On highly skewed fractional log‐stable noise sequences and their application

Abstract

Considering log‐LFSN (log‐linear fractional stable noise) sequences , driven by non‐Gaussian one‐sided LFSN with constant skewness intensity , for any and , we show that the auto‐covariance function (ACVF) exists if and only if is persistent, with stability index , Hurst exponent and extreme skewness (if ) or (if ). Within that range of existence, and in short, we calculate explicitly and establish persistence of too, by showing asymptotic proportionality of , as . We discuss explicit links of to a generalized co‐difference function of the driving one‐sided LFSN , and to the ACVF's of fractional Gaussian noise (FGN) and log‐FGN. The results are numerically demonstrated via ensemble simulation of synthetic time series generated by the considered log‐LFSN model fitted to time series of spatio‐temporal accumulations of rain rate data.