Estimation of Time-Varying Long Memory Parameter Using Wavelet Method

Abstract

Stationary long memory processes have been extensively studied over the past decades. When we deal with financial, economic, or environmental data, seasonality and time-varying long-range dependence can often be observed and thus some kind of non-stationarity exists. To take into account this phenomenon, we propose a new class of stochastic processes: locally stationary k-factor Gegenbauer process. We present a procedure to estimate consistently the time-varying parameters by applying discrete wavelet packet transform. The robustness of the algorithm is investigated through a simulation study. And we apply our methods on Nikkei Stock Average 225 (NSA 225) index series.

Keywords:

• Discrete wavelet packet transform
• Gegenbauer process
• Non stationarity
• Ordinary least square estimation

Mathematics Subject Classification:

• 60G99
• 62M10
• 65T60
• 91B70
• 91G60

Acknowledgment

The work of the first author was supported by “the Fundamental Research Funds for the Central Universities.”