PARAMETER ESTIMATION AND SPECTRUM OF FRACTIONAL ARIMA PROCESS

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...

Estimation of The Long-Range Dependence Parameter of Fractional Arima Processes

The most well-known models of long-range dependent processes are fractional Gaussian noise [7] (thus secondorder self-similarity) and fractional ARIMA [3, 4]. Each of these models has a corresponding long-range dependence parameter. Since the value of the parameter indicates the intensity of this dependence structure, it is important to have a better tool to estimate it. Such an estimator shoul...

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...

Fractional ARIMA Processes and Its

Power spectrum parameter estimation

The power spectrum of a zero-mean stationary Gaussian random process is assumed to be known except for one or more parameters which are to be estimated from an observation of the process during a finite time interval. The approximation is introduced that the coefficients of the Fourier series expansion of a realization of long-time duration are uncorrelated. Based on this approximation maximum ...