Multistep Prediction in Autoregressive Processes
نویسنده
چکیده
In this paper, two competing types of multistep predictors, i+e+, plug-in and direct predictors, are considered in autoregressive ~AR! processes+When a working model AR~k! is used for the h-step prediction with h . 1, the plug-in predictor is obtained from repeatedly using the fitted ~by least squares! AR~k! model with an unknown future value replaced by their own forecasts, and the direct predictor is obtained by estimating the h-step prediction model’s coefficients directly by linear least squares+ Under rather mild conditions, asymptotic expressions for the mean-squared prediction errors ~MSPEs! of these two predictors are obtained in stationary cases+ In addition, we also extend these results to models with deterministic time trends+ Based on these expressions, performances of the plug-in and direct predictors are compared+ Finally, two examples are given to illustrate that some stationary case results on these MSPEs can not be generalized to the nonstationary case+
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