Summary: | 碩士 === 淡江大學 === 水資源及環境工程學系 === 86 === Recently, the Hurvich and Tsai (1997) focused on the short time
series and made use of the minimizing the mean squared error to
establish the linear relationship between Zt+h and {Zt-k+1,...,
Zt} in order to increase the forecasting abilities. However,
the Hurvich and Tsai''s research only limited on analyzing the
synthetic data of some special models. Therefore, the following
study is not only probing into the suitable range for the method
that Hurvich and Tsai provide but also will focus on the monthly
riverflow discharge data of Taiwan to make a comprehensive
research.This study uses Burg (1978) and the traditional methods
that estimate the autocovariance to yield the estimates of the
predictor coefficients from Hurvich and Tsai. In the mean time,
this research adopts the maximum entropy and moment methods to
estimate the parameters of the time series model when the
difference display on the forecasting abilities between the
Hurvich and Tsai and the time series model. Three criteria,
AICC, AIC and FPE, are used as the model selection criteria for
identifying short time series model.The results of synthetic
data show that maximum entropy method has better parameters
estimating accuracy than moment method, whatever the data is
close to non-staionarity or stationarity with small sample size.
After using the maximum entropy estimator and the autocovariance
estimator (Burg) to estimate the parameters, the AICC criterion
has better quality of identifying model, especially when data
closes to non-stationarity. For the small sample, the
forecasting ability is better when the time series model is used
for examining the maximum entropy estimator. When the sample
size increases, the forecasting ability of both methods of
Hurvich and Tsai and time series models are very similar.In
general, the Hurvich and Tsai used the traditional method that
estimate the autocovariance showed the best forecasting ability
for the real data. However, the SAR model and the Hurvich and
Tsai have the same qualities of predication. The SAR model is
better for the monthly riverflow data of Taiwan if the principle
of parsimony of the parameter is considerable.
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