×

Selecting the forgetting factor in subset autoregressive modelling. (English) Zbl 1115.62083

The authors deal with the forgetting factor applied to observations \(y(t),t=1,2,\dots,T\), of the autoregressive(AR) model \(y(t)=\sum_{i=1}^pa_iy(t-i)=\varepsilon_t,\) where \(\varepsilon_t\) are i.i.d. zero mean random variables. Two procedures are proposed to determine the value of the forgetting factor in subset AR modelling. The first procedure uses the bootstrap to determine the value of a fixed forgetting factor. The second procedure is based on the time-recursive maximum likelihood estimation for on-line time updating of the variable forgetting factor. This procedure presents a computationally efficient method for the analysis of time series data. Subsequently, the value of a forgetting factor, which is allowed to change at each time instant, can be determined as time-updating process. The real exchange rates of a number of OECD and Asian countries and a stock market index are used for illustration. Subset AR models not including a forgetting factor act as a set of benchmarks for assessing ex ante forecasting performance, and consistently improved forecasting performance is demonstrated for the proposed procedures.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
91B28 Finance etc. (MSC2000)
62M20 Inference from stochastic processes and prediction
62P05 Applications of statistics to actuarial sciences and financial mathematics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1109/72.207612
[2] Caravannis C., Signal Processing 10 pp 335– (1986)
[3] DOI: 10.1109/78.136549
[4] DOI: 10.1016/0005-1098(81)90070-4
[5] DOI: 10.1109/78.388868
[6] Hannan E. J., The Statistical Theory of Linear Systems (1988) · Zbl 0641.93002
[7] Kavalieris L., Biometrika 73 (1) pp 119– (1986)
[8] Moscinski J., Advanced Control with MATLAB & SIMULINK (1995)
[9] Paulsen J., Journal of Time Series 5 pp 115– (1984) · Zbl 0556.62066
[10] Penm J. H., Econometric Reviews 16 pp 281– (1997)
[11] DOI: 10.1016/0304-4076(84)90056-3 · Zbl 0583.62097
[12] Communications in Statistics 13 pp 449– (1984)
[13] Penm J. H., Journal of Business and Economic Statistics 10 pp 213– (1992)
[14] IEEE Trans. on Signal Processing pp 322– (1995)
[15] Potscher B. M., The Annals of Statistics 7 pp 1257– (1989)
[16] DOI: 10.1109/29.1514 · Zbl 0635.93072
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.