This paper shows how a simple univariate stationary nonlinear process has an autocorrelation function suggesting that the underlying process has a long memory, although that is not the case. The conclusion is that just considering linear properties of a process may be misleading.

Nonnegativety constraints on the parameters of the GARCH (p, Q) model may be relaxed without giving up the requirement of the conditional variance remaining non- negative with probability one. This paper looks into the consequences of adopting these less severe constraints in the GARCH (2,2)...

In this paper, a necessary and sufficient condition for the existence of the unconditional fourth moment of the GARCH (p, q) process is given as well as an expression for the moment itself. Furthermore, the autocorrelation function of the centred and squared observations of this process is...

This paper contains a forecasting exercise on 30 time series, ranging on several fields, from economy to ecology. The statistical approach to artificial neural networks modelling developed by the author is compared to linear modelling and to other three well-known neural network modelling...

Smooth transition autoregressive models are a flixible family of nonlinear time series models that have also been used for modelling economic data. This paper contributes to the evaluation stage of a proposed specification, estimation, and evaluation cycle of this models by introducing a...

Properties of three well-known and frequently applied first-order models for modelling and forecasting volatility in financial series such as stock and exchange rate returns are considered. These are the standard Generalized Autoregressive Conditional Heteroskedasticity (GARCH), the Exponential...

In two recent papers, Granger and Ding (1995a, b) considered long return series that are first differences of logarithmed price series or price indices. They established a set of temporal and distributional properties for such series and suggested that the returns are well characterized by the...

This paper examines the power properties of several linearity tests applied in time series analysis. The tests are the ones Lee et al. (1993) used in their Monte Carlo study. The main tool used for power comparisons in this paper is the Pitman asymptotic relative efficiency. The results...

Over recent years, several nonlinear time series models have been proposed in the literature. One model that has found a large number of successful applications is the threshold autoregressive model (TAR). The TAR model is a piecewise linear process whose central idea is to change the parameters...

The constant conditional correlation GARCH model is probably the most frequently applied multivariate GARCH model. In this paper we consider an extension to this model and examine its fourth-moment structure. The extension, first considered by Jeantheau (1998), is motivated by the result found...