On the Estimation of Locally Stationary Long-Memory Processes

Abstract

This paper establishes the statistical properties of a spectrum-based Whittle parameter estimation procedure for long-range dependent locally stationary processes. Both theoretical and empirical behaviors are investigated. In particular, a central limit theorem for the Whittle likelihood estimation method is derived under mild distributional conditions, extending its application to a wide range of non-Gaussian time series. The finite sample properties of the estimators are examined via Monte Carlo experiments with Gamma and Log-normal noise distributions. These simulation studies demonstrate that the proposed method behaves properly even for small to moderate sample sizes. Finally, the practical application of this methodology is illustrated by means a well-known real-life data example.

Simultaneous variable selection and structural identification for time‐varying coefficient models

“…A locally stationary process, as introduced by Dahlhaus (1996,1997), is an extension of the linear stationary process and can be represented in terms of the spectral density as follows where is a stochastic process with a mean value equal to 0 and orthogonal increment, . Based on this framework, a large number of topics related to locally stationary processes have been studied, including bootstrap methods for the local periodogram (Sergides and Paparoditis 2008), hypothesis testing (Sakiyama and Taniguchi 2003), the locally stationary factor model (Eichler et al 2011) and estimation methods (Chan and Palma 2020), among many others.…”

“…) . Based on this framework, a large number of topics related to locally stationary processes have been studied, including bootstrap methods for the local periodogram (Sergides and Paparoditis 2008), hypothesis testing (Sakiyama and Taniguchi 2003), the locally stationary factor model (Eichler et al 2011) and estimation methods (Chan and Palma 2020), among many others.…”

Locally stationary processes with stable and tempered stable innovations

“…There is an extensive literature about estimation and hypothesis testing methods, e.g. Chan and Palma (2019) cites recent advanced papers on this topic.…”