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<p>This paper describes the first version of the <Emphasis FontCategory="NonProportional">MAR</Emphasis> package, designed to estimate Matrix-valued Auto-Regressive (MAR) models in <Emphasis FontCategory="NonProportional">gretl</Emphasis>. The current version of the package estimates the MAR(1) model via two techniques: Least Squares Estimation (LSE) and Maximum Likelihood Estimation (MLE). It provides standard estimation output in <Emphasis FontCategory="NonProportional">gretl</Emphasis> formats, including estimated coefficients, standard errors, <i>t</i>-statistics, <i>p</i>-values, and some basic regression statistics. The package also calculates and displays the impulse response functions. For ease of use, the package includes a simple Graphical User Interface (GUI), while offering full functionality via the <Emphasis FontCategory="NonProportional">gretl</Emphasis> scripting language. Two examples, one using real data and the other using simulated data, illustrate its relevance in economic modeling.</p>

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Matrix-valued AutoRegressive (MAR) models in gretl

  • 期刊论文

  • 发表日期：

    2026年2月24日

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  • Andrea Bucci,
  • Giulio Palomba,
  • Marco Tedeschi

摘要

This paper describes the first version of the MAR package, designed to estimate Matrix-valued Auto-Regressive (MAR) models in gretl. The current version of the package estimates the MAR(1) model via two techniques: Least Squares Estimation (LSE) and Maximum Likelihood Estimation (MLE). It provides standard estimation output in gretl formats, including estimated coefficients, standard errors, t-statistics, p-values, and some basic regression statistics. The package also calculates and displays the impulse response functions. For ease of use, the package includes a simple Graphical User Interface (GUI), while offering full functionality via the gretl scripting language. Two examples, one using real data and the other using simulated data, illustrate its relevance in economic modeling.