OJS  Vol.5 No.1 , February 2015
Forecasting High-Frequency Long Memory Series with Long Periods Using the SARFIMA Model
Abstract: This paper evaluates the efficiency of the SARFIMA model at forecasting high-frequency long memory series with especially long periods. Three other models, the ARFIMA, ARMA and PAR models, are also included to compare their forecasting performances with that of the SARFIMA model. For the artificial SARFIMA series, if the correct parameters are used for estimating and forecasting, the model performs as well as the other three models. However, if the parameters obtained by the WHI estimation are used, the performance of the SARFIMA model falls far behind that of the other models. For the empirical intraday volume series, the SARFIMA model produces the worst performance of all of the models, and the ARFIMA model performs best. The ARMA and PAR models perform very well both for the artificial series and for the intraday volume series. This result indicates that short memory models are competent in forecasting periodic long memory series.
Cite this paper: Li, H. and Ye, X. (2015) Forecasting High-Frequency Long Memory Series with Long Periods Using the SARFIMA Model. Open Journal of Statistics, 5, 66-74. doi: 10.4236/ojs.2015.51009.

[1]   Engle, R. (2005) Handbook of Financial Econometrics. North Holland, Amsterdam.

[2]   Granger, C.W.J. and Joyeux, R. (1980) An Introduction to Long-Memory Time Series Models and Fractional Differencing. Journal of Time Series Analysis, 1, 15-29.

[3]   Hosking, J.R.M. (1981) Fractional Differencing. Biometrika, 68, 165-176.

[4]   Franses, P.H. and Ooms, M. (1997) A Periodic Long-Memory Model for Quarterly UK Inflation. International Journal of Forecasting, 13, 117-126.

[5]   Porter-Hudak, S. (1990) An Application of the Seasonal Fractionally Differenced Model to the Monetary Aggregates. American Statistical Association, 85, 338-344.

[6]   Ooms, M. and Franses, P.H. (2001) A Seasonal Periodic Long Memory Model for Monthly River Flows. Environmental Modeling & Software, 16, 559-569.

[7]   Nasr, A.B. and Trabelsi, A. (2005) Seasonal and Periodic Long Memory Models in the Inflation Rates. European Financial Management Association 2005 Annual Meetings, 31.

[8]   Sowell, F. (1992) Maximum Likelihood Estimation of Stationary Univariate Fractionally Integrated Time Series Models. Journal of Econometrics, 53, 165-188.

[9]   Whittle, P. (1953) Estimation and Information in Stationary Time Series. Arkiv för Matematik, 2, 423-434.

[10]   Doornik, J.A. and Ooms, M. (2004) Inference and Forecasting for ARFIMA Models, with an Application to US and UK Inflation. Studies in Nonlinear Dynamics and Econometrics, 8, 1218.

[11]   Reisen, V.A., Rodrigues, A.L. and Palma, W. (2006) Estimation of Seasonal Fractionally Integrated Processes. Computational Statistics & Data Analysis, 50, 568-582.

[12]   Bisognin, C. and Lopes, S.R.C. (2007) Estimating and Forecasting the Long-Memory Parameter in the Presence of Periodicity. Journal of Forecasting, 26, 405-427.

[13]   Geweke, J. and Porter-Hudak, S. (1983) The Estimation and Application of Long Memory Time Series Models. Journal of Time Series Analysis, 4, 221-238.

[14]   Robinson, P.M. (1995) Log Periodogram Regression of Time Series with Long Range Dependence. Annals of Statistics, 23, 1048-1072.