For policy decisions, capturing seasonal effects in impulse responses are important for the correct specification of dynamic models that measure interaction effects for policy-relevant macroeconomic variables. In this paper, a new multivariate method is suggested, which uses the score-driven quasi-vector autoregressive(QVAR) model, to capture seasonal effects in impulse response functions (IRFs). The nonlinear QVAR-based method is compared with the existing linear VAR-based method. The following technical aspects of the newmethod are presented: (i) mathematical formulation of QVAR; (ii) first-order representation and infinite vectormoving average, VMA (∞), representation of QVAR; (iii) IRF of QVAR; (iv) statistical inference of QVAR and conditions of consistency and asymptotic normality of the estimates. Control data are used for the period of 1987:Q1 to 2013:Q2, from the following policy-relevant macroeconomic variables: crude oil real price, United States (US) inflation rate, and US real gross domestic product (GDP). A graphical representation of seasonal effects among variables is provided, by using the IRF. According to the estimation results, annual seasonal effects are almost undetected by using the existing linear VAR tool, but those effects are detected by using thenew QVAR tool.
macroeconomic time series data; quasi-vector autoregressive (qvar) model; score-driven time series models; stochastic seasonality