Reduced-bias whittle likelihood estimation for short- and long-memory processes

The Whittle likelihood is a widely used approximation to the Gaussian likelihood in the frequency domain, valued for its computational efficiency. However, parameter estimates derived from maximizing the Whittle likelihood can exhibit significant bias in small samples. A reduced-bias Whittle likelihood (RB-WL) estimation method is proposed, which incorporates a bias-reducing penalization directly into the Whittle likelihood function and does not require a separate correction step for the parameter estimate. Conditions are established for this method to reduce estimation bias in models allowing for both short- and long- range dependence. The small-sample properties of the RB-WL estimator are analyzed through analytical derivations and Monte Carlo experiments, demonstrating substantial improvements in bias reduction for short- and long-memory processes. The practical utility of the RB-WL method is illustrated through an application to data on the Southern Oscillation Index, which is useful for forecasting extreme environmental events such as floods and droughts.