Testing The Presence Of Heteroscedasticity In Unobserved Component Models

In the context of time series analysis, conditional heteroscedasticity has an important impact on the coverage of prediction intervals. Moreover, when prediction intervals are constructed using unobserved component models (UCM) the problem increases, this is due to the possible existence of several components which may or may not be conditional heteroscedastic and, consequently, the true coverage depends on the correct identification of the source of the heteroscedasticity. There are proposals for testing homoscedasticity applied to the auxiliary residuals of the UCM; however, in most cases, these procedures are not able, on average, to correctly identify the heteroscedastic component. The problem is associated with transmission of heteroscedasticity between the auxiliary residuals, this transmission may generate a wrongly identification of heteroscedasticity in the component with constant conditional variance. The idea of this paper is to focus on eliminating the transmission and then, using the auxiliary residuals, to correctly identify the conditional heteroscedastic components. In addition, we propose to use an nonparametric test for testing the presence of heteroscedasticity. Simulation results show an improvement in the power and the size of several homoscedasticity tests.