Journal of Empirical Finance 17 (2010) 460–470
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Journal of Empirical Finance
journal homepage: www.elsevier.com/locate/jempfin
Long memory in stock market volatility and the volatility-in-mean effect: The FIEGARCH-M Model Bent Jesper Christensen a,⁎, Morten Ørregaard Nielsen b, Jie Zhu c a b c
Aarhus University and Creates, Denmark Queen's University, Canada, and Creates, Denmark University of Southern Denmark, Aarhus University and Creates, Denmark
a r t i c l e
i n f o
a b s t r a c t
We extend the fractionally integrated exponential GARCH (FIEGARCH) model for daily stock return data with long memory in return volatility of Bollerslev and Mikkelsen (1996) by introducing a possible volatility-in-mean effect. To avoid that the long memory property of volatility carries over to returns, we consider a ﬁltered FIEGARCH-in-mean (FIEGARCH-M) effect in the return equation. The ﬁltering of the volatility-in-mean component thus allows the co-existence of long memory in volatility and short memory in returns. We present an application to the daily CRSP value-weighted cum-dividend stock index return series from 1926 through 2006 which documents the empirical relevance of our model. The volatility-inmean effect is signiﬁcant, and the FIEGARCH-M model outperforms the original FIEGARCH model and alternative GARCH-type speciﬁcations according to standard criteria. © 2009 Elsevier B.V. All rights reserved.
Article history: Received 7 August 2008 Received in revised form 27 June 2009 Accepted 4 September 2009 Available online 12 September 2009 JEL Classiﬁcation: C22
Keywords: FIEGARCH Financial leverage GARCH Long memory Risk-return tradeoff Stock returns Volatility feedback
1. Introduction Many of the salient features of daily stock returns are well described by the FIEGARCH (fractionally integrated exponential generalized autoregressive conditional heteroskedasticity) model introduced by Bollerslev and Mikkelsen (1996). Thus, in addition to time-varying volatility and volatility clustering (the ARCH and GARCH effects, as in Engle (1982) and Bollerslev (1986)), and the resulting unconditional excess kurtosis or heavier than normal tails, the model accounts for long memory in volatility (fractional integration, as in the FIGARCH model of Baillie et al. (1996)), as well as asymmetric volatility reaction to positive and negative return innovations (the exponential feature, as in Nelson's (1991) EGARCH model). In this paper, we introduce a ﬁltered in-mean generalization of the FIEGARCH model, which we label FIEGARCH-M. The generalization allows a volatility feedback or risk-return relation effect of changing conditional volatility on conditional expected stock returns, and generates unconditional skewness. Following recent literature (Ang et al., 2006, and Christensen and Nielsen, 2007), it is changes in volatility that enter the return equation. The ﬁltering of volatility when entering it in the return speciﬁcation implies that the long memory property of volatility (the fractionally integrated feature) does not spill over into returns, which would be empirically unrealistic. That volatility exhibits long memory is well established in the recent empirical literature. This ﬁnding is consistent across a number of studies1, and ﬁnancial theory may accommodate long memory in volatility as well, see Comte and Renault (1998). ⁎ Corresponding author. School of Economics and Management, Aarhus University, 1322 University Park, DK-8000 Aarhus C, Denmark. Tel.: +45 29 645 180. E-mail address: email@example.com (B.J. Christensen). 1 See, e.g., Robinson (1991), Crato and de Lima (1994), Baillie et al. (1996), Ding and Granger (1996), Breidt et al. (1998), Robinson (2001), and Andersen et al. (2003). 0927-5398/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jempﬁn.2009.09.008
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