Abstract:

Multivariate Time Series modelling plays a crucial role in analysing complex dynamic systems with interdependent variables. Model building typically involves five key steps: identification, specification, parameter estimation and hypothesis testing, diagnostic checking, and forecasting. Among these, the estimation of parameters in multivariate Vector Autoregressive (VAR) models is significantly more intricate than in univariate autoregressive models due to the interdependencies between variables and the multidimensional error structure. In this study, we focus on the estimation of parameters in multivariate VAR models using Maximum Likelihood Estimation (MLE) based on ordinary least squares regression. The dispersion matrix of model errors is estimated using internally Studentized residuals, ensuring robust inference. Furthermore, a likelihood ratio-based test procedure has been developed to determine the optimal number of lags in the VAR model, providing a systematic framework for model specification. The proposed methodology demonstrates the theoretical and practical advantages of combining MLE and likelihood ratio testing in the estimation and validation of multivariate time series models.

Description:

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