1 / 15

THE EXPONENTIAL GARCH MODEL

THE EXPONENTIAL GARCH MODEL. THE EXPONENTIAL GARCH MODEL. To allow for asymmetric effects between positive and negative asset returns, he considers the weighted innovation where θ and γ are real constants

micheal
Download Presentation

THE EXPONENTIAL GARCH MODEL

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. THE EXPONENTIAL GARCH MODEL

  2. THE EXPONENTIAL GARCH MODEL • To allow for asymmetric effects between positive and negative asset returns, he considers the weighted innovation • where θ and γ are real constants • Both t and | t | − E(|t |) are zero-mean iidsequences with continuous distributions

  3. Therefore E[g(t )] = 0 • The asymmetry of g(t ) can easily be seen by rewriting it as

  4. An EGARCH(m, s) model can be written as • where α0 is a constant • B is the back-shift (or lag) operator such that Bg(t ) =g(t−1)

  5. The use of g( t ) enables the model to respond asymmetrically to positive and negative lagged values of at

  6. To better understand the EGARCH model, let us consider the simple model with order (1, 0)

  7. Specifically, we have

  8. Example • We consider the monthly log returns of IBM stock from January 1926 to December 1997 for 864 observations. • An AR(1)-EGARCH(1, 0) model is entertained and the fitted model is

  9. For the 2-step ahead forecast

More Related