Score-driven non-linear multivariate dynamic location models

In this paper, we introduce a new model by extending the dynamic conditional score(DCS) model of the multivariate t-distribution and name it as the quasi-vectorautoregressive (QVAR) model. QVAR is a score-driven nonlinear multivariatedynamic location model, in which the conditional score vector of the log-likelihood (LL)updates the dependent variables. For QVAR, we present the details of theeconometric formulation, the computation of the impulse response function, and themaximum likelihood (ML) estimation and related conditions of consistency andasymptotic normality. As an illustration, we use quarterly data for period 1987:Q1 to2013:Q2 from the following variables: quarterly percentage change in crude oil realprice, quarterly United States (US) inflation rate, and quarterly US real gross domesticproduct (GDP) growth. We find that the statistical performance of QVAR is superior tothat of VAR and VARMA. Interestingly, stochastic annual cyclical effects withdecreasing amplitude are found for QVAR, whereas those cyclical effects are notfound for VAR or VARMA.The authors are thankful to Matthew Copley. Blazsek and Licht acknowledge funding from Universidad Francisco Marroquín. Escribano acknowledges financial support from Ministerio de Economía, Industria y Competitividad (Spain) (grants ECO2016-00105-001 and MDM 2014- 0431), and Comunidad de Madrid (grant MadEco-CM S2015/HUM-3444)