Abstract
Long-memory processes, such as Autoregressive Fractionally Integrated Moving-Average processes—ARFIMA—are likely to lead the observer to make serious misspecification errors. Nonstationary ARFIMA processes can easily be misspecified as ARIMA models, thus confusing a fractional degree of integration with an integer one. Stationary persistent ARFIMA processes can be misspecified as nonstationary ARIMA models, thus leading to a serious increase of out-of-sample forecast errors. In this paper, we discuss three prototypical misspecification cases and derive the corresponding increase in mean square forecasting error for different lead times.
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References
Box, G.E.P., Jenkins, G.M., and Reinsel, G.C. (1994)Time Series Analysis: Forecasting and Control (Prentice Hall, Englewood Cliffs, 3rd ed.).
Brockwell, Peter J. and Davis, Richard A. (1991)Time Series: Theory and Methods, 2nd ed. Springer-Verlag, New York.
Diebold, Francis X. and Rudebush, Glenn D. (1991) On the power of Dickey-Fuller tests against fractional alternatives,Economic Letters 35: 155–160.
Hassler, U. (1994) (Mis)specification of long-memory in seasonal time series,Journal of Time Series Analysis,15: 19–30.
Hassler, U. and Wolters, J. (1994) On the power of Dickey-Fuller tests against fractional alternatives,Economic Letters 45: 1–5.
Mandelbrot, B. B. (1972) Statistical methodology for nonperiodic cycles: from the covariance to the R/S analysis.Annals of Economic and Social Measurement 1: 259–290.
Pötscher, B.M. (1991) Effects of model selection on inference.Econometric Theory 7: 163–185.
Ray, B.K. (1993) Modeling long-memory processes for optimal long-range prediction.Journal of Time Series Analysis 14: 511–525.
Sowell, F. (1990) The fractional unit root distribution.Econometrica 58: 495–505
Yajima, Y. (1989) Asymptotic properties of estimates in incorrect ARMA models for long-memory time series, in: D. Brillingeret al., eds,New Directions in Time series Analysis, Part II. Springer-Verlag, New York: 375–382.
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We thank an anonymous referee for various comments which led to improvements of this paper.
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Crato, N., Taylor, H.M. Stationary persistent time series misspecified as nonstationary arima. Statistical Papers 37, 215–223 (1996). https://doi.org/10.1007/BF02926584
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DOI: https://doi.org/10.1007/BF02926584