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Efficiency improvements for minimum distance estimation of causal and invertible ARMA models

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  • Lobato, Ignacio N.
  • Velasco, Carlos

Abstract

In this note we analyze efficiency improvements over the Gaussian maximum likelihood (ML) estimator for frequency domain minimum distance (MD) estimation for causal and invertible autoregressive moving average (ARMA) models. The analysis complements Velasco and Lobato (2017) where optimal MD estimation, which employs information in higher order moments, is studied for the general possibly non causal or non-invertible case. We consider MD estimation that combines in two manners the information contained in second, third, and fourth moments. We show that for both MD estimators efficiency improvements over the Gaussian ML occur when the distribution of the innovations is platykurtic. In addition, we show that asymmetry alone is not associated with efficiency improvements.

Suggested Citation

  • Lobato, Ignacio N. & Velasco, Carlos, 2018. "Efficiency improvements for minimum distance estimation of causal and invertible ARMA models," Economics Letters, Elsevier, vol. 162(C), pages 150-152.
    • Handle: RePEc:eee:ecolet:v:162:y:2018:i:c:p:150-152
    DOI: 10.1016/j.econlet.2017.11.013
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    References listed on IDEAS

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    1. Lucia Alessi & Matteo Barigozzi & Marco Capasso, 2011. "Non‐Fundamentalness in Structural Econometric Models: A Review," International Statistical Review, International Statistical Institute, vol. 79(1), pages 16-47, April.
    2. Eric M. Leeper & Todd B. Walker & Shu‐Chun Susan Yang, 2013. "Fiscal Foresight and Information Flows," Econometrica, Econometric Society, vol. 81(3), pages 1115-1145, May.
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    More about this item

    Keywords

    Higher-order moments; Efficiency; Kurtosis;
    All these keywords.

    JEL classification:

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

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