Mode Identification of Volatility in Time-Varying Autoregression

Abstract

In many applications, time series exhibit nonstationary behavior that might reasonably be modeled as a time-varying autoregressive (AR) process. In the context of such a model, we discuss the problem of testing for modality of the variance function. We propose a test of modality that is local and, when used iteratively, can be used to identify the total number of modes in a given series. This problem is closely related to peak detection and identification, which has applications in many fields. We propose a test that, under appropriate assumptions, is asymptotically distribution free under the null hypothesis, even though nonparametric estimation of the AR parameter functions is involved. Simulation studies and applications to real datasets illustrate the behavior of the test.

KEY WORDS:

• Local stationarity
• Modality
• Time series

Acknowledgments

This work has been partially supported by the NSF grant # 0406431. The authors thank the referees and the associate editor for constructive criticisms, which led to a significant improvement of the original article.