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Maximum Likelihood Estimation of the Vector AutoRegressive To Anything (VARTA) model

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  • Andersson, Jonas

    (Dept. of Business and Management Science, Norwegian School of Economics)

  • Karlis, Dimitris

    (Dept. of Statistics, Athens University of Economics and Business)

Abstract

The literature on multivariate time series is, largely, limited to either models based on the multivariate Gaussian distribution or models specifically developed for a given application. In this paper we develop a general approach which is based on an underlying, unobserved, Gaussian Vector Autoregressive (VAR) model. Using a transformation, we can capture the time dynamics as well as the distributional properties of a multivariate time series. The model is called the Vector AutoRegressive To Anyting (VARTA) model and was originally presented by Biller and Nelson (2003) who used it for the purpose of simulation. In this paper we derive a maximum likelihood estimator for the model and investigate its performance. We also provide diagnostic analysis and how to compute the predictive distribution. The proposed approach can provide better estimates about the forecasting distributions which can be of every kind not necessarily Gaussian distributions as for the standard VAR models.

Suggested Citation

  • Andersson, Jonas & Karlis, Dimitris, 2025. "Maximum Likelihood Estimation of the Vector AutoRegressive To Anything (VARTA) model," Discussion Papers 2025/25, Norwegian School of Economics, Department of Business and Management Science.
    • Handle: RePEc:hhs:nhhfms:2025_025
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    File URL: https://hdl.handle.net/11250/5326928
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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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