2012/01/19 by Sílvia R. C. Lopes, Taiane Schaedler Prass, Lopes, Sílvia R. C. +1
Economics, Econometrics and Finance · #60G10 #62G05 #62G35 #62M10 #62M15 #62M20 #Applications (stat.AP) #FOS: Computer and information sciences #FOS: Mathematics #Financial Risk and Volatility Modeling #Market Dynamics and Volatility #Monetary Policy and Economic Impact #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1201.4129
openalex publication_date 2012/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Here we present a theoretical study on the main properties of Fractionally Integrated Exponential Generalized Autoregressive Conditional Heteroskedastic (FIEGARCH) processes. We analyze the conditions for the existence, the invertibility, the stationarity and the ergodicity of these processes. We prove that, if \Xt\_t ∈ \mathdsZ is a FIEGARCH(p,d,q) process then, under mild conditions, \ln(Xt2)\_t∈\mathdsZ is an ARFIMA(q,d,0), that is, an autoregressive fractionally integrated moving average process. The convergence order for the polynomial coefficients that describes the volatility is presented and results related to the spectral representation and to the covariance structure of both processes \ln(Xt2)\_t∈\mathdsZ and ln(σt2)\_t∈\mathdsZ are also discussed. Expressions for the kurtosis and the asymmetry measures for any stationary FIEGARCH(p,d,q) process are also derived. The h-step ahead forecast for the processes \Xt\_t ∈ \mathdsZ, \ln(σt2)\_t∈\mathdsZ and \ln(Xt2)\_t∈\mathdsZ are given with their respective mean square error forecast. The work also presents a Monte Carlo simulation study showing how to generate, estimate and forecast based on six different FIEGARCH models. The forecasting performance of six models belonging to the class of autoregressive conditional heteroskedastic models (namely, ARCH-type models) and radial basis models is compared through an empirical application to Brazilian stock market exchange index.