| Abstract: | 近來, Hurvich和Tsai(1997)針對短時間序列, 以最小均方預測誤差建立Z/sub t+h/與{Z/sub t-k+1/, ..., Z/sub t/}之線性關係, 提升其預測能力。然其研究僅侷限於某些特殊模式之合成資料, 故本研究將探討Hurvich和Tsai所提方法之適用範圍, 同時亦針對台灣河川月流量資料做一整體性探討。本研究比較Hurvich和Tsai所提方法與傳統時間序列模式於定常性及接近非定常性序列上預測能力之差異,研究中在Hurvich和Tsai方法時, 採用Burg(1978)與傳統兩種推估自相關變異數之方法推求參數。 結果顯示, 就合成資料而言, 利用Burg所提之自相關變異數推估法, 無論對接近非定常性或定常性模式, 其參數推估精確度皆較利用傳統自相關變異數推估法為優; 當模式為接近非定常性模式時, Hurvich和Tsai利用Burg所提之自相關變異數推估法之預測能力均優於傳統時間序列預測方法, 然當模式為定常性時, 本研究所引用之 Hurvich和Tsai方法與時間序列方法, 其預測結果相差不大。實測資料預測結果, 以Hurvich和Tsai利用傳統自相關變異數法之預測能力表現最優, 但SAR模式與Hurvich和Tsai利用傳統自相關變異數兩者預測能力相當, 如考慮參數之精簡原則, 則以SAR模式較為適用於台灣河川月流量資料。
Recently, Hurvich-Tsai (1997) employed the minimizing the mean squared error to establish the linear relationship between Z/sub t+h/ and {Z/sub t-k+1/,...,Z/sub t/} in order to increase the forecasting abilities for short time series. However, Hurvich-Tsai's research is only limited on analyzing the synthetic data of some specified models. Therefore, the following study is not only probing into the suitable range for Hurvich-Tsai method, but also investigating the monthly riverflow discharge data of Taiwan. In this study, the forecasting abilities of Hurvich- Tsai and the traditional time series models are compared for the data obeying stationarity and non-stationarity. For Hurvich-Tsai method, Burg (1978) and the traditional method for estimating the autocovariance were used to estimate the predictor parameters. The results of synthetic data show that Burg method has better parameters estimating accuracy than traditional method, whatever the data is close to non-stationarity or stationarity with small sample size. For the data close to non-stationarity, the Burg method has better forecasting ability than traditional time series model. When the data is stationary, the forecasting ability of both Hurvich-Tsai and traditional methods are very similar. In general, Hurvich-Tsai with the traditional method for estimating the autocovariance has the better forecasting ability for the real data. However, the SAR model and Hurvich-Tsai with the traditional method for estimating the autocovariance have the same accuracy of predication. The SAR model is better for the monthly riverflow data of Taiwan if the principle of parsimony of the parameter is considered. |
