Abstract:

Building a multivariate time series model involves five pivotal steps: Identification Specification, Estimation and Hypothesis Testing, Diagnostic Assessment, and Forecasting. Estimating parameters in a multivariate Vector Autoregressive (VAR) model presents a greater challenge compared to univariate autoregressive models. Under the assumption of normality in error distributions, Maximum Likelihood Estimation (MLE) and the Likelihood Ratio test are applicable in the context of multivariate VAR models. In this research article, we embark on a journey to estimate the parameters of a multivariate VAR model. We employ the method of Maximum Likelihood Estimation based on ordinary least squares regression. To enhance the accuracy of our model, we estimate the dispersion matrix of errors using Internally Studentized residuals. Furthermore, we introduce a test procedure for determining the optimal number of lags for variables within the multivariate VAR model, leveraging the power of the Likelihood Ratio test.

Description:

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