A note on the estimated GARCH coefficients from the S&P1500 universe

ABSTRACT

We employ 1440 stocks listed in the S&P Composite 1500 Index of the NYSE. Three benchmark GARCH models are estimated for the returns of each individual stock under three alternative distributions (Normal, t and GED). We provide summary statistics for all the GARCH coefficients derived from 11,520 regressions. The EGARCH model with GED errors emerges as the preferred choice for the individual stocks in the S&P 1500 universe when non-negativity and stationarity constraints in the conditional variance are imposed. 57% of the constraint’s violations are taking place in the S&P small cap stocks.

KEYWORDS:

• GARCH
• GJR-GARCH
• EGARCH
• alternative distributions
• volatility
• time-series

JEL CLASSIFICATION:

• C13
• C12
• C22

Acknowledgements

The authors would like to thank Dimitrios Thomakos for his useful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Nelson and Cao (1992) derived the necessary and sufficient conditions for the non-negativity of the conditional variance in higher-order GARCH models. The GARCH(2,2) case has been studied in detail by He and Terasvirta (1999).

² The unit root tests and the summary statistics of all series are available from the authors upon request.

³ The moment structure of the EGARCH(1,1) model has also been discussed in He, Teräsvirta, and Malmsten (2002) and Karanasos and Kim (2003).

⁴ Bollerslev and Wooldridge (1992), pointed out that the assumption of the normality of the standardized conditional errors may be too strong and can cause misspecification of the likelihood function. To deal with this, they suggest the use of Quasi Maximum Likelihood Estimation (QMLE). All estimations have been carried out in EViews 8.