Fractionally Integrated Multivariate Score-Driven Location Models with an Application to Climate Data

Abstract We introduce the quasi-vector autoregressive fractionally integrated (QVAR-FI) model to the literature on score-driven models. We apply QVAR-FI to climate data on global sea ice volume, carbon dioxide (CO 2 ) concentration in Earth’s atmosphere, and land surface temperature in Antarctica for the period of 798,000 to 1,000 years ago. In the QVAR-FI model, known as the fractionally integrated score-driven ice-age model, we control for the Milankovitch cycles (i.e. eccentricity and obliquity of Earth’s orbit and precession of the equinoxes) as exogenous explanatory variables. We consider alternative VAR, QVAR, and QVAR-FI models, using different specifications of the exogenous orbital explanatory variables and deterministic and stochastic seasonality components. We estimate the QVAR-FI model and its alternatives using the maximum likelihood (ML) method. Model diagnostics support the QVAR-FI specifications. We estimate the impulse response functions (IRFs) for QVAR-FI and compare them with those of the VAR and QVAR filters for the conditional mean. The in-sample statistical and out-of-sample multi-step-ahead forecasting performances of QVAR-FI improve those of the VAR and QVAR models.