Identification and validation of stable ARFIMA processes with application to UMTS data

In this paper we present an identification and validation scheme for stable autoregressive fractionally integrated moving average (ARFIMA) time series. The identification part relies on a recently introduced estimator which is a generalization of that of Kokoszka and Taqqu and a new fractional differencing algorithm. It also incorporates a low-variance estimator for the memory parameter based on the sample mean-squared displacement. The validation part includes standard noise diagnostics and backtesting procedure. The scheme is illustrated on Universal Mobile Telecommunications System (UMTS) data collected in an urban area. We show that the stochastic component of the data can be modeled by the long memory ARFIMA. This can help to monitor possible hazards related to the electromagnetic radiation.