We derive a weighted least squares approximate restricted likelihood estimator for a k-dimensional pth-order autoregressive model with intercept. Exact likelihood optimization of this model is generally infeasible due to the parameter space, which is complicated and high-dimensional, involving...

Let X1,X2,...,Xn be a sample from a stationary Gaussian time series and let I(·) be the sample periodogram. Some researchers have either proved heuristically or claimed that under general conditions, the asymptotic behaviour of is equivalent to that of the discrete version of the integral...

The restricted likelihood has been found to provide a well-behaved likelihood ratio test in the predictive regression model even when the regressor variable exhibits almost unit root behavior. Using the weighted least squares approximation to the restricted likelihood obtained in Chen and Deo,...

Restricted maximum likelihood (REML) estimation has recently been shown to provide less biased estimates in autoregressive series. A simple weighted least squares approximate REML procedure has been developed that is particularly useful for vector autoregressive processes. Here, we compare the...