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Gaussian mixture vector autoregression

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  • Kalliovirta, Leena
  • Meitz, Mika
  • Saikkonen, Pentti

Abstract

This paper proposes a new nonlinear vector autoregressive (VAR) model referred to as the Gaussian mixture vector autoregressive (GMVAR) model. The GMVAR model belongs to the family of mixture vector autoregressive models and is designed for analyzing time series that exhibit regime-switching behavior. The main difference between the GMVAR model and previous mixture VAR models lies in the definition of the mixing weights that govern the regime probabilities. In the GMVAR model the mixing weights depend on past values of the series in a specific way that has very advantageous properties from both theoretical and practical point of view. A practical advantage is that there is a wide diversity of ways in which a researcher can associate different regimes with specific economically meaningful characteristics of the phenomenon modeled. A theoretical advantage is that stationarity and ergodicity of the underlying stochastic process are straightforward to establish and, contrary to most other nonlinear autoregressive models, explicit expressions of low order stationary marginal distributions are known. These theoretical properties are used to develop an asymptotic theory of maximum likelihood estimation for the GMVAR model whose practical usefulness is illustrated in a bivariate setting by examining the relationship between the EUR–USD exchange rate and a related interest rate data.

Suggested Citation

  • Kalliovirta, Leena & Meitz, Mika & Saikkonen, Pentti, 2016. "Gaussian mixture vector autoregression," Journal of Econometrics, Elsevier, vol. 192(2), pages 485-498.
  • Handle: RePEc:eee:econom:v:192:y:2016:i:2:p:485-498
    DOI: 10.1016/j.jeconom.2016.02.012
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    References listed on IDEAS

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    Cited by:

    1. Chiu, Ching-Wai (Jeremy) & Mumtaz, Haroon & Pinter, Gabor, 2016. "VAR models with non-Gaussian shocks," LSE Research Online Documents on Economics 86238, London School of Economics and Political Science, LSE Library.
    2. Leena Kalliovirta & Tuomas Malinen, 2015. "Nonlinearity and cross-country dependence of income inequality," Working Papers 358, ECINEQ, Society for the Study of Economic Inequality.
    3. Jan Pablo Burgard & Matthias Neuenkirch & Matthias Nöckel, 2016. "State-Dependent Transmission of Monetary Policy in the Euro Area," Research Papers in Economics 2016-15, University of Trier, Department of Economics.
    4. Ching-Wai (Jeremy) Chiu & Haroon Mumtaz & Gabor Pinter, 2016. "Bayesian Vector Autoregressions with Non-Gaussian Shocks," CReMFi Discussion Papers 5, CReMFi, School of Economics and Finance, QMUL.
    5. Mika Meitz & Daniel Preve & Pentti Saikkonen, 2018. "A mixture autoregressive model based on Student's $t$-distribution," Papers 1805.04010, arXiv.org.

    More about this item

    Keywords

    Mixture models; Nonlinear vector autoregressive models; Regime switching;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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