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 paper, 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 paper 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.

中文翻译：

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广义发散的局部惠特尔似然方法

估计谱密度有多种方法。关于参数方法，在拟合特定的光谱密度参数族时提出了不同的发散度。此外，考虑到我们无法指定过程模型的情况，非参数方法也很常见。在本文中，我们开发了一种基于一般得分函数的局部惠特尔似然方法，在一些特殊情况下，该方法适用于更多应用。本文重点介绍了我们的一般局部 Whittle 估计量的有效渐近性，并与其他估计量进行了比较。此外，对于特殊情况，我们基于评分函数的形式构建了一步超前预测器。随后，我们表明它比经典的指数加权线性预测器具有更小的预测误差。提供的数值研究显示了我们本地 Whittle 估计器的一些有趣特征。