The goal of this paper is to search for conclusive evidence against the stationarity of the global air surface temperature, which is one of the most important indicators of climate change. For this purpose, possible long-range dependencies are investigated in the frequency-domain. Since...

For typical sample sizes occurring in economic and financial applications, the squared bias of estimators for the memory parameter is small relative to the variance. Smoothing is therefore a suitable way to improve the performance in terms of the mean squared error. However, in an analysis of...

In this paper, it is proposed to modify autoregressive fractionally integrated moving average (ARFIMA) processes by introducing an additional parameter to comply with the criticism of Hauser et al . (1999) that ARFIMA processes are not appropriate for the estimation of persistence, because of...

This paper is concerned with subjecting two popular assumptions about the behavior of stock market prices to empirical tests: first, the random walk hypothesis developed by Bachelier (1900), Osborne (1959), and Mandelbrot (1963); second, the stable distributions hypothesis by Mandelbrot (1963)...

Based on a reparametrization of the Gaussian density and a natural prior for the parameters, a Bayesian model selection criterion is derived, which differs from Schwarz' (1978) criterion by a term which does not vanish as the sample size increases.

It is shown that in the linear normal regression model asymptotically the expected value of the penalty term implied by the Akaike-BIC can, under certain circumstances, be smaller than that implied by the AIC. Consequences for consistency are discussed.