Seasonality Detection in Small Samples using Score-Driven Nonlinear Multivariate Dynamic Location Models

Abstract

We suggest a new mechanism to detect stochastic seasonality of multivariate macroeconomic variables, by using an extension of the score-driven first-order multivariate t-distribution model. We name the new model as the quasi-vector autoregressive (QVAR) model. QVAR is a nonlinear extension of Gaussian VARMA (VAR moving average). The location of dependent variables for QVAR is updated by the score function, thus QVAR is robust to extreme observations. For QVAR, we present the econometric formulation, computation of the impulse response function (IRF), maximum likelihood (ML) estimation, and conditions of the asymptotic properties of ML that include invertibility. We use quarterly macroeconomic data for the period of 1987:Q1 to 2013:Q2 inclusive, which include extreme observations from three I(0) variables: percentage change in crude oil real price, United States (US) inflation rate, and US real gross domestic product (GDP) growth. The sample size of these data is relatively small, which occurs frequently in macroeconomic analyses. The statistical performance of QVAR is superior to that of VARMA and VAR. Annual seasonality effects are identified for QVAR, whereas those effects are not identified for VARMA and VAR. Our results suggest that QVAR may be used as a practical tool for seasonality detection in small macroeconomic datasets.