Interminable Long Memory Model And Its Hybrid For Time Series Modeling
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Date
2019-08
Authors
Alhaji, Jibrin Sanusi
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
The financial and economic indices are nonstationary, long-range dependence and volatile. These are very serious problems because each affect the accuracy, validity and reliability of model fitting and the forecasting of the studied series. In view of this, our current study proposes fractional filter to decompose the nonstationary and Interminable Long Memory (ILM) time series with fractional differencing value in the interval of 1<𝑑<2 into a white noise process. First, the ILM model, named Auto Regressive Fractional Unit Root Integral Moving Average (ARFURIMA) is developed. Next, each of the basic and asymptotic properties of the proposed ARFURIMA and its fractional filter were derived respectively. This follows by proposing the fractional differenced return filter and developing the ARFURIMA-GARCH model, where the GARCH component will adequately capture the volatility in the series. Consequently, the arfurima and arfurimafdrgarch packages in R were developed to run the proposed fractional filters, and to fit the ARFURIMA and ARFURIMA-GARCH models developed. The proposed filter (a fractional filter which can also be called a ILM filter) is compared with both the first differenced filter for ARIMA (which is not a fractional filter) and two fractional filters in ARFIMA and ARTFIMA models. Results found that the proposed fractional filter is better both in terms of minimum measures of variability and AIC values. The ARFURIMA models are compared with the ARIMA, ARFIMA and ARTFIMA models by fitting to ten different financial and economic index.
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Keywords
Interminable Long Memory , Time Series Modeling