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Abstract

This study proposes a Generalized Autoregressive Conditional Heteroscedasticity (GARCH) with modified Grey prediction model to investigate the transmission of volatility through analysis of the error terms. Generally, the higher the sample size, the better GARCH models describe variation. However, the GARCH( $p$ , $q$ ) model often causes the problem of time delay by assuming that the conditional variance and the squared error term have lags $p$ and $q$ periods, respectively. Consequently, this paper utilizes a Grey Model (GM), modified for general residual sequences and generalizing the squared error terms to incorporate influence by unexpected factors such as previous process states or delayed impact of information. Furthermore, this study illustrates the proposed model with daily NASDAQ closing prices for a total of 1265 observations. The modified Grey-GARCH model demonstrates improved accuracy over the Grey-GARCH model and the traditional GARCH model. The results of this study have practical implications for optimal investment strategies.

Keywords

Grey model GARCH Grey-GARCH residual sequences modified Grey-GARCH

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A GARCH model with modified grey prediction model for US stock return volatility

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