Threshold integrated moving average models: does size matter? maybe so

Abstract

The aim of this paper is to identify permanent and transitory shocks. This identification is done according to the size of the shocks or the size of some other important economic variable. In order to be able to carry this identification scheme on, we introduce a new class of threshold models: threshold integrated moving average models (TIMA). These are integrated models with a unit root in the moving average of one regime and an invertible moving average in the other regime. The former regime corresponds to transitory shocks,while the latter corresponds to permanent shocks. The paper analyzes the impulse response function generated by TIMA models and its invertibility. Consistency and asymptotic normality of least squares estimators are established and hypothesis tests for TIMA models are developed. The paper concludes with an application to exchange rates and stock market prices.