DIRECT AUTOREGRESSIVE PREDICTORS FOR MULTISTEP PREDICTION: ORDER SELECTION AND PERFORMANCE RELATIVE TO THE PLUG IN PREDICTORS
DIRECT AUTOREGRESSIVE PREDICTORS FOR MULTISTEP PREDICTION: ORDER SELECTION AND PERFORMANCE RELATIVE TO THE PLUG IN PREDICTORS
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发表时间：
1997
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通讯作者：
R. Bhansali
中科院分区：
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作者：
R. Bhansali
平稳时间序列多步预测的一种直接方法是用线性回归方法对每一个提前期h拟合一个新的自回归，并从数据中选择拟合的顺序。相比之下，更常见的“插入”方法涉及初始k阶自回归的最小二乘拟合；然后从模型方程中得到多步预测，但用自己的预测代替了未知的未来值。导出了有限自回归过程h阶预测常数的直接估计和插入估计的渐近分布及其预测的均方误差；并给出了在这种情况下用直接法代替插入法在预测效率和参数估计效率上的损失比较的显式渐近表达式。通过仿真研究了这两种方法预测误差的有限样本特性。
A direct method for multistep prediction of a stationary time series con- sists of fitting a new autoregression for each lead time, h, by a linear regression procedure and to select the order to be fitted from the data. By contrast, a more usual 'plug in' method involves the least-squares fitting of an initial kth order autoregression; the multistep forecasts are then obtained from the model equa- tion, but with the unknown future values replaced by their own forecasts. The asymptotic distributions of the direct and plug in estimates of the h-step predic- tion constants and their respective mean squared errors of prediction are derived for a finite autoregressive process; explicit asymptotic expressions for comparing the loss in predictive and parameter estimation efficiency due to using the direct method instead of the plug in method in this situation are also given. The finite sample behaviour of the prediction errors with these two methods is investigated by a simulation study.