| Summary: | 碩士 === 國立彰化師範大學 === 統計資訊研究所 === 99 === Autoregressive model is a popular method for analyzing the time series data, where selection of order parameter is imperative. Two commonly used selection criteria are the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). However, the two criteria are known to suffer the potential problems regarding overfit and underfit, respectively. Therefore, using a specific criterion may perform well in some situations, but poorly in others. In this thesis, we use the concept of generalized degrees of freedom to measure the complexity of a modeling procedure involved in AIC or BIC criterion. We propose an approximately unbiased estimator of mean squared prediction errors based on a data perturbation technique for selecting between AIC and BIC criteria. Then we choose the final order parameter according to the selected criterion. Some numerical experiments are performed for illustrating the superiority of the proposed method, and some technique details are also presented. Finally, we demonstrate an application of the proposed method by analyzing the retail price index of China from 1952 to 2008.
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