In this paper we study the distributional tail behavior of the solution to a linear stochastic differential equation driven by infinite variance [alpha]-stable Lévy motion. We show that the solution is regularly varying with index [alpha]. An important step in the proof is the study of...

The squares of a GARCH(p,q) process satisfy an ARMA equation with white noise innovations and parameters which are derived from the GARCH model. Moreover, the noise sequence of this ARMA process constitutes a strongly mixing stationary process with geometric rate. These properties suggest to...

Consider a data network model in which sources begin to transmit at renewal time points {Sn}. Transmissions proceed for random durations of time {Tn} and transmissions are assumed to proceed at fixed rate unity. We study M(t), the number of active sources at time t, a process we term the...

We study Poisson limits for U-statistics with non-negative kernels. The limit theory is derived from the Poisson convergence of suitable point processes of U-statistics structure. We apply these results to derive infinite variance stable limits for U-statistics with a regularly varying kernel...

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 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 theoretically explained if one assumes that the data is...

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...