| Summary: | 碩士 === 國立臺北大學 === 統計學系 === 91 === Transform Function is one topic of time series analysis. Up to the present day, we only have two methods to identify the Transform Function. One is Cross Correlation Function (CCF) which is proposed by Box & Jenkins (1976) and the other is Linear Transform Function (LTF) which is proposed by Lin & Hanssens (1982). Therefore, looking for the new identification method for Transform Function is the reworded-dicsussing subject.
After constructing the Transform function model, we always use traditional criterion ,such as AIC、BIC and H&Q for model selection. However, AIC criterion always overfit and parameter estimator is not consistency for large sample size ,and BIC criterion is not consistency efficiency, and H&Q criterion always underfit for small sample size. For above defects, Chen et al.(1993) proposed Resampling methods for determining the order of autoregressive process.
As we know, Transform Function is a special case of bivariate autoregression function. Therefore, in this thesis we extend the results of Chen(1996) for multivariate autoregressive processes using resampling methods to the Transform Function.
In this paper, we prove the mean square error of prediction is monotone decreasing. Under this prerequisite, we can build the model selection criterion and prove the Yule-Walker estimators of the resampling test series are weak consistency.
In simulation aspect, our method will have good choice for large sample size or low order.
Key words: Transform Function、Resampling method、AIC
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