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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?

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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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  • $\begingroup$ Could you please add the link, which you managed to search? $\endgroup$
    – bhutes
    Commented May 16, 2019 at 8:52
  • $\begingroup$ I just added the reference source for you to look it. Please provide the suggestion. Thanks. $\endgroup$
    – user506602
    Commented May 16, 2019 at 9:47

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