This paper investigates if component GARCH models introduced by Engle and Lee (1999) and Ding and Granger (1996) can capture the long-range dependence observed in measures of time-series volatility. Long-range dependence is assessed through the sample autocorrelations, two popular semiparametric estimators of the long-memory parameter, and the parametric fractionally integrated GARCH (FIGARCH) ...

Abstract The Standard Generalised Autoregressive Conditionally Heteroskedastic (sGARCH) model and the Functional (fGARCH) were applied to study volatility of Fractionally Integrated Moving Average (ARFIMA) model, which is primary objective this study. other goal paper expand on researchers’ previous work by examining long memory volatilities simultaneously, using ARFIMA-sGARCH hybrid comparing ...

The present study models the risk of investment in the petrochemical industry considering the impacts of exchange rate (US dollar to Iran's Rial) movements using the time series data from November 2008 to March 2019 and ARFIMA-FIGARCH framework. The empirical results prove the existence of the Fractal Market Hypothesis, FMH, and the Long Memory property in both the risk and return of the petroc...

This paper develops a bivariate Markov Switching FIGARCH (MS-FIGARCH) process with constant and time varying transition probabilities as a way of modeling spot futures dynamics. An application of the model illustrates that the S&P500 and its futures exhibit long memory in volatility and structural breaks that are driven by changes in the cost of carry. The model with constant transition probabi...

This paper proposes an easy test for independence between two stationary autoregressive fractionally integrated moving average (ARFIMA) processes via AR approximations. We prove that an ARFIMA (p, d, q) process, φ(L)(1 − L)yt = θ(L)et, d ∈ (0, 0.5), where et is a white noise, can be approximated well by an autoregressive (AR) model and establish the theoretical foundation of Haugh’s (1976) stat...

We analyze the S&P 500 index data for the 13-year period, from January 1, 1984 to December 31, 1996, with one data point every 10 min. For this database, we study the distribution and clustering of volatility return intervals, which are defined as the time intervals between successive volatilities above a certain threshold q. We find that the long memory in the volatility leads to a clustering ...

Keywords: Bayesian model selection Reversible jump Markov chain Monte Carlo Autoregressive fractional integrated moving average models Long memory processes a b s t r a c t Various model selection criteria such as Akaike information criterion (AIC; Akaike, 1973), Bayesian information criterion (BIC; Akaike, 1979) and Hannan–Quinn criterion (HQC; Hannan, 1980) are used for model specification in...

Aims: To model the concentration variation of PM2.5 and PM10 in selected locations Delhi.
 Study Design: ARFIMA-GARCH model.
 Place Duration Study: The study was conducted by using daily (24 hour interval) data from three air quality monitoring stations Delhi namely, Narela, Okhla Phase II Pusa.
 Methodology: ARFIMA is applied as mean GARCH variance Results: series are stationary...