Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-28T05:24:03.516Z Has data issue: false hasContentIssue false
  • English
  • Français

On the first-order bilinear time series model

Published online by Cambridge University Press:  14 July 2016

Tuan Dinh Pham  and
Lanh Tat Tran
Tuan Dinh Pham*
Affiliation:
Indiana University
Lanh Tat Tran*
Affiliation:
Indiana University
*
∗Postal address: Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A.
∗Postal address: Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

The paper investigates some properties of the first-order bilinear time series model: stationarity and invertibility. Estimates of the parameters are obtained by a modified least squares method and shown to be strongly consistent.

Keywords

BILINEAR MODELSCOVARIANCE FUNCTIONINVERTIBILITYLEAST SQUARES ESTIMATESTATIONARITYSTRONG CONSISTENCY
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 3 , September 1981 , pp. 617 - 627
Copyright
Copyright © Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Research partly supported by NSF Grant No. MCS 76–00951.

References

[1] Bruni, C., Dupillo, G. and Koch, G. (1974) Bilinear systems: an appealing class of nearly linear systems in theory and application. IEEE Trans. Auto. Control AC-19, 334–338.CrossRefGoogle Scholar
[2] Granger, C. W. J. and Andersen, A. (1978a) Non-linear time series modelling. In Applied Time Series Analysis, ed. Findley, D. F., Academic Press, New York, 25–38.CrossRefGoogle Scholar
[3] Granger, C. W. J. and Andersen, A. (1978b) On the invertibility of time series models. Stoch. Proc. Appl. 8, 87–92.CrossRefGoogle Scholar
[4] Granger, C. W. J. and Andersen, A. (1978c) An Introduction to Bilinear Time Series Models. Vanderhoeck and Reprecht, Gottingen.Google Scholar
[5] Mohler, R. R. (1973) Bilinear Control Processes (with Applications to Engineering, Ecology and Medicine). Academic Press, New York.Google Scholar
[6] Subba Rao, T. (1978a) On the estimation of parameters of bilinear time series models. Technical Report No. 79, Department of Mathematics, University of Manchester Institute of Science and Technology.Google Scholar
[7] Subba Rao, T. (1978b) On the theory of bilinear time series models. Technical Report No. 87, Department of Mathematics, University of Manchester Institute of Science and Technology.Google Scholar
[8] Subba Rao, T. (1979) On the theory of bilinear time series models, II. Technical Report No. 121, Department of Mathematics, University of Manchester Institute of Science and Technology.Google Scholar