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The Inverse Kullback–Leibler Method for Fitting Vector Moving Averages

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  • Tucker McElroy
  • Anindya Roy

Abstract

A new method for the estimation of a vector moving average (VMA) process is presented. The technique uses Kullback–Leibler discrepancy with inverse spectra, and yields a Yule–Walker system of equations in inverse autocovariances for the VMA coefficients. This provides a direct formula for the coefficients, which always results in a stable matrix polynomial. The paper provides asymptotic results, as well as an analysis of the method's performance, in terms of speed, bias, and precision. Applications to preliminary estimation of VMA models are discussed, and the method is illustrated on retail data.

Suggested Citation

  • Tucker McElroy & Anindya Roy, 2018. "The Inverse Kullback–Leibler Method for Fitting Vector Moving Averages," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(2), pages 172-191, March.
    • Handle: RePEc:bla:jtsera:v:39:y:2018:i:2:p:172-191
    DOI: 10.1111/jtsa.12276
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    Cited by:

    1. McElroy Tucker, 2021. "A Diagnostic for Seasonality Based Upon Polynomial Roots of ARMA Models," Journal of Official Statistics, Sciendo, vol. 37(2), pages 367-394, June.

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