Authors:
Saad Kazem Hamza,Shareen Ali Hussein,DOI NO:
https://doi.org/10.26782/jmcms.2020.08.00014Keywords:
ARFIMA (p,d,q) models,long term memory,smoothed periodogram method,air pollution,spectrum function,Abstract
This paper exploring the stability to be achieved in the stochastic processes and operations which are called the autoregressive moving average and symbolized by ARMA Model(the roots of the equation should be out of this model circle. Although these models are not stable and become stable after so many conversions and differences. These new models called the autoregressive methods for integrated moving average which is symbolized ARFIMA (p, d, q) and these differences would be integers or fractional numbers. It is worth to be mentioned that the time series which depending on the long term (long memory) so this stability achieved by snapping the fractional differences which are located within the enclosed period (-0.5, 0.5) and are referred shortly ((ARFIMA (p,d,q))). Models which are located within the enclosed period (-0.5, 0.5). This search aims to estimate the parameter of fractional differences (d), three ways by using real data from the Ministry of Environment that include the rates of air pollution in Baghdad City with Nitrogen oxides(NO²), Ozone(Oᶟ) materials…these ways are: firstly, the way logarithm periodogram chart regression method which is called (Geweke and Porter- Hudak), symbolized (GPH) Secondly, smoothed periodogram regression. Thirdly, the way that called (KASHYAP AND EOM) and it has been used the standard error squares and standard error (SD) as two scale standards among these three ways to estimate the parameter. Akaike standard has been used for choosing the best model of linear models assumed.In this study, we will be dealt with the fractional differencesRefference:
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