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Inference For A Special Bilinear Time-Series Model

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  • Shiqing Ling
  • Liang Peng
  • Fukang Zhu

Abstract

type="main" xml:id="jtsa12092-abs-0001"> It is well known that estimating bilinear models is quite challenging. Many different ideas have been proposed to solve this problem. However, there is not a simple way to do inference even for its simple cases. This article proposes a generalized autoregressive conditional heteroskedasticity-type maximum likelihood estimator for estimating the unknown parameters for a special bilinear model. It is shown that the proposed estimator is consistent and asymptotically normal under only finite fourth moment of errors.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:36:y:2015:i:1:p:61-66
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    File URL: http://hdl.handle.net/10.1111/jtsa.12092
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    References listed on IDEAS

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    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. Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 1999. "The sample ACF of a simple bilinear process," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 1-14, September.
    3. Shiqing Ling, 2004. "Estimation and testing stationarity for double‐autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 63-78, February.
    4. Granger, C. W. J. & Andersen, Allan, 1978. "On the invertibility of time series models," Stochastic Processes and their Applications, Elsevier, vol. 8(1), pages 87-92, November.
    5. Dennis Kristensen, 2009. "On stationarity and ergodicity of the bilinear model with applications to GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 125-144, January.
    6. Francesco Giordano & Cosimo Vitale, 2003. "CLS asymptotic variance for a particular relevant bilinear time series model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 12(2), pages 169-185, December.
    7. Jian Liu, 1989. "A Simple Condition For The Existence Of Some Stationary Bilinear Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(1), pages 33-39, January.
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    Cited by:

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    2. Predrag M. Popović & Hassan S. Bakouch, 2020. "A bivariate integer-valued bilinear autoregressive model with random coefficients," Statistical Papers, Springer, vol. 61(5), pages 1819-1840, October.

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