We consider the estimation of the location of the pole and memory parameter, λ0 and α respectively, of covariance stationary linear processes whose spectral density function f(λ) satisfies f(λ) ∼ C|λ − λ0|−α in a neighbourhood of λ0. We define a consistent estimator of λ0 and...

Order selection based on criteria by Akaike (1974), AIC, Schwarz (1978), BIC or Hannan and Quinn (1979) HIC is often applied in empirical examples. They have been used in the context of order selection of weakly dependent ARMA models, AR models with unit or explosive roots and in the context of...

We frequently observe that one of the aims of time series analysts is to predict future values of the data. For weakly dependent data, when the model is known up to a finite set of parameters, its statistical properties are well documented and exhaustively examined. However, if the model was...

We show that it is possible to adapt to nonparametric disturbance autocorrelation in time series regression in the presence of long memory in both regressors and disturbances by using a smoothed nonparametric spectrum estimate in frequency-domain generalized least squares. When the collective...

For linear processes, semiparametric estimation of the memory parameter, based on the log-periodogram and local Whittle estimators, has been exhaustively examined and their properties are well established. However, except for some specific cases, little is known about the estimation of the...

We examine a test for the hypothesis of weak dependence against strong cyclical components. We show that the limiting distribution of the test is a Gumbel distribution, denoted G(·). However, since G(·) may be a poor approximation to the finite sample distribution, being the rate of the...