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Vector ARIMA Models

Transfer functions assume that the independent variables and associated lags influence the direction and magnitude of the forecast series. These models are said NOT to allow for what is termed "feedback". A system is said to include feedback if values of the input variable X depend in some fashion on the past or current levels of the dependent variable. Vector ARIMA models allow for this feedback process to occur. For example, say current sales Z1(t) depends not only on previous sales Z1(t-1), but also on advertising expense in the previous period Z2(t-1). Feedback is said to exist if current advertising expense, Z2(t) was influenced by sales in the previous period, Z1(t-1). Being able to describe the duality relationship between autoregressive processes and moving average processes enables the forecaster to use the autocorrelation and partial autocorrelation functions to identify potential forms of univariate models. This is not the case in Vector ARIMA. The vector model does not allow us to move from the infinite representation of one process to the finite representation of the other. Therefore, we need different tools to help us identify these processes than what is generally used in univarite ARIMA modeling. This tool is called a CCF.