We give the theoretical basis of a possible explanation for two stylized facts observed in long log-return series: the long-range dependence (LRD) in volatility and the integrated GARCH (IGARCH). Both these effects can be explained theoretically if one assumes that the data are nonstationary. ©...

Our study supports the hypothesis of global non-stationarity of the return time series. We bring forth both theoretical and empirical evidence that the long range dependence (LRD) type behavior of the sample ACF and the periodogram of absolute return series and the IGARCH effect documented in...

In this paper we propose a goodness of fit test that checks the resemblance of the spectral density of a GARCH process to that of the log-returns. The asymptotic behavior of the test statistics are given by a functional central limit theorem for the integrated periodogram of the data. A...

Our study supports the hypothesis of global non-stationarity of the return time series. We bring forth both theoretical and empirical evidence that the long range dependence (LRD) type behavior of the sample ACF and the periodogram of absolute return series and the IGARCH effect documented in...

Estimators of regression coefficients are known to be asymptotically normally distributed, provided certain regularity conditions are satisfied. In small samples and if the noise is not normally distributed, this can be a poor guide to the quality of the estimators. The paper addresses this...

We get a criterion for the strong law of large numbers for ruled sums of i.i.d. random variables indexed by finite sets. As applications we obtain strong laws of large numbers for rectangular sums of independent random variables.

In the time series literature one can often find the claim that the periodogram ordinates of an iid sequence at the Fourier frequencies behave like an iid standard exponential sequence. We review some results about functions of these periodogram ordinates, including the convergence of extremes,...