In this paper we introduce a new class of covariance stationary long-memory models on the positive half-line. The overall structure of the models is related to that of GARCH processes of Engle (1982) and Bollerslev (1986), whereby sequence of random variables of interest have multiplicative...

This paper investigates the issue of temporal ordering of the range-based volatility and volume in the Indian stock market for the period 1995-2007. We examine the dynamics of the two variables and their respective uncertainties using a bivariate dual long-memory model. We distinguish between...

Mathematical programs with equilibrium (or complementarity) constraints, MPECs for short, form a difficult class of optimization problems. The feasible set of MPECs is described by standard equality and inequality constraints as well as additional complementarity constraints that are used to...

The study aimed at determining a set of superior generalized orthogonal-GARCH (GO-GARCH) models for forecasting time-varying conditional correlations and variances of five foreign exchange rates vis-à-vis the Nigerian Naira. Daily data covering the period 02/01/2009 to 19/03/2015 was used, and...

We use a discrete time analysis, giving necessary and sufficient conditions for the almost sure convergence of ARCH(1) and GARCH(1,1) discrete time models, to suggest an extension of the (G)ARCH concept to continuous time processes. Our COGARCH (continuous time GARCH) model, based on a single...

We use a discrete time analysis, giver necessary and sufficient conditions for the almost sure convergence of ARCH(1) and GARCH(1,1) discrete time models, to suggest an extension of the (G)ARCH concept to continuous time processes. The models, based on a single background driving Lévy process,...

The recent paper by Ling and Tong (2005) considered a quasi-likelihood ratio test for the threshold in moving average models with errors. This article generalizes their results to the case with GARCH errors, and a new quasi-likelihood ratio test is derived. The generalization is not direct since...