Title: Bootstrap seasonal unit root test under seasonal heterogeneity
Authors: Nan Zou - University of Toronto (Canada) [presenting]
Dimitris Politis - University of California, San Diego (USA)
Abstract: Both seasonal unit root and seasonal heterogeneity are common in seasonal data. When testing seasonal unit roots under seasonal heterogeneity, it is unknown if we can apply existing tests designed for seasonal homogeneous settings, for example, HEGY test, and it is unclear what test we should implement if they fail. To answer these questions, the validity of augmented HEGY test and unaugmented HEGY test under seasonal heterogeneity is firstly analyzed. It turns out that the asymptotic null distributions of the HEGY statistics testing the single roots at 1 or -1 are standard and pivotable and are identical to the asymptotic null distributions under seasonal homogeneity. On the other hand, the asymptotic null distributions of the statistics testing any coexistence of roots are non-standard and not directly pivotable and are different from the asymptotic null distributions under seasonal homogeneity. Therefore, HEGY tests are not directly applicable to the joint tests for any concurrence of seasonal unit roots under seasonal heterogeneity. Bootstrap is secondly proposed as a remedy. In particular, we bootstrap augmented HEGY test with seasonal iid bootstrap and unaugmented HEGY test with seasonal block bootstrap. The consistency of these bootstrap procedures is established. The finite-sample behavior of these bootstrap tests is more desirable than their competitors'. These bootstrap tests are used to detect the seasonal unit roots in UK seasonal consumption data.