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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. repec:cup:etheor:v:7:y:1991:i:4:p:487-96 is not listed on IDEAS
    4. 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.
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    Citations

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    Cited by:

    1. 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.
    2. Manuel A. Hernandez & Raul Ibarra & Danilo R. Trupkin, 2014. "How far do shocks move across borders? Examining volatility transmission in major agricultural futures markets," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 41(2), pages 301-325.
    3. Sbrana, Giacomo & Silvestrini, Andrea, 2013. "Aggregation of exponential smoothing processes with an application to portfolio risk evaluation," Journal of Banking & Finance, Elsevier, vol. 37(5), pages 1437-1450.
    4. Poloni, Federico & Sbrana, Giacomo, 2019. "Closed-form results for vector moving average models with a univariate estimation approach," Econometrics and Statistics, Elsevier, vol. 10(C), pages 27-52.
    5. BenSaïda, Ahmed, 2019. "Good and bad volatility spillovers: An asymmetric connectedness," Journal of Financial Markets, Elsevier, vol. 43(C), pages 78-95.
    6. Conlon, Thomas & Cotter, John & Gençay, Ramazan, 2018. "Long-run wavelet-based correlation for financial time series," European Journal of Operational Research, Elsevier, vol. 271(2), pages 676-696.
    7. Sisi Qin & Wee‐Yeap Lau, 2023. "Cross‐border and cross‐commodity volatility spillover effects of Chinese soybean futures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(12), pages 1836-1852, December.
    8. Patrick Richard, 2009. "Improving the accuracy of the analytical indirect inference estimator for MA models," Economics Bulletin, AccessEcon, vol. 29(4), pages 2795-2802.
    9. Ufuk Devrim Demirel, 2015. "Identification of technology shocks using misspecified VARs," Canadian Journal of Economics, Canadian Economics Association, vol. 48(4), pages 1321-1349, November.

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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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