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Activity Number: 601
Type: Contributed
Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 PM
Sponsor: Business and Economic Statistics Section
Abstract - #307765
Title: Predictor Selection for Non-Negative Autoregressive Processes
Author(s): Chiao-Yi Yang*+ and Ching-Kang Ing
Companies: Institute of Statistical Science Academia Sinica and Institute of Statistical Science Academia Sinica, Taiwan
Keywords: Accumulated prediction error ; Mean squared prediction error ; Moment bound ; Non-negative autoregressive model ; Predictor selection ; Unit root
Abstract:

Let observations $y_{1}, \cdots, y_{n}$ be generated from a non-negative first-order autoregressive (AR) process. In both the stationary and unit root cases, we derive moment bounds and limiting distributions of an extreme value estimator of the AR coefficient. These results enable us to provide an asymptotic expression for the mean squared prediction error (MSPE) of the corresponding predictor, denoted by $\hat{y}_{n+1}$, of $y_{n+1}$. Based on this expression, we compare the performance of $\hat{y}_{n+1}$ and the least squares predictor from the MSPE point of view. Our comparison reveals that the better predictor between these two predictors is determined not only by whether a unit root exists or not, but also by the behavior of the underlying error distribution near the origin, and hence is difficult to be identified in practice. To circumvent this difficulty, we suggest choosing the predictor with the smaller accumulated prediction error and show that the predictor chosen in this way is asymptotically equivalent to the better one. Both real and simulated data sets are used to illustrate the proposed method


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