A study on the effect of power transformation in the ARMA\((p,q)\) model. (English) Zbl 0993.62081
Summary: In time series analysis, the Box-Cox power transformation is generally used for variance stabilization. We show that the order and the first step ahead forecast of the transformed model are approximately invariant to those of the original model under certain assumptions on the mean and variance. A small Monte Carlo simulation is performed to support the results.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62M20 | Inference from stochastic processes and prediction |
Software:
SAS/ETSReferences:
| [1] | ANDREWS P. E., The Data: A Collection of Problems from Statistics. (1985) |
| [2] | DOI: 10.2307/2287831 · Zbl 0464.62058 · doi:10.2307/2287831 |
| [3] | BOX G. E. P., Journal of the Royal Statistical Society 26 pp 211– (1964) |
| [4] | DOI: 10.1093/biomet/80.4.885 · Zbl 0799.62079 · doi:10.1093/biomet/80.4.885 |
| [5] | DOI: 10.1080/02664769922043 · Zbl 0940.62085 · doi:10.1080/02664769922043 |
| [6] | GRANGER C. W. J., Journal of the Royal Statistical Society 38 pp 189– (1976) |
| [7] | DOI: 10.2307/2988129 · doi:10.2307/2988129 |
| [8] | DOI: 10.1080/03610928508828918 · doi:10.1080/03610928508828918 |
| [9] | SAS/ETS User’s Guide, Version 6, (1993) |
| [10] | DOI: 10.2307/2287976 · doi:10.2307/2287976 |
| [11] | WEI W. W. S., Time Series Analysis. Univariate and Multivariate Method (1994) |
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