A study on marginal model of vector autoregressive model

Abstract

A vector autoregression (VAR) is a statistical model used to capture the linear interdependencies among multiple time series data. Recently, a large dimensional VAR models are often used to analysis vector time series data. We suggested a method to find a marginal model of a VAR model of time-lag order 1 or VAR(1) model. First, we derived a formula for the marginal models of a VAR(1) model. Next, we explored properties of marginal models of a VAR model along with some examples of marginal models with their graphical displays. We then proposed some patterns of the coefficient matrix of a VAR model which yield VAR marginal models. We compared the two types of fitted values of time series; one type obtained under a whole (against marginal) VAR model and the other type obtained through the marginalization formula derived in the thesis.