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...

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...

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 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...

This paper discusses nonparametric kernel regression with the regressor being a d-dimensional ß-null recurrent process in presence of conditional heteroscedasticity. We show that the mean function estimator is consistent with convergence rate p n(T)hd, where n(T) is the number of regenerations...

The estimation of inflation volatility is important to Central Banks as it guides their policy initiatives for achieving and maintaining price stability. This paper employs three models from the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) family with a view to providing a...