A Sieve Bootstrap-Based Test for Multiple Unit Roots

• Activity Number: 489
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Xiao Zhong*+ and V A Samaranayake
• Companies: Missouri S&T and Missouri University of Science and Technology
• Keywords: Integrated Processes ; Unit Root Tests ; Multiple Unit Roots ; Sieve Bootstrap ; ARIMA

Abstract

We introduce a sieve bootstrap based test for determining if an autoregressive process has two unit roots. This is in contrast to the standard procedure of determining the number of unit roots by first conducting a unit root test, then differencing the series if the null hypothesis of a unit root process is not rejected and repeating the unit root test on the differenced series. It's shown how the proposed procedure can easily be extended to the case of three or more unit roots. In addition, we develop a bootstrap version of a sequential test proposed by Dickey and Pantula in 1987. A Monte Carlo simulation study is carried out to investigate the properties of the two tests. Results show that the sieve bootstrap based test has reasonable small sample properties when the sample size is large and that the Dickey-Pantula test has good power.