Co-integration and common trends analysis with score-driven models : an application to US macroeconomic data

Abstract

We study co-integration and common trends for time series variables, by introducing a new nonlinear multivariate dynamic conditional score (DCS) model that is robust to outliers. The new model is named the t-QVARMA (quasi-vector autoregressive moving average) model, which is a score-driven location model for the multivariate t-distribution. Classical VAR models of co-integrated time series are estimated by using the outlier-sensitive vector error correction model (VECM) representation. In t-QVARMA, the I(0) and I(1) components of the variables are separated in a way that is similar to the Granger-representation of VAR models. We show that a limiting special case of t-QVARMA, named Gaussian-QVARMA, is a Gaussian-VARMA specification with I(0) and I(1) components. For t-QVARMA, we present the reduced-form and the structural-form representations and the impulse response function (IRF). As an application, we study the relationship between federal funds rate and United States (US) inflation rate for the period of July 1954 to January 2019, since those variables are I(1) and co-integrated. We present the outlier-discounting property of t-QVARMA and compare the estimates of the t- QVARMA, Gaussian-QVARMA and Gaussian-VAR alternatives. We find that the statistical performance of t-QVARMA is superior to that of the classical Gaussian-VAR model.