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Frequency‐Domain Estimation Of Bilinear Time Series Models

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  • S. A. O. Sesay
  • T. Subba Rao

Abstract

. Two frequency‐domain methods of estimation of the parameters of linear time series models–one based on maximum likelihood, called the ‘Whittle criterion’, and the other based on least squares, called the ‘Taniguchi criterion’–are discussed in this paper. A heuristic justification for their use in models such as bilinear models is given. The estimation theory and associated asymptotic theory of these methods are numerically illustrated for the bilinear model BL(p,0, p, 1). For that purpose, an approach based on the calculus of Kronecker product matrices is used to obtain the derivatives of the spectral density function of the state‐space form of the model.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:13:y:1992:i:6:p:521-545
    DOI: 10.1111/j.1467-9892.1992.tb00124.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. Maria Eduarda Silva & Vera Lúcia Oliveira, 2005. "Difference Equations for the Higher Order Moments and Cumulants of the INAR(p) Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(1), pages 17-36, January.
    3. Maria Eduarda Da Silva & Vera Lúcia Oliveira, 2004. "Difference Equations for the Higher‐Order Moments and Cumulants of the INAR(1) Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(3), pages 317-333, May.
    4. Isabel Silva & M. Eduarda Silva & Isabel Pereira & Nélia Silva, 2005. "Replicated INAR(1) Processes," Methodology and Computing in Applied Probability, Springer, vol. 7(4), pages 517-542, December.

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