Why EWMA Volatility Forecasts Use Lagged Squared Errors

Summary

The document addresses a timing question about an exponentially weighted volatility model: if the residual at time t uses the actual value at t, why forecast volatility for that same time? The response points out that the equation as written may have its error term at the wrong time index. In an EWMA forecast, the squared residual from the previous period is used to update the variance estimate for the next period, so the forecast is available before that next observation is known.

The answer supports this interpretation by citing two research papers on EWMA volatility and value-at-risk, but it does not derive the update equation or compare alternative parameter choices. Its explanation is brief, and the original question's equation may reflect a notation or transcription issue. The central practical lesson is to distinguish an in-sample variance update after observing a return from a forecast made before observing it.

Key ideas

• An EWMA volatility forecast should use information available before the period being forecast.
• A squared residual observed in one period can update the variance forecast for the following period.
• The timing of the error term determines whether an equation describes an update or a genuine forecast.
• The response cites research on EWMA volatility but does not assess model performance or parameter selection.

Tags

# A volatility model developed by JP Morgan


# A volatility model developed by JP Morgan












I am quite confused with this predicting volatility equation:

σ2t = βσ2t-1 + (1-β)ε2t

Here is a section from Capital Market Expectations: CFA Level 3 Volume 3 Curriculum (page 27)

https://ibb.co/37Z2M8r

If we have the residual error (Actual Value - Predicted Value) at time t, that means we already have known the actual variance at time t. Then why do we still need to forecast the volatility at time t anyway?

## Answer by alexbougias (score 2)

https://quant.stackexchange.com/a/45633

A quick Google search, showed that your equation is not correct, as the error term should be taken at lag 1. If that is the case, forecasting has a direct meaning.

Indicatively, check the following:

- Bollen, B., 2015. What should the value of lambda be in the exponentially weighted moving average volatility model?. Applied Economics, 47(8), pp.853-860

- Gabrielsen, A., Kirchner, A., Liu, Z., & Zagaglia, P. (2015). Forecasting value-at-risk with time-varying variance, skewness and kurtosis in an exponential weighted moving average framework. Annals of Financial Economics, 10(01), 1550005

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.