Realized stochastic volatility with general asymmetry and long memory

Abstract

The paper develops a novel realized stochastic volatility model of asset returns and realized volatility that incorporates general asymmetry and long memory (hereafter the RSV-GALM model). The contribution of the paper ties in with Robert Basmann's seminal work in terms of the estimation of highly non-linear model specifications ("Causality tests and observationally equivalent representations of econometric models", Journal of Econometrics, 1988), especially for specifying causal effects from returns to future volatility. This paper discusses asymptotic results of a Whittle likelihood estimator for the RSV-GALM model and a test for general asymmetry, and analyses the finite sample properties. The paper also develops an approach to obtain volatility estimates and out-of-sample forecasts. Using high frequency data for three US financial assets, the new model is estimated and evaluated. The paper compares the forecasting performance of the new model with a realized conditional volatility model.

Realized stochastic volatility models with generalized Gegenbauer long memory

“…By excluding the data of x t , the model reduces to the class of generalized long memory SV models, encompassing the long memory SV model of Breidt, Crato, and de Lima (1998) with k = 0, and the Gegenbauer ARMA SV (GARMASV) model of Artiach and Arteche (2012) with k = 1 and d = 0. Furthermore, the RSV-GGLM model extends the long memory part of the realized SV models of Shirota, Hizu, and Omori (2014) and Asai, Chang, and McAleer (2017).…”

“…Fo modeling asset returns and realized volatility measure simultaneously, Hansen, Huang, and Shek (2012) suggested a realized GARCH framework (see also Hansen and Huang (2016)). The corresponding structure for SV is often referred to as the 'realized SV' (RSV) model, which is considered by Takahashi, Omori, and Watanabe (2009), Koopman and Scharth (2013), Shirota, Hizu, and Omori (2014), and Asai, Chang, and McAleer (2017), among others. Shirota, Hizu, and Omori (2014) and Asai, Chang, and McAleer (2017) accommodated the ARFIMA process in the volatility process.…”

“…The corresponding structure for SV is often referred to as the 'realized SV' (RSV) model, which is considered by Takahashi, Omori, and Watanabe (2009), Koopman and Scharth (2013), Shirota, Hizu, and Omori (2014), and Asai, Chang, and McAleer (2017), among others. Shirota, Hizu, and Omori (2014) and Asai, Chang, and McAleer (2017) accommodated the ARFIMA process in the volatility process. While Shirota, Hizu, and Omori (2014) use the Markov chain Monte Carlo technique, Asai, Chang, and McAleer (2017) estimated their model using the Whittle likelihood.…”

“…Shirota, Hizu, and Omori (2014) and Asai, Chang, and McAleer (2017) accommodated the ARFIMA process in the volatility process. While Shirota, Hizu, and Omori (2014) use the Markov chain Monte Carlo technique, Asai, Chang, and McAleer (2017) estimated their model using the Whittle likelihood.…”

“…In this paper, we develop an RSV model with general Gegenbauer long memory. If the Gegenbauer frequencies of log-volatility are predetermined, we can use the Whittle likelihood estimator of Hosoya (1997) and Zaffaroni (2009) to estimate the RSV model, as in Asai, Chang, and McAleer (2017). However, the Gegenbauer frequencies are unknown, and so we use the non-parametric estimator of Hidalgo and Soulier (2004), as in Artiach and Arteche (2012), who investigated the long memory property of the level and variance of the number of sunspots.…”