Maximum Likelihood Estimation for Non-Stationary Location Models with Mixture of Normal Distributions
研究了一个非平稳位置模型，其中位置变量为随机游走，误差来自混合正态分布，并给出了最大似然估计的强一致性和渐近正态性条件，模拟和实证显示该方法在电力现货价格预测中优于其他模型。
We consider an observation-driven location model where the unobserved location variable is modeled as a random walk process and where the error variable is from a mixture of normal distributions. The time-varying location can be extended with a stationary process to account for cyclical and/or higher order autocorrelation. The mixed normal distribution can accurately approximate many continuous error distributions. We obtain a flexible modeling framework for the robust filtering and forecasting based on time-series models with non-stationary and nonlinear features. We provide sufficient conditions for strong consistency and asymptotic normality of the maximum likelihood estimator of the parameter vector in the specified model. The asymptotic properties are valid under correct model specification and can be generalized to allow for potential misspecification of the model. A simulation study is carried out to monitor the forecast accuracy improvements when extra mixture components are added to the model. In an empirical study we show that our approach is able to outperform alternative observation-driven location models in forecast accuracy for a time-series of electricity spot prices.