series int) : the Bucket index in buckets, that holds the vah Bucket
val_bucket_index (series int) : the Bucket index in buckets, that holds the val Bucket
poc (series float) : the according price level marking the Point Of Control
vah (series float) : the according price level marking the Value Area High
val (series float) : the according price level marking the Value Area Low
plot_poc (Line type from robbatt/lib_plot_objects/24)
plot_vah (Line type from robbatt/lib_plot_objects/24)
plot_val (Line type from robbatt/lib_plot_objects/24)
plot_poc_label (Label type from robbatt/lib_plot_objects/24)
plot_vah_label (Label type from robbatt/lib_plot_objects/24)
plot_val_label (Label type from robbatt/lib_plot_objects/24)
plot_va_fill (LineFill type from robbatt/lib_plot_objects/24)
plot_profile_bg (Box type from robbatt/lib_plot_objects/24)
Percentile Based Trend StrengthThe "Percentile Based Trend Strength" (PBTS) calculates trend strength based on percentile values of high and low prices for various length periods and then identifies the current trend as either Bullish, Bearish, or N/A (No Trend). Here's a step-by-step explanation of the code:
Percentile Calculations:
For each specified length period (13, 21, 34, 55, 89, and 144 - Fibonacci numbers), the code calculates the 75th percentile of high prices (e.g., percentile_13H) and the 25th percentile of low prices (e.g., percentile_13L). These percentiles represent levels that prices need to exceed or fall below to indicate a strong trend.
Calculate Highest High and Lowest Low:
The highest high (75th percentile high price of longest length) and lowest low (25th percentile low price of longest length) for the longest length period (144) are calculated as highest_high and lowest_low. These values represent threshold price levels .
Trend Strength Conditions:
The code calculates various conditions to determine trend strength. For each percentile value and each length period, it checks if the percentile value is greater than the highest high (trendBull) or less than the lowest low (trendBear). These conditions are used to assess the strength of the bullish and bearish trends.
Count Bull and Count Bear:
The countBull and countBear variables count the number of bullish and bearish conditions met, respectively. These counts help evaluate trend strength.
Weak Bull and Weak Bear Count:
The code calculates the number of weak bullish and bearish conditions. Weak conditions occur when a percentile value falls within the range defined by the highest high and lowest low but doesn't meet the strong trend criteria.
Bull Strength and Bear Strength:
bullStrength and bearStrength are calculated based on the counts of bullish, bearish, weak bullish, and weak bearish conditions. These values represent the overall strength of the bullish and bearish trends.
Strong Bull and Bear Conditions:
These conditions occur when the 75th percentile of high prices (for bull conditions) or the 25th percentile of low prices (for bear conditions) exceeds or falls below the highest high or lowest low, respectively, for the specified length period.
Strong bull conditions indicate a strong upward trend, while strong bear conditions indicate a strong downward trend.
Strong conditions are indicative of more significant price movements and are considered as primary signals of trend strength.
Weak Bull and Bear Conditions:
Weak bull and bear conditions are more nuanced. They occur when the 75th percentile of high prices (for weak bull conditions) or the 25th percentile of low prices (for weak bear conditions) falls within the range defined by the highest high and lowest low for the specified length period.
In other words, prices are not strong enough to reach the extreme levels represented by the highest high or lowest low, but they still exhibit some bullish or bearish tendencies within that range.
Weak conditions suggest a less robust trend. They may indicate that while there is some bias toward a bullish or bearish trend, it is not as strong or decisive as in the case of strong conditions.
Current Trend Identification:
The current trend is determined by comparing bullStrength and bearStrength. If bullStrength is greater, it's considered a Bull trend; if bearStrength is greater, it's a Bear trend. If they are equal, the trend is identified as N/A (No Trend).
Displaying Trend Information:
The code creates a table to display the current trend, reversal probability (strength), count of bullish and bearish conditions, weak bullish and weak bearish counts, and colors the text accordingly.
Plotting Percentiles:
Finally, the code plots the percentile lines for visualization, with 20% transparency. It also plots the highest high and lowest low lines (75th and 25th percentile of the longest length 144) using their original colors.
In summary, this indicator calculates trend strength based on percentile levels of high and low prices for different length periods. It then counts the number of bullish and bearish conditions, factors in weak conditions, and compares the strengths to identify the current trend as Bullish, Bearish, or No Trend. It provides a table with trend information and visualizes percentile lines on the chart.
