This paper studies the self-weighted least squares estimator (SWLSE) of the ARMA model with GARCH noises. It is shown that the SWLSE is consistent and asymptotically normal when the GARCH noise does not have a finite fourth moment. Using the residuals from the estimated ARMA model, it is shown...

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,...

This study examines the reaction of four major equity markets of the world to the US equity market fear index, i.e., the Chicago Board of Trade Volatility Index (VIX). The VIX is designed to perform as a leading indicator of the volatility in equity markets. Our paper examines the daily data for...

The inhomogeneity of the cross-sectional distribution of realized assets' volatility is explored and used to build a novel class of GARCH (Generalized Autoregressive Conditional Heteroskedasticity) models. The inhomogeneity of the cross-sectional distribution of realized volatility is captured...

The statistical analysis of financial time series is a rich and diversified research field whose inherent complexity requires an interdisciplinary approach, gathering together several disciplines, such as statistics, economics, and computational sciences. This special issue of the Journal of...

This paper attempted to calculate the market risk in the Tehran Stock Exchange by estimating the Conditional Value at Risk. Since the Conditional Value at Risk is a tail-related measure, Extreme Value Theory has been utilized to estimate the risk more accurately. Generalized Autoregressive...

Sequential Monte Carlo (SMC) methods are widely used for non-linear filtering purposes. However, the SMC scope encompasses wider applications such as estimating static model parameters so much that it is becoming a serious alternative to Markov-Chain Monte-Carlo (MCMC) methods. Not only do SMC...

In this paper, we study the asymptotic behavior of the sequential empirical process and the sequential empirical copula process, both constructed from residuals of multivariate stochastic volatility models. Applications for the detection of structural changes and specification tests of the...

In this paper we extend the traditional GARCH(1,1) model by including a functional trend term in the conditional volatility of a time series. We derive the main properties of the model and apply it to all agricultural commodities in the Mexican CPI basket, as well as to the international prices...