Abstract
This work is devoted to the study of the parameter test for the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model. Based on the daily GARCH model, using the parameter estimator obtained by intraday high-frequency data, the adjusted Likelihood Ratio test statistic and Wald test statistic are provided. Asymptotic distributions of the two adjusted test statistics are deducted and a way to select the optimal sampling frequency is also discussed. Simulation studies show that the proposed test statistics have better size and power than traditional ones (without using intraday high-frequency data). An empirical study is given to illustrate the potential applications of the proposed tests. The results show the idea of this article is of certain superiority and it can be extended to other GARCH type models.
Highlights
Volatility modeling is an important tool for policymaking, asset pricing, investment analysis, and risk management [1]
This paper is to study the Wald test and Likelihood Ratio (LR) test of the daily Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model by introduction high-frequency data
The proposed test statistics are based on the Quasi Maximum Likelihood Estimate (QMLE) of daily GARCH model which introduces the intraday high-frequency data, and their distribution are proved to be asymptotic chi-square
Summary
Volatility modeling is an important tool for policymaking, asset pricing, investment analysis, and risk management [1]. The model has been developed into many extensions [4,5,6,7,8,9,10,11,12,13] From these literature, we can find that most studies on the GARCH model adopt the standard form based on daily close-to-close returns. A case in point is Visser’s work [26], where the information of intraday high-frequency data is firstly transferred to a daily volatility proxy and such a proxy is adopted to improve daily GARCH model estimation. The proposed test statistics are based on the QMLE of daily GARCH model which introduces the intraday high-frequency data, and their distribution are proved to be asymptotic chi-square. Through the theoretical and simulation results, the provided tests are of a certain novelty and superiority
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