Identification and estimation of noninvertible non-Gaussian MA(q) processes

Abstract

Traditional estimation procedures, such as OLS or Box-Jenkins ARIMA modelling, which are based on second-order properties, are incapable of distinguishing among autocorrelation-equivalent MA model specifications; this ambiguity is usually resolved by imposing therestriction of invertibility. This paper presents an estimation procedure based on higher-order moments which is capable of distinguishing between these alternative specifications without recourse to the invertibility assumption. The true sequence of innovations that drives the MA process can be estimated once the correct model is determined. Also discussed is the finding that the application of OLS to a noninvertible MA process may generate residuals with an ARCH structure. Monte Carlo simulations are run to assess the statistical properties of the estimator. Some evidence of noninvertibility is presented for the prime rate and expenditure for new plant and equipment series.