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Estimation Of The Vector Moving Average Model By Vector Autoregression

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  • John Galbraith
  • Aman Ullah
  • Victoria Zinde-Walsh

Abstract

We examine a simple estimator for the multivariate moving average model based on vector autoregressive approximation. In finite samples the estimator has a bias which is low where roots of the characteristic equation are well away from the unit circle, and more substantial where one or more roots have modulus near unity. We show that the representation estimated by this multivariate technique is consistent and asymptotically invertible. This estimator has significant computational advantages over Maximum Likelihood, and more importantly may be more robust than ML to mis-specification of the vector moving average model. The estimation method is applied to a VMA model of wholesale and retail inventories, using Canadian data on inventory investment, and allows us to examine the propagation of shocks between the two classes of inventory.

Suggested Citation

  • John Galbraith & Aman Ullah & Victoria Zinde-Walsh, 2002. "Estimation Of The Vector Moving Average Model By Vector Autoregression," Econometric Reviews, Taylor & Francis Journals, vol. 21(2), pages 205-219.
    • Handle: RePEc:taf:emetrv:v:21:y:2002:i:2:p:205-219
    DOI: 10.1081/ETC-120014349
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    References listed on IDEAS

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    1. Lütkepohl, Helmut & Poskitt, D.S., 1991. "Estimating Orthogonal Impulse Responses via Vector Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 7(4), pages 487-496, December.
    2. Lütkepohl, Helmut, 1988. "Asymptotic Distribution of the Moving Average Coefficients of an Estimated Vector Autoregressive Process," Econometric Theory, Cambridge University Press, vol. 4(1), pages 77-85, April.
    3. Lewis, Richard & Reinsel, Gregory C., 1985. "Prediction of multivariate time series by autoregressive model fitting," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 393-411, June.
    4. repec:cup:etheor:v:7:y:1991:i:4:p:487-96 is not listed on IDEAS
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    5. Patrick Richard, 2009. "Improving the accuracy of the analytical indirect inference estimator for MA models," Economics Bulletin, AccessEcon, vol. 29(4), pages 2795-2802.
    6. Stefan Bruder, 2014. "Comparing several methods to compute joint prediction regions for path forecasts generated by vector autoregressions," ECON - Working Papers 181, Department of Economics - University of Zurich, revised Dec 2015.
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    More about this item

    Keywords

    Vector autoregression; Vector moving average; JEL Classification: ; C12; C22;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: 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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