Building Econometric Models

Extensions to the Basic GARCH Model

• ‘Introductory Econometrics for Finance’ © Chris Brooks 2013

• Since the GARCH model was developed, a huge number of extensions and variants have been proposed. Three of the most important examples are EGARCH, GJR, and GARCH-M models.
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• Problems with GARCH(p,q) Models:
• - Non-negativity constraints may still be violated
• - GARCH models cannot account for leverage effects
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• Possible solutions: the exponential GARCH (EGARCH) model or the GJR model, which are asymmetric GARCH models.
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The EGARCH Model

• ‘Introductory Econometrics for Finance’ © Chris Brooks 2013

• Suggested by Nelson (1991). The variance equation is given by
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• Advantages of the model
• - Since we model the log(t2), then even if the parameters are negative, t2
• will be positive.
• - We can account for the leverage effect: if the relationship between
• volatility and returns is negative, , will be negative.

The GJR Model

• ‘Introductory Econometrics for Finance’ © Chris Brooks 2013

• Due to Glosten, Jaganathan and Runkle
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• where It-1 = 1 if ut-1 < 0
• = 0 otherwise
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• For a leverage effect, we would see  > 0.
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• We require 1 +   0 and 1  0 for non-negativity.

An Example of the use of a GJR Model

• ‘Introductory Econometrics for Finance’ © Chris Brooks 2013

• Using monthly S&P 500 returns, December 1979- June 1998
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• Estimating a GJR model, we obtain the following results.
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