Local Whittle Likelihood Approach for Generalized Divergence

There are many approaches in the estimation of spectral density. With regard to parametric approaches, different divergences are proposed in fitting a certain parametric family of spectral densities. Moreover, nonparametric approaches are also quite common considering the situation when we cannot specify the model of process. In this chapter we develop a local Whittle likelihood approach based on a general score function, with some special cases of which, the approach applies to more applications. This chapter highlights the effective asymptotics of our general local Whittle estimator, and presents a comparison with other estimators. Additionally, for a special case, we construct the one-step ahead predictor based on the form of the score function. Subsequently, we show that it has a smaller prediction error than the classical exponentially weighted linear predictor. The provided numerical studies show some interesting features of our local Whittle estimator. This chapter is mainly based on Xue and Taniguchi (2020).