A note on the properties of power-transformed returns in long-memory stochastic volatility models with leverage effect

Abstract

a b s t r a c tThe autocorrelation function (acf) of powered absolute returns and their cross-correlations with original returns are derived, for any value of the power parameter, in the context of long-memory stochastic volatility models with leverage effect and Gaussian noises. These autocorrelations and cross-correlations generalize and correct recent results on the acf of squared and absolute returns.

On the macro-drivers of realized volatility: the destabilizing impact of UK policy uncertainty across Europe

“…The optimal estimation of the power term and the asymmetric response to positive and negative shocks embedded in the time-varying volatility pattern have already proved to be one of the most pivotal innovations in the GARCH family of models (see, for example, Brooks et al, 2000). Among others, Pérez et al (2009, see the references therein for more details) show that the presence of an asymmetric response of volatility to positive and negative returns shows up in non-zero cross-correlations between original returns and future powers of absolute returns. One of our main …ndings is that each of the two powered conditional variances is signi…cantly a¤ected by the …rst lags of both power transformed variables, that is, squared negative returns, and realized variance (or, for the latter, its negative signed values).…”

Asymmetric stochastic volatility models: Properties and particle filter-based simulated maximum likelihood estimation

“…Taylor (1994Taylor ( , 2007 provide expressions for the variance and kurtosis of returns and the autocorrelation function of squared observations for the asymmetric autoregressive SV (A-ARSV) model of Harvey and Shephard (1996) which is obtained when f ( t−1 ; θ ) = γ 1 t−1 . For the same model and still assuming normality of standardized returns, Pérez et al (2009) derive the autocorrelation and cross-correlation functions of the power-transformed absolute returns. Asai and McAleer (2011) derive the first and second order moments of returns and Yu (2012a) derives the moments of returns and the conditions for stationarity, strict stationarity and ergodicity in extended specifications of the A-ARSV model.…”

Maximally Autocorrelated Power Transformations: A Closer Look at the Properties of Stochastic Volatility Models

“…An extension of the model to include leverage effect, i.e., the asymmetric response of volatility to negative and positive returns, is given by Ruiz and Veiga (2008). However, as shown in Pérez et al (2009), in that model the autocorrelations of absolute and squared returns are nearly the same regardless of the presence of leverage effect. Therefore, for the goal of this paper, we focus on the symmetric LMSV(1,d,0) model in (2.1).…”