Forecasting with Exponential Smoothing and EWMA Volatility
Summary
The discussion distinguishes smoothing a price series from forecasting future values. It gives a recursive exponential-smoothing forecast in which the next estimate updates the current forecast in proportion to the latest observation's forecasting error. This is presented as a general time-series method, while the answer cautions that low autocorrelation in returns may make return forecasts weak. The method also omits seasonal patterns and linear trends unless extended.
The answer identifies EWMA as more commonly useful for volatility estimation: squared asset log returns are weighted with a prior variance estimate to produce a conditional variance forecast. It characterizes this variance recursion as a special case of an IGARCH model and provides a decay parameter example. The exchange explains the distinction between a technical-analysis EMA used to smooth prices and an EWMA model used to forecast volatility, but supplies no empirical test of predictive performance. Results therefore depend on the series, parameter choice, and model assumptions.
Key ideas
- Exponential smoothing updates a forecast using the latest observation and the prior forecast.
- The update can be viewed as proportional to the current forecast error.
- Low return autocorrelation may limit the usefulness of return forecasts from this approach.
- The described EWMA variance recursion uses squared returns and a prior variance estimate.
- EWMA volatility estimation is presented as a special case of an IGARCH model.
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Full text
# How can I forecast the Exponential Moving Average of the next day?
# How can I forecast the Exponential Moving Average of the next day?
I am trying to forecast prices with exponential moving average method. The equation for EMA = [(Closing * k) + (EMA(y) * (1-k)] where: Closing is closing price of today, k is the weighted multiplier, EMA(y) is the previous EMA, and 1 - k is 1 - weighted multipler. This gives the EMA for today. I would like to know how can I modify this equation to forecast the EMA of the next day without knowing the closing price of the next day?
## Answer by Kevin (score 2, accepted)
https://quant.stackexchange.com/a/46804
You can forecast your time series $(X_t)$ as follows $$F_{t+1} = k X_t + (1-k)F_t,$$ where $F_t$ is your forecast for today and $X_t$ the observed value for today (today's log-return). Note that the above equation is equivalent to $$F_{t+1}-F_t = k(X_t-F_t)$$ and hence, the change in the forecast value is proportional to the current forecasting error.
Due to low autocorrelation in return series however, I doubt how succesfulsuch forecasts are. By the way, this version of an EWMA does not incorporate seasonal patterns or (linear) trends but may be adjusted.
Note that the formula you quoted is used as exponential smoothing in order to reduce the ''roughness'' of an observed time series. In technical analysis, one frequently applies SMA, WMA or EMA in order to identify trends.
I typically see an EMWA used in time series analysis to forecast volatility (squared returns have a significant autocorrelation). Here, the EMWA formula (which is a special case of an IGARCH(1,1) model) for forecasting the conditional variancce reads as follows $$ \hat{s}_t^2 = (1-\lambda)X_{t-1}^2 + \lambda \hat{s}^2_{t-1},$$ where $\lambda=0.94$ and $(X_t)$ are the log-returns of your asset. Then, you can estimate tomorrow's volatility using today's log-return and variance estimate.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.