Strategy Gaussian Anomaly DerivativeConcept behind this Strategy :
Considering a normal "buy/sell" situation, an asset would be bought in average at the median price following a Gaussian like concept. A higher or lower average trend would significate that the current perceived value is respectively higher or lower than the current median price, which mean that the buyers are evaluating the price underpriced or overpriced.
This behaviour would be even more relevent depending on its derivative evolution.
Therefore, this Strategy setup is based on this Gaussian like concept anomaly of average close positionning compare to high-low average derivative, such as the derivative of the following ploted basic signal : 1-(high+low)/(2*close).
This Strategy can actually be used like a trend change and continuation strength indicator aswell.
In the Setup Signal part :
You can define the filtering of the basis signal "1-(high+low)/(2*close)" on EMA or SMA as you wish.
You can define the corresponding period and the threathold as a mutiply of the average 1/3 of all time value of the basis signal.
You can define the SMA filtering period of the Derivative signal and the corresponding threathold on the same mutiply of the average 1/3 of all time value of the derivative.
In the Setup Strategy part :
You can set up your strategy assesment based on Long and/or Short. You can also define the considered period.
The most successful tuned strategies I did were based on the derivative indicator with periods on the basis signal and the derivative under 30, can be 1 to 3 of te derivative and 7 to 21 for the basis signal. The threathold depends on the asset volatility aswell, 1 is usually the most efficient but 0 to 10 can be relevent depending on the situation I met. You can find an example of tuning for this strategy based on Kering's case hereafter.
I hoping that you will enjoy using this Strategy, don't hesitate to comment, to question, to correct or complete it ! I would be very curious about similar famous approaches that would have already been made.
Thank to you !
Paytience DistributionPaytience Distribution Indicator User Guide
Overview:
The Paytience Distribution indicator is designed to visualize the distribution of any chosen data source. By default, it visualizes the distribution of a built-in Relative Strength Index (RSI). This guide provides details on its functionality and settings.
Distribution Explanation:
A distribution in statistics and data analysis represents the way values or a set of data are spread out or distributed over a range. The distribution can show where values are concentrated, values are absent or infrequent, or any other patterns. Visualizing distributions helps users understand underlying patterns and tendencies in the data.
Settings and Parameters:
Main Settings:
Window Size
- Description: This dictates the amount of data used to calculate the distribution.
- Options: A whole number (integer).
- Tooltip: A window size of 0 means it uses all the available data.
Scale
- Description: Adjusts the height of the distribution visualization.
- Options: Any integer between 20 and 499.
Round Source
- Description: Rounds the chosen data source to a specified number of decimal places.
- Options: Any whole number (integer).
Minimum Value
- Description: Specifies the minimum value you wish to account for in the distribution.
- Options: Any integer from 0 to 100.
- Tooltip: 0 being the lowest and 100 being the highest.
Smoothing
- Description: Applies a smoothing function to the distribution visualization to simplify its appearance.
- Options: Any integer between 1 and 20.
Include 0
- Description: Dictates whether zero should be included in the distribution visualization.
- Options: True (include) or False (exclude).
Standard Deviation
- Description: Enables the visualization of standard deviation, which measures the amount of variation or dispersion in the chosen data set.
- Tooltip: This is best suited for a source that has a vaguely Gaussian (bell-curved) distribution.
- Options: True (enable) or False (disable).
Color Options
- High Color and Low Color: Specifies colors for high and low data points.
- Standard Deviation Color: Designates a color for the standard deviation lines.
Example Settings:
Example Usage RSI
- Description: Enables the use of RSI as the data source.
- Options: True (enable) or False (disable).
RSI Length
- Description: Determines the period over which the RSI is calculated.
- Options: Any integer greater than 1.
Using an External Source:
To visualize the distribution of an external source:
Select the "Move to" option in the dropdown menu for the Paytience Distribution indicator on your chart.
Set it to the existing panel where your external data source is placed.
Navigate to "Pin to Scale" and pin the indicator to the same scale as your external source.
Indicator Logic and Functions:
Sinc Function: Used in signal processing, the sinc function ensures the elimination of aliasing effects.
Sinc Filter: A filtering mechanism which uses sinc function to provide estimates on the data.
Weighted Mean & Standard Deviation: These are statistical measures used to capture the central tendency and variability in the data, respectively.
Output and Visualization:
The indicator visualizes the distribution as a series of colored boxes, with the intensity of the color indicating the frequency of the data points in that range. Additionally, lines representing the standard deviation from the mean can be displayed if the "Standard Deviation" setting is enabled.
The example RSI, if enabled, is plotted along with its common threshold lines at 70 (upper) and 30 (lower).
