Can one use the Durbin-Levinson algorithm to generate infinite variance fractional ARIMA time series? (Q2740038)

Long-range dependence in a finite variance stationary time series occurs when the correlations decrease slowly to zero at large lags like a power function. The fractional ARIMA (FARIMA) linear sequences are often used to model long-range dependence. The FARIMA sequences are linear transformations with i.i.d. innovations. Such time series offer great versatility because they capture not only the short- and long-range dependence structures, but also extreme departures from Gaussianity. The difficulty is that there is no efficient way to simulate them.NEWLINENEWLINENEWLINEThe goal of this paper is to investigate whether one may continue to use the fast Durbin-Levinson algorithm [\textit{P.J. Brockwell} and \textit{R.A. Davis}, Time series: theory and methods. 2nd ed. (1991; Zbl 0709.62080)]. This algorithm is used to generate Gaussian time series with a given covariance structure. This is the most efficient way to simulate Gaussian FARIMA time series, linear sequences with i.i.d. Gaussian innovations which exhibit long-range dependence. This paper studies the applicability of the Durbin-Levinson algorithm to simulations of infinite variance FARIMA sequences including \(\alpha\)-stable FARIMA.