Abstract
In this paper, Autoregressive Fractionally Integrated Moving Average (ARFIMA) model was modified and was used for modeling the daily Malaysia Stock Price Index (MSPI). The long and slow decline in autocorrelation function of the data showed the presence of Long Memory (LM) structure. Therefore, the Mandelbrot and Lo rescaled-range tests were used to test the presence of LM. The ARFIMA model then is further extend to the Autoregressive Fractionally Unit Root Integrated Moving Average (ARFURIMA) model. The Geweke and Porter-Hudak (GPH), Local Whittle Estimator (LWE), and Hurst Exponent (HE) were used as the estimation methods to obtain the LM parameters d of both ARFIMA and ARFURIMA models. The best model was identified for each of ARFIMA and ARFURIMA models respectively based on the minimum Akaike Information Criteria (AIC) values. The best fitted model were specified as ARFIMA (2,0.989,0) and ARFURIMA (1,1.069,0). Having compared the residuals analysis of the two models, we conclude that the ARFURIMA model was better in estimating series that exhibit Interminable LM (ILM).
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References
Box, G.C., Jenkins, G.E.P., Reinsel, G.M.: Time Series Analysis: Forecasting and Control, 4th edn. Wiley, Hoboken, NJ (2008)
Charfeddine, L., Guégan, D.: Breaks or long memory behaviour: an empirical investigation. Phys. A 391(22), 5712–5726 (2012). https://doi.org/10.1016/j.physa.2012.06.036
 Qu, Z.: A test against spurious long memory a test against spurious long memory. J. Bus. Econ. Stat. 29(3), 423–438 (2011). https://doi.org/10.11981/jbes.2010.09153
Hurst, E.: Long-term storage capacity of reservoirs. Trans. Am. Soc. Civ. Eng. 116, 770–799 (1951)
Whittle, B.Y.P.: On the variation of yield variance with plot size. Biometrika 43(3), 337–343 (1956). 202.170.60.251
Mandelbrot, B.B.: Statistical methodology for non-periodic cycles: from the covariance to R/S analysis, vol. 1, pp. 259–290 (1972). http://www.nber.org/chapters/c9433.pdf
Mcleaod, A.I., Hipel, K.W.: Preservation of the rescaled adjusted range I: a reassessment of the Hurst phenomenon. Water Resour. Res. 14, 491–508 (1978). https://doi.org/10.1029/wr014i003p00491
Lo, A.W.: Long-term memory in stock market prices. Econometrica 59, 1279–1313 (1991). https://doi.org/10.2307/2938368
Geweke, J., Porter-Hudak, S.: The estimation and application of long memory time series models. J. Time Ser. Anal. 4(4), 221–238 (1983). https://doi.org/10.18488/journal.8/2016.4.3/8.3.142.152
Shimotsu, K., Phillips, P.C.B.: Local Whittle estimation of fractional integration. Ann. Stat. 33, 1890–1933 (2005). https://doi.org/10.1214/009053605000000309
Nezhad, M.Z., Raoofi, A., Akbarzdeh, M.H.: The existence of long memory property in OPEC oil prices. Asian J. Econ. Model. 4(3), 142–152 (2016). https://doi.org/10.18488/journal.8/2016.4.3/8.3.142.152
Jibrin, S.A., Musa, Y., Zubair, U.A., Saidu, A.S.: ARFIMA modelling and investigation of structural break(s) in West Texas Inter-mediate and Brent series. CBN J. Appl. Stat. 6(2), 59–79 (2015). http://www.econstor.eu/handle/10419/142106
Charfeddine, L., Ajmi, A.N.: The Tunisian stock market index volatility: long memory vs. switching regime. Emerg. Mark. Rev. 16, 170–182 (2013). https://doi.org/10.1016/j.ememar.2013.05.003
Arouri, M.E.H., Hammoudeh, S., Lahiani, A., Nguyen, D.K.: Long memory and structural breaks in modeling the return and volatility dynamics of precious metals. The Qur. Rev. Econ. Financ. 52(2), 207–218 (2012). http://dx.doi.org/10.1016/j.qref.2012.04.004
Jibrin, S.A.: Data Mining and Modeling of Crude Oil Prices. M.Sc Diss. (2015). http://scholar.google.com/scholar?cluster=117008-92651303445542&hl
Baillie, R.T., Kapetanios, G., Papailias, F.: Bandwidth selection by cross-validation for forecasting long memory financial time series. J. Empir. Financ. 29, 129–143 (2014). http://doi.org/10.1016/j.jempfin.2014.04.002
Dalla, V.: Power transformations of absolute returns and long memory estimation. J. Empir. Financ. 33, 1–18 (2015). https://doi.org/10.1016/j/jempfin.2015.05.002
Granger, C., Joyeux, R.: An introduction to long memory time series models and fractional differencing. J. Time Ser. Anal. 1(1), 15–29 (1980)
Box, G., Jenkins, G.: Time series analysis: forecasting and control, revised edn. Holden-Day (1976)
Hosking, J.R.M.: Fractional differencing. Biometrika Trust. 68(1), 165–176 (1981). https://doi.org/10.1093/biomet/68.1.165
Laurent, S., Doornik, J.A.: G@RCH 7.0: OxMetrics Package for testing LM, Estimating and Forecasting ARFIMA models (2012)
Cottrell, A., Lucchetti, R.: Gretl Function Package Guide, gretl documentation (2016). http://sourceforge.net/projects/gretl/files/manual/
Francq, C., Zakoian, J.M.: Bartlett’s formula for a general class of nonlinear processes. J. Time Ser. Anal. 30, 449–465 (2009)
Jarque, C.M., Bera, A.K.: A test for normality of observations and regression residuals. Int. Stat. Rev. 55(2), 163–172 (1987)
Engle, R.F.: Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50(4), 987–1007 (1982)
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Rahman, R.A., Jibrin, S.A. (2019). A Modified Long Memory Model for Modeling Interminable Long Memory Process. In: Kor, LK., Ahmad, AR., Idrus, Z., Mansor, K. (eds) Proceedings of the Third International Conference on Computing, Mathematics and Statistics (iCMS2017). Springer, Singapore. https://doi.org/10.1007/978-981-13-7279-7_29
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