Understanding the Paytience Distribution Indicator
1. What is a Distribution?
A distribution represents the spread of data points across different values, showing how frequently each value occurs. For instance, if you're looking at a stock's closing prices over a month, you may find that the stock closed most frequently around $100, occasionally around $105, and rarely around $110. Graphically visualizing this distribution can help you see the central tendencies, variability, and shape of your data distribution. This visualization can be essential in determining key trading points, understanding volatility, and getting an overview of the market sentiment.
2. The Rounding Mechanism
Every asset and dataset is unique. Some assets, especially cryptocurrencies or forex pairs, might have values that go up to many decimal places. Rounding these values is essential to generate a more readable and manageable distribution.
Why is Rounding Needed? If every unique value from a high-precision dataset was treated distinctly, the resulting distribution would be sparse and less informative. By rounding off, the values are grouped, making the distribution more consolidated and understandable.
Adjusting Rounding: The `Round Source` input allows users to determine the number of decimal places they'd like to consider. If you're working with an asset with many decimal places, adjust this setting to get a meaningful distribution. If the rounding is set too low for high precision assets, the distribution could lose its utility.
3. Standard Deviation and Oscillators
Standard deviation is a measure of the amount of variation or dispersion of a set of values. In the context of this indicator:
Use with Oscillators: When using oscillators like RSI, the standard deviation can provide insights into the oscillator's range. This means you can determine how much the oscillator typically deviates from its average value.
Setting Bounds: By understanding this deviation, traders can better set reasonable upper and lower bounds, identifying overbought or oversold conditions in relation to the oscillator's historical behavior.
4. Resampling
Resampling is the process of adjusting the time frame or value buckets of your data. In the context of this indicator, resampling ensures that the distribution is manageable and visually informative.
Resample Size vs. Window Size: The `Resample Resolution` dictates the number of bins or buckets the distribution will be divided into. On the other hand, the `Window Size` determines how much of the recent data will be considered. It's crucial to ensure that the resample size is smaller than the window size, or else the distribution will not accurately reflect the data's behavior.
Why Use Resampling? Especially for price-based sources, setting the window size around 500 (instead of 0) ensures that the distribution doesn't become too overloaded with data. When set to 0, the window size uses all available data, which may not always provide an actionable insight.
5. Uneven Sample Bins and Gaps
You might notice that the width of sample bins in the distribution is not uniform, and there can be gaps.
Reason for Uneven Widths: This happens because the indicator uses a 'resampled' distribution. The width represents the range of values in each bin, which might not be constant across bins. Some value ranges might have more data points, while others might have fewer.
Gaps in Distribution: Sometimes, there might be no data points in certain value ranges, leading to gaps in the distribution. These gaps are not flaws but indicate ranges where no values were observed.
In conclusion, the Paytience Distribution indicator offers a robust mechanism to visualize the distribution of data from various sources. By understanding its intricacies, users can make better-informed trading decisions based on the distribution and behavior of their chosen data source.
Bursa Malaysia Index SeriesBursa Malaysia Index Series. The index computation is as follows:-
Current aggregate Market Capitalisation/Base Aggregate Market Capitalisation x 100.
The Bursa Malaysia Index Series is calculated and disseminated on a real-time basis at 60-second intervals during Bursa’s trading hours.
Label_Trades Enter your trade information to display on chartThis indicator is an overlay for your main chart. It will display your trade entry and trade close positions on your chart.
After you place the indicator on you shart you will need to enter the trade information that you want to display.
You can open thte input setting by clicking on the gear sprocket that appears when you hover your mouse over the indicator name. There are 7 seting you will want to fill in.
Date and Time Bought
Date and Time Sold
Trade Lot Size
Select whether the trades was 'long' or 'short'
The price for buying the Trade
The price for selling the Trade
On the third tab
The code is straightforward. Using a conditional based on whtehr the trade was 'long' or 'short' determines where the labels will be placed and whether they show a long trade or short trade. It also displays a tool tip when you hover over the label. The tooltip will display the number of lots bought or sold and the price.
The lable.new() function is the meat of the indicator. I will go over a line to explainthe options available.
Pinscript manual(www.tradingview.com)
The function parameters can be called out as in the example above or the values can be placed comma seperated. If you do the latter you must enter the parameters in order. I like anming the parameters as I place them so I can easily see what I did.
label.new(
x=t_bot, // x is the time the transaction occured
y=na, // y is the for the y-axis it is not used here so 'na' tells pinescript to ignore the parameter
xloc=xloc.bar_time, // x_loc is specifying that x is a time value
yloc=yloc.belowbar, // y-loc specifies to place the label under the bar. There are other locations to use. See language reference ((www.tradingview.com)
style=label.style_triangleup, // This parameter selects the lable style. There are many other style to use, see the manual.
color=color.green, // the Label fill color
size=size.small, // the label size
tooltip=str.tostring(lot_size) + " lots bought at $" + str.tostring(bot_val)) // Some parameters are tricky. This one needs to be a string but we are using an integer value(lot_size) and a float value(bol_val). They are all concatenated via the "+" sign. In oorder to do this the numeric values need to be cast or converted into strings. The string function str.tostring() does this.
