Co-integration with score-driven models: an application to US real GDP growth, US inflation rate, and effective federal funds rate Articles uri icon

publication date

  • January 2023

start page

  • 203

end page

  • 223


  • 1


  • 27

International Standard Serial Number (ISSN)

  • 1365-1005

Electronic International Standard Serial Number (EISSN)

  • 1469-8056


  • Nonlinear 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.


  • Economics
  • Statistics


  • nonlinear co-integration; nonlinear common trends; dynamic conditional score (dcs); generalized autoregressive score (gas); quasi-vector autoregressive moving average (qvarma)