Conditional Heteroskedasticity in Long-Memory Model “FIMACH” for Return Volatilities in Equity Markets

Abstract

This paper incorporates conditional heteroscedasticity properties in the long memory model and applies the model on squared returns of BRICS (Brazil, Russia, India, China, and South Africa), UK and USA equity markets to capture the volatility of stock return. The conditional first-and second-order moments are provided.The CLS, FGLS and QML are discussed and 2SQML estimator is proposed. The simulation study suggests that the proposed 2SQML estimator performs better than the other three estimators. Both in simulation and empirical studies, we find that the proposed model FIMACH outperforms FIGARCH in terms of eliminating serial correlations.

Equity Market Contagion in Return Volatility during Euro Zone and Global Financial Crises: Evidence from FIMACH Model

“…Total observations in the main dataset stand at 4227. The squared stock index return is used as a volatility measure of stock indices (Quoreshi and Mollah 2019). We use the terms level series or volatility of stock indexes to refer the squared stock index return series.…”

“…The parameters Granger and Joyeux (1980) propose that the d j may be approximated by A j −d , for j ≥ 1. Quoreshi and Mollah (2019) assume that the u t is an independent and identically distributed (i.i.d.) sequence of random variables.…”

“…The FIMACH model is developed to capture long memory property in squared return for stock index data. In this paper, in line with Quoreshi and Mollah (2019), we use the squared returns of the stock index as a volatility measure. Moreover, Quoreshi and Mollah (2019) show that FIMACH performs better than FIGARCH and GARCH models in terms of removing serial correlations.…”

“…In this paper, in line with Quoreshi and Mollah (2019), we use the squared returns of the stock index as a volatility measure. Moreover, Quoreshi and Mollah (2019) show that FIMACH performs better than FIGARCH and GARCH models in terms of removing serial correlations. In this paper, we intend to study the contagion effect between squared return of stock indexes.…”

“…Hence, the choice of a long memory model is obvious in estimating squared index return series. Quoreshi and Mollah (2019) develop a long memory model incorporating conditional heteroscedasticity properties and subsequently apply the model for the squared returns of stock indices using data from BRICS countries, UK and US markets. The model is called fractionally integrated moving average conditional heteroskedasticity (FIMACH).…”