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Maximum likelihood estimation in space time bilinear models

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  • YUQING DAI
  • L. BILLARD

Abstract

The space time bilinear (STBL) model is a special form of a multiple bilinear time series that can be used to model time series which exhibit bilinear behaviour on a spatial neighbourhood structure. The STBL model and its identification have been proposed and discussed by Dai and Billard (1998). The present work considers the problem of parameter estimation for the STBL model. A conditional maximum likelihood estimation procedure is provided through the use of a Newton–Raphson numerical optimization algorithm. The gradient vector and Hessian matrix are derived together with recursive equations for computation implementation. The methodology is illustrated with two simulated data sets, and one real‐life data set.

Suggested Citation

  • Yuqing Dai & L. Billard, 2003. "Maximum likelihood estimation in space time bilinear models," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 25-44, January.
    • Handle: RePEc:bla:jtsera:v:24:y:2003:i:1:p:25-44
    DOI: 10.1111/1467-9892.00291
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    References listed on IDEAS

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    1. Yuqing Dai & L. Billard, 1998. "A Space‐Time Bilinear Model and its Identification," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(6), pages 657-679, November.
    2. Boonchai K. Stensholt & Dag Tjøstheim, 1987. "Multiple Bilinear Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(2), pages 221-233, March.
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