Global Semiparametric Estimation of Long-memory Signal Plus Noise Processes

Abstract

We propose semiparametric estimation of the memory parameter that controls persistence of autocorrelation in stationary long-memory signal plus white noise processes, including an important extension to long-memory stochastic volatility (LMSV) models. The proposed estimation is constructed from the Whittle likelihood based on fractional exponential (FEXP) models, which is called a global or broadband semiparametric estimation. We establish that the estimators are consistent without Gaussianity. A numerical examination reveals that the proposed estimation works well in finite samples. Finally, we provide an illustrative example of volatility analysis by using the LMSV model.