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Estimation For The First‐Order Diagonal Bilinear Time Series Model

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  • Won Kyung Kim
  • L. Billard
  • I. V. Basawa

Abstract

. The problem of estimation of the parameter b in the simple diagonal bilinear model {Xt}, Xt=et+bet‐1Xt‐1, is considered, where {et} is Gaussian white noise with zero mean and possibly unknown variance s̀2. The asymptotic normality of the moment estimator of b is established for the two cases when s̀2 is known and s̀2 is unknown. It is noted that the limit distribution of the least‐squares cannot easily be derived analytically. A bootstrap comparison of the sampling distributions of the least‐squares and moment estimates shows that both are asymptotically normal with the least‐squares estimate being the more efficient.

Suggested Citation

  • Won Kyung Kim & L. Billard & I. V. Basawa, 1990. "Estimation For The First‐Order Diagonal Bilinear Time Series Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 11(3), pages 215-229, May.
    • Handle: RePEc:bla:jtsera:v:11:y:1990:i:3:p:215-229
    DOI: 10.1111/j.1467-9892.1990.tb00053.x
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    Cited by:

    1. T. Grahn, 1995. "A Conditional Least Squares Approach To Bilinear Time Series Estimation," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(5), pages 509-529, September.
    2. Brunner, Allan D. & Hess, Gregory D., 1995. "Potential problems in estimating bilinear time-series models," Journal of Economic Dynamics and Control, Elsevier, vol. 19(4), pages 663-681, May.
    3. Hai‐Bin Wang, 2005. "Parameter Estimation and Subset Selection for Separable lower Triangular Bilinear Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(5), pages 743-757, September.
    4. Philip Hans Franses, 2019. "Model‐based forecast adjustment: With an illustration to inflation," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 38(2), pages 73-80, March.
    5. Roberto Leon-Gonzalez & Fuyu Yang, 2017. "Bayesian inference and forecasting in the stationary bilinear model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(20), pages 10327-10347, October.

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