Stationary persistent time series misspecified as nonstationary arima. (English) Zbl 0858.62085
Summary: 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. We discuss three prototypical misspecification cases and derive the corresponding increase in mean square forecasting error for different lead times.
MSC:
| 62M20 | Inference from stochastic processes and prediction |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
Keywords:
long-memory models; overdifferencing; nonstationary ARFIMA processes; autoregressive fractionally integrated moving-average processes; misspecification errors; fractional degree of integration; mean square forecasting errorReferences:
| [1] | Box, G. E.P.; Jenkins, G. M.; Reinsel, G. C., Time Series Analysis: Forecasting and Control (1994), Englewood Cliffs: Prentice Hall, Englewood Cliffs · Zbl 0858.62072 |
| [2] | Brockwell, Peter J.; Davis, Richard A., Time Series: Theory and Methods (1991), New York: Springer-Verlag, New York · Zbl 0709.62080 |
| [3] | Diebold, Francis X.; Rudebush, Glenn D., On the power of Dickey-Fuller tests against fractional alternatives, Economic Letters, 35, 155-160 (1991) · doi:10.1016/0165-1765(91)90163-F |
| [4] | Hassler, U., (Mis)specification of long-memory in seasonal time series, Journal of Time Series Analysis, 15, 19-30 (1994) · Zbl 0794.62059 · doi:10.1111/j.1467-9892.1994.tb00174.x |
| [5] | Hassler, U.; Wolters, J., On the power of Dickey-Fuller tests against fractional alternatives, Economic Letters, 45, 1-5 (1994) · Zbl 0800.62532 · doi:10.1016/0165-1765(94)90049-3 |
| [6] | Mandelbrot, B. B., Statistical methodology for nonperiodic cycles: from the covariance to the R/S analysis, Annals of Economic and Social Measurement, 1, 259-290 (1972) |
| [7] | Pötscher, B. M., Effects of model selection on inference, Econometric Theory, 7, 163-185 (1991) · doi:10.1017/S0266466600004382 |
| [8] | Ray, B. K., Modeling long-memory processes for optimal long-range prediction, Journal of Time Series Analysis, 14, 511-525 (1993) · Zbl 0779.62088 · doi:10.1111/j.1467-9892.1993.tb00161.x |
| [9] | Sowell, F., The fractional unit root distribution, Econometrica, 58, 495-505 (1990) · Zbl 0727.62025 · doi:10.2307/2938213 |
| [10] | Yajima, Y.; Brillinger, D., Asymptotic properties of estimates in incorrect ARMA models for long-memory time series, New Directions in Time series Analysis, Part II, 375-382 (1989), New York: Springer-Verlag, New York · Zbl 0767.62075 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
