Exponentially Weighted Moving Average Oscillator [BackQuant]Exponentially Weighted Moving Average (EWMA)
The Exponentially Weighted Moving Average (EWMA) is a quantitative or statistical measure used to model or describe a time series. The EWMA is widely used in finance, the main applications being technical analysis and volatility modeling.
The moving average is designed as such that older observations are given lower weights. The weights fall exponentially as the data point gets older – hence the name exponentially weighted.
Applications of the EWMA
The EWMA is widely used in technical analysis. It may not be used directly, but it is used in conjunction with other indicators to generate trading signals. A well-known example is the Negative Volume Index (NVI), which is used in conjunction with its EWMA.
Why is it different from the In-Built TradingView EWMA
Adaptive Algorithms: If your strategy requires the alpha parameter to change adaptively based on certain conditions (for example, based on market volatility), a for loop can be used to adjust the weights dynamically within the loop as opposed to the fixed decay rate in the standard EWMA.
Customization: A for loop allows for more complex and nuanced calculations that may not be directly supported by built-in functions. For example, you might want to adjust the weights in a non-standard way that the typical EWMA calculation doesn't allow for.
Use of the Oscillator
This mainly comes from 3 main premises, this is something I like to do personally since it is easier to work with them in the context of my system. E.g. Using them to spot clear trends without noise on longer timeframes.
Clarity: Plotting the EWMA as an oscillator provides a clear visual representation of the momentum or trend strength. It allows traders to see overbought or oversold conditions relative to a normalized range.
Comparison: An oscillator can make it easier to compare different securities or timeframes on a similar scale, especially when normalized. This is because the oscillator values are typically bounded within a range (like -1 to 1 or 0 to 100), whereas the actual price series can vary significantly.
Focus on Change: When plotted as an oscillator, the focus is on the rate of change or the relative movement of the EWMA, not on the absolute price levels. This can help traders spot divergences or convergences that may not be as apparent when the EWMA is plotted directly on the price chart. This is also one reason there is a conditional plotting on the chart.
Trend Strength: When normalized, the distance of the oscillator from its midpoint can be interpreted as the strength of the trend, providing a quantitative measure that can be used to make systematic trading decisions.
Here are the backtests on the 1D Timeframe for
BITSTAMP:BTCUSD
BITSTAMP:ETHUSD
COINBASE:SOLUSD
When using this script the user is able to define a source and period, which by extension calculates the alpha. An option to colour the bars accord to trend.
This makes it super easy to use in a system.
I recommend using this as above the midline (0) for a positive trend and below the midline for negative trend.
Hence why I put a label on the last bar to ensure it is easier for traders to read.
Lastly, The decreasing colour relative to RoC, this also helps traders to understand the strength of the indicator and gain insight into when to potentially reduce position size.
This indicator is best used in the medium timeframe.
Ewma
HMA w/ SSE-Dynamic EWMA Volatility Bands [Loxx]This indicator is for educational purposes to lay the groundwork for future closed/open source indicators. Some of thee future indicators will employ parameter estimation methods described below, others will require complex solvers such as the Nelder-Mead algorithm on log likelihood estimations to derive optimal parameter values for omega, gamma, alpha, and beta for GARCH(1,1) MLE and other volatility metrics. For our purposes here, we estimate the rolling lambda (λ) value used to calculate EWMA by minimizing of the sum of the squared errors minus the long-run variance--a rolling window of the one year mean of squared log-returns. In practice, practitioners will use a λ equal to a standardized value put out by institutions such as JP Morgan. Even simpler than this, others use a ratio of (per - 1) / (per + 1) to derive λ where per is the lookback period for EWMA. Due to computation limits in Pine, we'll likely not see a true GARCH(1,1) MLE on Pine for quite some time, but future closed source indicators will contain some very interesting industry hacks to get close by employing modifications to EWMA. Enjoy!
