Return Innovation Distribution in Best-Fit GARCH Models for High-Frequency Data

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This paper offers empirical evidence to extant literature on choice of return innovation distribution in GARCH family models. Statistical software packages have Gaussian distribution as default option and offer other distribution options to choose as per properties of data series. Most common choices are Gaussian, t-distribution, and GED. The choice of appropriate return innovation distribution for best-fit GARCH model is still an open inquiry. We posit that choice of return innovation distribution is influenced by frequency of data, time horizon, and symmetric or asymmetric models. This paper estimates four symmetric and asymmetric GARCH models with three return innovation distributions using high frequency and long horizon stock market return series. Daily log returns of NIFTY50 index over the period January 1, 1996, to December 31, 2019, a total of 5,971 observations are analyzed. Results suggest significant evidence in support of volatility clustering, fat-tailedness, mean reversion, volatility persistence, leverage effect, and long memory in return series. Results recommend student’s t-distribution as ideal return innovation process for both symmetric and asymmetric GARCH models. The basic models have serial correlations, but no remaining GARCH effects. After multiple trials, it is observed that the ARMA (1,1)-GARCH (1,1) models have better log likelihood values, minimum information criterion values, no serial correlations, and no remaining GARCH effects. Finally, among the three asymmetric models, ARMA-EGARCH model has superior information criterion values. We recommend ARMA-GARCH (1,1) as best-fit symmetric model and ARMA-EGARCH (1,1) as best-fit asymmetric model for high-frequency data spread over long horizon.

Keywords: Volatility Modeling, Distribution Density, GARCH Models, High-Frequency Data, Long Horizon

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