Abstract
AbstractNonlinear co-integration is studied for score-driven models, using a new multivariate dynamic conditional score/generalized autoregressive score model. The model is named t-QVARMA (quasi-vector autoregressive moving average model), which is a location model for the multivariate t-distribution. In t-QVARMA, I(0) and co-integrated I(1) components of the dependent variables are included. For t-QVARMA, the conditions of the maximum likelihood estimator and impulse response functions (IRFs) are presented. A limiting special case of t-QVARMA, named Gaussian-QVARMA, is a Gaussian-VARMA specification with I(0) and I(1) components. As an empirical application, the US real gross domestic product growth, US inflation rate, and effective federal funds rate are studied for the period of 1954 Q3 to 2020 Q2. Statistical performance and predictive accuracy of t-QVARMA are superior to those of Gaussian-VAR. Estimates of the short-run IRF, long-run IRF, and total IRF impacts for the US data are reported.
Highlights
In this paper, the quasi-vector autoregressive moving average location model is presented for the multivariate t-distribution, to study relationships among I(0) and co-integrated I(1) macroeconomic variables
T-Quasi-vector autoregressive moving average (QVARMA) has been introduced for the analysis of dynamic interactions effects among I(0) and co-integrated I(1) time series variables
The reduced-form and the structuralform representations of t-QVARMA have been presented, and tools have been provided for impulse response functions (IRFs) analysis
Summary
The quasi-vector autoregressive moving average location model (hereinafter, t-QVARMA) is presented for the multivariate t-distribution, to study relationships among I(0) and co-integrated I(1) macroeconomic variables. The t-QVARMA(p,q,r) model of the present paper is in relation to the works of Harvey (2013) and Creal et al (2014). As further contributions to the literature, for t-QVARMA(p,q,r), technical details of the model formulation for I(0) and co-integrated I(1) dependent variables, first-order representation, impulse response analysis, and statistical inference procedures are presented. For t-QVARMA(p,q,r), technical details of reduced-form and structural-form representations, and sign restrictions-based impulse response functions (IRFs) are presented in our paper. Estimation and forecasting results for t-QVARMA, Gaussian-VAR, and co-integrated Gaussian-VAR for vector error correction model (VECM) representation are presented. Technical details of the statistical inference and model specifications, and IRF estimates for t-QVARMA, Gaussian-QVARMA, and Gaussian-VAR are presented in Supplementary Material
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