Abstract: This study establishes the statistical properties of a spectrum-based Whittle parameter estimation procedure for locally stationary long-range dependent 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 using Monte Carlo experiments with gamma and gamma-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 using a well-known real-life data example.

Key words and phrases: Local stationarity, long-range dependence, nonstationarity, Whittle estimation.