Z-Score Based Momentum Zones with Advanced Volatility ChannelsThe indicator "Z-Score Based Momentum Zones with Advanced Volatility Channels" combines various technical analysis components, including volatility, price changes, and volume correction, to calculate Z-Scores and determine momentum zones and provide a visual representation of price movements and volatility based on multi timeframe highest high and lowest low values.
Note: THIS IS A IMPROVEMNT OF "Multi Time Frame Composite Bands" INDICATOR OF MINE WITH MORE EMPHASIS ON MOMENTUM ZONES CALULATED BASED ON Z-SCORES
Input Options
look_back_length: This input specifies the look-back period for calculating intraday volatility. correction It is set to a default value of 5.
lookback_period: This input sets the look-back period for calculating relative price change. The default value is 5.
zscore_period: This input determines the look-back period for calculating the Z-Score. The default value is 500.
avgZscore_length: This input defines the length of the momentum block used in calculations, with a default value of 14.
include_vc: This is a boolean input that, if set to true, enables volume correction in the calculations. By default, it is set to false.
1. Volatility Bands (Composite High and Low):
Composite High and Low: These are calculated by combining different moving averages of the high prices (high) and low prices (low). Specifically:
a_high and a_low are calculated as the average of the highest (ta.highest) and lowest (ta.lowest) high and low prices over various look-back periods (5, 8, 13, 21, 34) to capture short and long-term trends.
b_high and b_low are calculated as the simple moving average (SMA) of the high and low prices over different look-back periods (5, 8, 13) to smooth out the trends.
high_c and low_c are obtained by averaging a_high with b_high and a_low with b_low respectively.
IDV Correction Calulation : In this script the Intraday Volatility (IDV) is calculated as the simple moving average (SMA) of the daily high-low price range divided by the closing price. This measures how much the price fluctuates in a given period.
Composite High and Low with Volatility: The final c_high and c_low values are obtained by adjusting high_c and low_c with the calculated intraday volatility (IDV). These values are used to create the "Composite High" and "Composite Low" plots.
Composite High and Low with Volatility Correction: The final c_high and c_low values are obtained by adjusting high_c and low_c with the calculated intraday volatility (IDV). These values are used to create the "Composite High" and "Composite Low" plots.
2. Momentum Blocks Based on Z-Score:
Relative Price Change (RPC):
The Relative Price Change (rpdev) is calculated as the difference between the current high-low-close average (hlc3) and the previous simple moving average (psma_hlc3) of the same quantity. This measures the change in price over time.
Additionally, std_hlc3 is calculated as the standard deviation of the hlc3 values over a specified look-back period. The standard deviation quantifies the dispersion or volatility in the price data.
The rpdev is then divided by the std_hlc3 to normalize the price change by the volatility. This normalization ensures that the price change is expressed in terms of standard deviations, which is a common practice in quantitative analysis.
Essentially, the rpdev represents how many standard deviations the current price is away from the previous moving average.
Volume Correction (VC): If the include_vc input is set to true, volume correction is applied by dividing the trading volume by the previous simple moving average of the volume (psma_volume). This accounts for changes in trading activity.
Volume Corrected Relative Price Change (VCRPD): The vcrpd is calculated by multiplying the rpdev by the volume correction factor (vc). This incorporates both price changes and volume data.
Z-Scores: The Z-scores are calculated by taking the difference between the vcrpd and the mean (mean_vcrpd) and then dividing it by the standard deviation (stddev_vcrpd). Z-scores measure how many standard deviations a value is away from the mean. They help identify whether a value is unusually high or low compared to its historical distribution.
Momentum Blocks: The "Momentum Blocks" are essentially derived from the Z-scores (avgZScore). The script assigns different colors to the "Fill Area" based on predefined Z-score ranges. These colored areas represent different momentum zones:
Positive Z-scores indicate bullish momentum, and different shades of green are used to fill the area.
Negative Z-scores indicate bearish momentum, and different shades of red are used.
Z-scores near zero (between -0.25 and 0.25) suggest neutrality, and a yellow color is used.
