Fractional ARIMA with stable innovations

A characterization of ARMA and Fractional ARIMA models with infinitely divisible innovations

The object of this paper is to study the asymptotic dependence structure of the linear time series models with infinitely divisible innovations by the use of their characteristic functions. Autoregressive moving-average (ARMA) models and fractional autoregressive integrated moving-average (FARIMA) models are analyzed. As examples of infinitely divisible innovations, the class of radially absolu...

Fractional ARIMA Processes and Its

Estimation of Fractional Arima Models for the Uk Unemployment

Financial support from ESRC grant number L116251013, Macroeconomic Modelling and Policy Analysis in a Changing Word is gratefully acknowledged. The usual disclaimer applies. Fractional integrated ARMA (ARFIMA) models are investigated in this article for different measures of the UK unemployment. The analysis is carried out using the Sowell (1992) procedure of estimating by maximum likelihood in...

Least squares detection of multiple changes in fractional ARIMA processes

We address the problem of estimating changes in fractional integrated ARMA (FARIMA) processes. These changes may be in the Long Range Dependence (LRD) parameter or the ARMA parameters. The signal is divided into “elementary” segments: the objective is then to estimate the segments in which the changes occur. This estimation is achieved by minimizing a penalized least-squares criterion based on ...

Parameter Estimation for In nite Variance Fractional ARIMA

Consider the fractional ARIMA time series with innovations that have innnite variance. This is a nite parameter model which exhibits both long-range dependence (long memory) and high variability. We prove the consistency of an estimator of the unknown parameters which is based on the periodogram and derive its asymptotic distribution. This shows that the results of Mikosch, Gadrich, Kl uppelber...