No abstract

No abstract

No abstract

Wald tests of restrictions on the coefficients of vector autoregressive (VAR) processes are known to have nonstandard asymptotic properties for 1(1) and cointegrated systems of variables. A simple device is proposed which guarantees that Wald tests have asymptotic x2-distributio~ls under general conditions. If the true generation process is a VAR(p) it is proposed to fit a VAK(p+-1) to t h e data and perform a Wald test on the coefficients of the first p lags only. The power properties of the modified tests are studied both analytically and nunierically by means of simple illustrative examples.

n n n xvi CONTENTS 2.3.8 Distributions of Functions of Random Variables 2.4 Mathematical Expectation 2.4.1 Expected Value of a Random Variable 2.4.2 Expectation of a Function of a Single Random Variable 2.4.3 Expectations of Functions of Several Random Variables 2.4.4 Moments ' 2.4.