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Abstract
We study a special case of the GARCH-in-Mean model proposed by Christensen et al. (Citation2012), where a different specification for the conditional variance was adopted as compared to the traditional GARCH-M model. The conditions about geometric ergodicity are discussed and by checking the conditions of Lemma A.1 in Jensen and Rahbek (Citation2004), the asymptotic normality of the quasi maximum likelihood estimators for the model is established. Simulations demonstrate that the estimation procedure performs well and the given empirical studies indicate the considered model can have comparable performance in data modeling as compared to the standard one.
Mathematics Subject Classification:
Acknowledgments
The authors are grateful to the referees for their useful comments, which led to improvements in the presentation of the article. The first two and the fourth authors were supported by research grants from the Research Committee of The Hong Kong Polytechnic University. The third author's work was partially supported by National Natural Science Foundation of China (Grant No. 10971042).
Notes
Notes. (1) Number of replications =1, 000; (2) as indicated in Sec. 3.1, different error distributions are used.
The objective of the empirical studies is to compare the performance between the considered model and the traditional one, while it should be noted that Christensen et al. (Citation2012) has shown semiparametric GARCH-in-Mean models may be more practical when analyzing the real data.