Template-Type: ReDIF-Paper 1.0
Author-Name:Skrobotov Anton
Author-Name-First: Anton 
Author-Name-Last:Skrobotov 
Author-Workplace-Name: RANEPA 
Author-Name:Cavaliere Giuseppe 
Author-Name-First: Giuseppe 
Author-Name-Last:Cavaliere 
Author-Workplace-Name: Department of Statistical Sciences, University of Bologna 
Author-Name:Taylor Robert 
Author-Name-First: Robert 
Author-Name-Last:Taylor 
Author-Workplace-Name: Essex Business School, University of Essex 
Title: Wild Bootstrap Seasonal Unit Root Tests for Time Series with Periodic Non-Stationary Volatility
Abstract: This paper investigates the behaviour of the well-known HEGY (Hylleberg, Engle, Granger and Yoo, 1990, Journal of Econometrics, vol.44, pp.215-238) regression-based seasonal unit root
tests in cases where the driving shocks are allowed to display periodic non-stationary volatility and conditional heteroskedasticity. Our set up allows for periodic heteroskedasticity, non-stationary
volatility and (seasonal) GARCH as special cases. We show that the limiting null distributions of the HEGY tests depend, in general, on nuisance parameters which derive from the underlying
volatility process. Monte Carlo simulations show that the standard HEGY tests can be substantially over-sized in the presence of such effects. As a consequence, we propose bootstrap implementations
of the HEGY tests, based around a seasonal block wild bootstrap principle. This is shown to deliver asymptotically pivotal inference under our general conditions on the shocks. Simulation evidence
is presented which suggests that our proposed bootstrap tests perform well in practice, largely correcting the size problems seen with the standard HEGY tests even under extreme patterns of
heteroskedasticity, yet not losing finite sample relative to the standard HEGY tests.

Classification-JEL: C12, C22
Keywords:  seasonal unit roots, (periodic) non-stationary volatility, conditional heteroskedasticity, wild bootstrap
Creation-Date: 2016
Revision-Date:2016
Length: 37 pages
File-URL: https://www.iep.ru/files/RePEc/gai/wpaper/wpaper-2016-269.pdf
File-Format: application/pdf
File-Function: Revised version, 2016
Handle: RePEc:gai:wpaper:wpaper-2016-269