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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
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.
Author information
Authors and Affiliations
Additional information
We thank an anonymous referee for various comments which led to improvements of this paper.
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02926584