Properties of Predictors in Misspecified Autoregressive Time Series Models
研究了在拟合p阶自回归模型时，真实模型为自回归移动平均模型的情况下，误设定对最小二乘估计的偏误和均方误差以及预测均方误差的影响，并考虑了估计与预测过程的相关性及非高斯分布的影响。
Abstract This article investigates major effects of misspecification in stationary linear time series models when we fit a pth-order autoregressive model. The true model can be an autoregressive moving average model. We derive the formulas of bias and mean squared error (MSE) of the least squares estimator and the hth period ahead prediction MSE in the time domain. Contrary to previous studies, the process in estimation is not necessarily independent of the process in prediction, and the distribution of process is not necessarily Gaussian. We examine the effects of this dependence and nonnormality on prediction in misspecified models. Key Words: MisspecificationAutoregressive modelsAutoregressive moving average modelsLeast squares methodPredictionNon-Gaussian process