Frequentist Unit Root Tests in Stochastic Volatility Models

• Activity Number: 98
• Type: Contributed
• Date/Time: Monday, August 4, 2003 : 9:00 AM to 10:50 AM
• Sponsor: Business & Economics Statistics Section
• Author(s): Zeynep Kalaylioglu*+ and Sastry G. Pantula and Sujit Kumar Ghosh
• Companies: North Carolina State University and North Carolina State University and North Carolina State University
• Keywords: unit root test ; stochastic volatility models

Abstract

In stochastic volatility models the unit root test on the time series of the unobserved log-volatilities may be performed by applying the commonly used frequentist unit root tests. For instance, augmented Dickey-Fuller tests based on the log-squared mean corrected returns can be used. The log-squared mean corrected returns have the same second-order properties as those of an autoregressive moving average process. However, we observed that the moving average parameter of the resulting process (based on the log-squared mean corrected returns) is typically close to the autoregressive parameter. For this reason, the unit root tests applied to stochastic volatility models tend to reject the unit root in finite samples. We propose a method for performing the frequentist unit root tests in stochastic volatility models based on the finite sampling distribution of the well-known test statistics. The performance of these tests is demonstrated by a simulation study. We illustrate the testing procedures by applying them to four sets of exchange rates.