Modelling long-memory volatilities with leverage effect: A-LMSV versus FIEGARCH

Abstract

A new stochastic volatility model, called A-LMSV, is proposed to cope simultaneously with leverage effect and long-memory in volatility. Its statistical properties are derived and compared with the properties of the FIEGARCH model. It is shown that the dependence of the autocorrelations of squares on the parameters measuring the asymmetry and the persistence is different in both models. The kurtosis and autocorrelations of squares do not depend on the asymmetry in the A-LMSV model while they increase with the asymmetry in the FIEGARCH model. Furthermore, the autocorrelations of squares increase with the persistence in the A-LMSV model and decrease in the FIEGARCH model. On the other hand, if the correlation between returns and future volatilities is negative, the autocorrelations of absolute returns increase with the magnitude of the asymmetry in the FIEGARCH model while they decrease in the A-LMSV model. Finally, the cross-correlations between squares and original observations are, in general, larger in absolute value in the FIEGARCH model than in the A-LMSV model. The results are illustrated by fitting both models to represent the dynamic evolution of volatilities of daily returns of the S&P500 and DAX indexes.

Modelling Long Memory Volatility in Agricultural Commodity Futures Returns

“…Several previous papers have observed and provided application of fractional integrated models in many fields, namely stock returns , Degiannakis (2004) and Niguez % (2007), Lux and Kaizoji (2007), Kang and Yoon (2007), Jefferis and Thupayagale (2008), Ruiz and Veiga (2008)); exchange rate (Baillie et al (1996), Davidson (2004), and Conrad and Lamla (2007)) and inflation rate (Baillie et al (2002)). However, in the literature to date, there have been few applications of the fractionally integrated GARCH class models to commodity futures markets.…”

Long Memory in Asymmetric Volatility of Asean Exchange-Traded Funds

“…In contrast with FIGARCH model, HYGARCH allows combining the desired properties of hyperbolically decaying impulse response coefficients and covariance stationary [18].…”

“…By using ARFIMA-FIGARCH models, found that no significant long memory process can be found between Green ETFs [17]. Ruiz and Viega used A new stochastic volatility model (A-LMSV) and FIEGARCH models and found leverage effect and long memory in volatility of the daily return of the Standard & Poor 500 S&P 500 and Deutscher Aktien IndeX (DAX) indexes [18], [19]. Tang and Shieh revealed that HYGARCH model was outperformed for investigate the long memory for the S&P 500, Nasdag 100 and futures prices [20].…”

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

“…In this note, we derive the expressions of the acf of the power-transformed returns, |y t | c , and of the cross-correlations between y t and |y t+k | c for any positive power c > 0. Therefore, we generalize the results in Ruiz and Veiga (2008) allowing a more precise description of the dynamics of returns generated by A-LMSV models. Furthermore, when c = 1, we obtain, as a particular case, the acf of absolute returns which corrects the wrong expression in Ruiz and Veiga (2008).…”

“…Furthermore, 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. Recently, Ruiz and Veiga (2008) derive the properties of the A-LMSV model with Gaussian errors and compare them with those of the FIEGARCH model. In particular, they derive, among other moments, the acf of powers of absolute observations, |y t | c , and the cross-correlations between y t and |y t+k | c , for c = 1 and 2, where c is the power parameter.…”