Building Econometric Models

Out-of-Sample Forecast Evaluation

• ‘Introductory Econometrics for Finance’ © Chris Brooks 2013

• They evaluate the forecasts in two ways:
• The first is by regressing the realised volatility series on the forecasts plus a constant:
• (7)
• where is the “actual” value of volatility, and is the value forecasted for it during period t.
• Perfectly accurate forecasts imply b0 = 0 and b1 = 1.
• But what is the “true” value of volatility at time t ?
• Day & Lewis use 2 measures
• 1. The square of the weekly return on the index, which they call SR.
• 2. The variance of the week’s daily returns multiplied by the number of trading days in that week.

Out-of Sample Model Comparisons

• ‘Introductory Econometrics for Finance’ © Chris Brooks 2013

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Encompassing Test Results: Do the IV Forecasts Encompass those of the GARCH Models?

• ‘Introductory Econometrics for Finance’ © Chris Brooks 2013

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Conclusions of Paper

• ‘Introductory Econometrics for Finance’ © Chris Brooks 2013

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• Within sample results suggest that IV contains extra information not contained in the GARCH / EGARCH specifications.
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• Out of sample results suggest that nothing can accurately predict volatility!

Stochastic Volatility Models

• ‘Introductory Econometrics for Finance’ © Chris Brooks 2013

• It is a common misconception that GARCH-type specifications are stochastic volatility models
• However, as the name suggests, stochastic volatility models differ from GARCH principally in that the conditional variance equation of a GARCH specification is completely deterministic given all information available up to that of the previous period
• There is no error term in the variance equation of a GARCH model, only in the mean equation 
• Stochastic volatility models contain a second error term, which enters into the conditional variance equation.