Testing for nonzero impulse responses in vector autoregressive processes

Abstract

Impulse response functions are often used to investigate the relationships between the components of a VAR (vector autoregressive) process. A hypothesis of particular interest is that a variable does not react to impulses in another variable, i.e., the impulse responses are zero. Two types of tests for such hypotheses are considered. The first type is based on finite-order VAR assumptions and the second allows for possibly infinite-order processes. It is found that both types of tests have to be used cautiously because small sample and asymptotic properties may differ substantially.