Abstract
This paper considers a flexible class of time series models generated by Gegenbauer polynomials incorporating the long memory in stochastic volatility (SV) components in order to develop the General Long Memory SV (GLMSV) model. We examine the corresponding statistical properties of this model, discuss the spectral likelihood estimation and investigate the finite sample properties via Monte Carlo experiments. We provide empirical evidence by applying the GLMSV model to three exchange rate return series and conjecture that the results of out-of-sample forecasts adequately confirm the use of GLMSV model in certain financial applications.
Highlights
IntroductionIn the light of this evidence, Breidt et al (1998) developed the long memory Stochastic Volatility (SV) (LMSV) model, in which log-volatility follows the ARFIMA(p, d, q) process
Consider the well known ARFIMA(p, d, q) model given by: φ(B)Yt = θ(B) t, (1)where Yt = (1 − B)dXt, d ∈ (−1, 0.5), { t} is a sequence of uncorrelated random variables such that Var( t) = σ2, and φ(B) and θ(B) are stationary AR(p) and invertible MA(q) polynomials, respectively.In recent years, there has been a great deal of developments with time dependent instantaneous innovation variances related in modeling financial volatility
We show the empirical results for the General Long Memory SV (GLMSV) models as compared with those of the GIEGARCH model
Summary
In the light of this evidence, Breidt et al (1998) developed the long memory SV (LMSV) model, in which log-volatility follows the ARFIMA(p, d, q) process. In the general case of (5), the corresponding stationary and invertible solutions can be obtained from: Xt = ψ(L) × ψ (L)vt, and vt = [ψ (L)]−1 × (1 − 2ηL + L2)dXt, respectively, where ψ (L) = [φ(L)]−1θ(L) (see Dissanayake et al (2016) for further details).
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