×

Difference equations for higher-order moments and cumulants for the bilinear time series model BL(p,0,p,1). (English) Zbl 0714.62081

Summary: We obtain difference equations for higher-order moments and cumulants for the time series \(\{X_ t\}\) satisfying the bilinear model BL(p,0,p,1). These equations are similar to the well-known Yule-Walker equations for the autoregressive moving-average model which are in terms of the second- order covariances. Thus they can be used for the tentative identification of bilinear models. Another application of these equations is in the computation of preliminary estimates of the parameters of the model. We shall illustrate this by means of simulations for two simple examples of bilinear models.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62E15 Exact distribution theory in statistics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Akamanam S. I., J. Time Ser. Anal. 7 (3) pp 157– (1986)
[2] Brillinger D. R., Time Series:Data Analysis and Theory. (1975)
[3] Friedlander B., Proc. ICASSP-89, Glasgow 4 pp 2314– (1989)
[4] Gabr M. M., J. Time Ser. Anal. 9 (1) pp 11– (1988)
[5] C. W. J. Granger(1980 ) Forecasting white noise. UCSD Discussion Paper 80-31.
[6] Granger C. W. J., An Introduction to Bilinear Time Series Models. (1978) · Zbl 0379.62074
[7] Kumar K., J. Time Ser. Anal. 7 pp 117– (1986)
[8] DOI: 10.1137/1104031 · Zbl 0087.33701 · doi:10.1137/1104031
[9] Li W. K., J. Time Ser. Anal. 5 pp 173– (1984)
[10] DOI: 10.1016/0304-4149(85)90216-9 · Zbl 0588.62162 · doi:10.1016/0304-4149(85)90216-9
[11] DOI: 10.1016/0304-4149(86)90042-6 · Zbl 0614.60062 · doi:10.1016/0304-4149(86)90042-6
[12] B. Porat, and B. Friedlander(1989 ) Performance analysis of parameter estimation algorithms based on higher order moments. Int. J. Adap. Control Signal Process., to be published. · Zbl 0728.93071
[13] S. A. O. Sesay(1985 ) Frequency-domain methods of estimation and higher order moment analysis for the bilinear model BL(p,0,p, 1) . Ph.D. Thesis , University of Manchester Institute of Science and Technology.
[14] Sesay S. A. O., J. Time Ser. Anal. 9 (4) pp 385– (1988)
[15] Speed T. P., Aust. J. Statist 25 pp 378– (1983)
[16] Subba Rao T., J. R. Statist. Soc. Ser. B 43 (2) pp 244– (1981)
[17] T. SubbaRao, A. Eduarda, and M. DaSilva(1980 ) Identification and estimation of bilinear time series models. Technical Report 195, Department of Mathematics, University of Manchester Institute of Science and Technology.
[18] Subba Rao T., J. Time Ser. Anal. 1 (2) pp 145– (1980)
[19] Subba Rao T., An Introduction to Bispectral Analysis and Bilinear Time Series Models. (1984) · Zbl 0543.62074
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.