VAR Processes with Parameter Constraints

In Chapter 3, we have discussed estimation of the parameters of a

K

-dimensional stationary, stable VAR(

p

) process of the form

5.1.1

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$$ y_t = \nu + A_1 y_{t - 1} + \ldots + A_p y_{t - p} + u_t , $$

where all the symbols have their usual meanings. In the investment/income/consumption example considered throughout Chapter 3, we found that many of the coefficient estimates were not significantly different from zero. This observation may be interpreted in two ways. First, some of the coefficients may actually be zero and this fact may be reflected in the estimation results. For instance, if some variable is not Granger-causal for the remaining variables, zero coefficients are encountered. Second, insignificant coefficient estimates are found if the information in the data is not rich enough to provide sufficiently precise estimates with confidence intervals that do not contain zero