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Noncausal vector AR processes with application to economic time series

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  • Davis, Richard A.
  • Song, Li

Abstract

Inference procedures for noncausal autoregressive (AR) models have been well studied and applied in a variety of applications from environmental to financial. For such processes, the observation at time t may depend on both past and future shocks in the system. In this paper, we consider extension of the univariate noncausal AR models to the vector AR (VAR) case. The extension presents several interesting challenges since even a first-order VAR can possess both causal and noncausal components. Assuming a non-Gaussian distribution for the noise, we show how to compute an approximation to the likelihood function. Under suitable conditions, it is shown that the maximum likelihood estimator (MLE) of the vector of AR parameters is asymptotically normal. The estimation procedure is illustrated with a simulation study for a VAR(1) process and with two real data examples.

Suggested Citation

  • Davis, Richard A. & Song, Li, 2020. "Noncausal vector AR processes with application to economic time series," Journal of Econometrics, Elsevier, vol. 216(1), pages 246-267.
    • Handle: RePEc:eee:econom:v:216:y:2020:i:1:p:246-267
    DOI: 10.1016/j.jeconom.2020.01.017
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    References listed on IDEAS

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    1. Lanne, Markku & Saikkonen, Pentti, 2013. "Noncausal Vector Autoregression," Econometric Theory, Cambridge University Press, vol. 29(3), pages 447-481, June.
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    Cited by:

    1. Numan Ülkü & Kexing Wu, 2023. "Stock Market's Response to Real Output Shocks in China: A VARwAL Estimation," China & World Economy, Institute of World Economics and Politics, Chinese Academy of Social Sciences, vol. 31(5), pages 1-25, September.
    2. Christis Katsouris, 2023. "Structural Analysis of Vector Autoregressive Models," Papers 2312.06402, arXiv.org, revised Feb 2024.
    3. Gianluca Cubadda & Francesco Giancaterini & Alain Hecq & Joann Jasiak, 2023. "Optimization of the Generalized Covariance Estimator in Noncausal Processes," Papers 2306.14653, arXiv.org, revised Jan 2024.
    4. Anders Rygh Swensen, 2022. "On causal and non‐causal cointegrated vector autoregressive time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 178-196, March.
    5. Christian Gouriéroux & Yang Lu, 2023. "Noncausal affine processes with applications to derivative pricing," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 766-796, July.
    6. Xuanling Yang & Dong Li & Ting Zhang, 2024. "A simple stochastic nonlinear AR model with application to bubble," Papers 2401.07038, arXiv.org.

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    More about this item

    Keywords

    Vector autoregressive model; Noncausal; Non-Gaussian;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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