Let Xt be a moving average process defined by Xt=[summation operator]k=0[infinity][psi]k[var epsilon]t-k, t=1,2,... , where the innovation {[var epsilon]k} is a centered sequence of random variables and {[psi]k} is a sequence of real numbers. Under conditions on {[psi]k} which entail that {Xt}...

We propose a simple method of constructing quasi-likelihood functions for dependent data based on conditional-mean–variance relationships, and apply the method to estimating the fractal dimension from box-counting data. Simulation studies were carried out to compare this method with the...

Comparison of treatment effects in an experiment is usually done through analysis of variance under the assumption that the errors are normally and independently distributed with zero mean and constant variance. The traditional approach in dealing with non-constant variance is to apply a...

The estimation of the variance function of a linear regression model used in the asymptotic quasi-likelihood approach is considered. It is shown that the variance function used in the determination of the asymptotic quasi-likelihood estimates encompasses the variance functions commonly found in...

This paper is concerned with R/S analysis given a fractional ARIMA(p,d,q) model with finite variance where the aim is to estimate the intensity of long-range dependence of the particular series. This is done through what is commonly referred to as the Hurst parameter (denoted by H). H is a...

One of the tasks in studies of stochastic regression models or multiparameter statistic inference problems is to find sufficient conditions for the strong law of large numbers for multivariate martingales with random norming. For that purpose, we give a weaker sufficient condition for the random...

This paper studies a nonlinear cointegrating regression model with nonlinear nonstationary heteroskedastic error processes. We establish uniform consistency for the conventional kernel estimate of the unknown regression function and develop atwo-stage approach for the estimation of the...