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A Conditional Least Squares Approach To Bilinear Time Series Estimation

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  • T. Grahn

Abstract

. In this paper a conditional least squares (CLS) procedure for estimating bilinear time series models is introduced. This method is applied to a special superdiagonal bilinear model which includes the classical linear autoregressive moving‐average model as a particular case and it is proven that the limiting distribution of the CLS estimates is Gaussian and that the law of the iterated logarithm holds.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:16:y:1995:i:5:p:509-529
    DOI: 10.1111/j.1467-9892.1995.tb00251.x
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    References listed on IDEAS

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    1. S. A. O. Sesay & T. Subba Rao, 1992. "Frequency‐Domain Estimation Of Bilinear Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(6), pages 521-545, November.
    2. 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.
    3. S. A. O. Sesay & T. Subba Rao, 1991. "DIFFERENCE EQUATIONS FOR HIGHER‐ORDER MOMENTS AND CUMULANTS FOR THE BILINEAR TIME SERIES MODEL BL(p, 0, p, 1)," Journal of Time Series Analysis, Wiley Blackwell, vol. 12(2), pages 159-177, March.
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    Cited by:

    1. Shiqing Ling & Liang Peng & Fukang Zhu, 2015. "Inference For A Special Bilinear Time-Series Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(1), pages 61-66, January.
    2. Charemza, Wojciech W. & Lifshits, Mikhail & Makarova, Svetlana, 2005. "Conditional testing for unit-root bilinearity in financial time series: some theoretical and empirical results," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 63-96, January.
    3. 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.
    4. Abdelouahab Bibi & Ahmed Ghezal, 2016. "On periodic time-varying bilinear processes: structure and asymptotic inference," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(3), pages 395-420, August.
    5. Wojciech Charemza & Mikhail Lifshits & Svetlana Makarova, 2002. "A Simple Test for Unit Root Bilinearity," EUSP Department of Economics Working Paper Series Ec-01/02, European University at St. Petersburg, Department of Economics, revised 29 Mar 2002.
    6. Wojciech Charemza & Mikhail Lifshits & Svetlana Makarova, 2002. "A Simple Test for Unit Root Bilinearity," EUSP Department of Economics Working Paper Series 2002/01, European University at St. Petersburg, Department of Economics, revised 29 Mar 2002.
    7. Bibi, Abdelouahab & Ghezal, Ahmed, 2015. "Consistency of quasi-maximum likelihood estimator for Markov-switching bilinear time series models," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 192-202.

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