Bootstrap-Based Tests for Seasonal Unit Roots in Autoregressive Processes with GARCH (1, 1) Innovations

• Activity Number: 41
• Type: Contributed
• Date/Time: Sunday, July 31, 2016 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Xiao Zhong* and V A Samaranayake
• Companies: Missouri University of Science and Technology and Missouri University of Science and Technology
• Keywords: Seasonal Time Series ; Conditional Heteroscedasticity ; Dickey-Hasza-Fuller Tests ; Re-Sampling

Abstract

Dickey, Hasza and Fuller were the first to propose a test (DHF test) to determine if a seasonal unit root exists in a time series with independent and identically distributed errors. In 2000, Psaradakis introduced a bootstrap-based unit root test for purely seasonal time series with independent errors that exhibited higher powers than the DHF test. His method is recognized as difference based because it calculates the residuals by fitting an AR(p) model to the differenced non-seasonal time series, whereas the method announced by Palm, Smeekes, and Urbain in 2008 is called residual based because it computes the residuals by fitting the DF regression model to the differenced series. In this paper, we consider extending the DHF test and developing bootstrap-based unit root test for seasonal time series with GARCH(1,1) errors using the residual-based method. A Monte-Carlo simulation study, carried out to investigate the properties of the test, shows that our bootstrap-based seasonal unit root test has reasonable small sample properties with respect to both size and power.