Exponentially weighted volatility and its relationship to GARCH(1,1)
Exponentially weighted volatility--also called exponentially weighted moving average volatility (EWMA)--puts more weight on more recent observations. EWMA is calculated as follows:
σ*2 = λσ(n - 1)^2 + (1 − λ)u(n - 1)^2
The estimate, σn, of the volatility for day n (made at the end of day n − 1) is calculated from σn −1 (the estimate that was made at the end of day n − 2 of the volatility for day n − 1) and u^n−1 (the most recent daily percentage change).
The EWMA approach has the attractive feature that the data storage requirements are modest. At any given time, we need to remember only the current estimate of the variance rate and the most recent observation on the value of the market variable. When we get a new observation on the value of the market variable, we calculate a new daily percentage change to update our estimate of the variance rate. The old estimate of the variance rate and the old value of the market variable can then be discarded.
The EWMA approach is designed to track changes in the volatility. Suppose there is a big move in the market variable on day n − 1 so that u2n−1 is large. This causes our estimate of the current volatility to move upward. The value of λ governs how responsive the estimate of the daily volatility is to the most recent daily percentage change. A low value of λ leads to a great deal of weight being given to the u(n−1)^2 when σn is calculated. In this case, the estimates produced for the volatility on successive days are themselves highly volatile. A high value of λ (i.e., a value close to 1.0) produces estimates of the daily volatility that respond relatively slowly to new information provided by the daily percentage change.
The RiskMetrics database, which was originally created by JPMorgan and made publicly available in 1994, used the EWMA model with λ = 0.94 for updating daily volatility estimates. The company found that, across a range of different market variables, this value of λ gives forecasts of the variance rate that come closest to the realized variance rate. In 2006, RiskMetrics switched to using a long memory model. This is a model where the weights assigned to the u(n -i)^2 as i increases decline less fast than in EWMA.
GARCH(1,1) Model
The EWMA model is a particular case of GARCH(1,1) where γ = 0, α = 1 − λ, and β = λ. The “(1,1)” in GARCH(1,1) indicates that σ^2 is based on the most recent observation of u^2 and the most recent estimate of the variance rate. The more general GARCH(p, q) model calculates σ^2 from the most recent p observations on u2 and the most recent q estimates of the variance rate.7 GARCH(1,1) is by far the most popular of the GARCH models. Setting ω = γVL, the GARCH(1,1) model can also be written:
σ(n)^2 = ω + αu(n-1)^2 + βσ(n-1)^2
What this indicator does
Calculate log returns log(close/close(1))
Calculates Lambda (λ) dynamically by minimizing the sum of squared errors. I've restricted this to the daily timeframe so as to not bloat the code with additional logic required to derive an annualized EWMA historical volatility metric.
After the Lambda is derived, EWMA is calculated one last time and the result is the daily volatility
This daily volatility is multiplied by the source and the multiplier +/- the HMA to create the volatility bands
Finally, daily volatility is multiplied by the square-root of days per year to derive annualized volatility. Years are trading days for the asset, for most everything but crypto, its 252, for crypto is 365.
EWMA Implied Volatility based on Historical VolatilityVolatility is the most common measure of risk.
Volatility in this sense can either be historical volatility (one observed from past data), or it could implied volatility (observed from market prices of financial instruments.)
The main objective of EWMA is to estimate the next-day (or period) volatility of a time series and closely track the volatility as it changes.
The EWMA model allows one to calculate a value for a given time on the basis of the previous day's value.
The EWMA model has an advantage in comparison with SMA, because the EWMA has a memory.
The EWMA remembers a fraction of its past by a factor A, that makes the EWMA a good indicator of the history of the price movement if a wise choice of the term is made.
Full details regarding the formula :
www.investopedia.com
In this scenario, we are looking at the historical volatility using the anual length of 252 trading days and a monthly length of 21.
Once we apply all of that we are going to get the yearly volatility.
After that we just have to divide that by the square root of number of days in a year, or weeks in a year or months in a year in order to get the daily/weekly/monthly expected volatility.
Once we have the expected volatility, we can estimate with a high chance where the market top and bottom is going to be and continue our analysis on that premise.
If you have any questions, please let me know !
