本文主要探討的議題是預測五年期公債殖利率，十年期公債殖利率與台灣景氣領先指標，而以往常見的時間序列在複變數的預測模型有向量自我迴歸(Vector Autoregressive,VAR) 與誤差修正模型(Error Correction Model,ECM) ，但兩者模型有使用上之差異，前者只能在變數為定態(Stationary) 時使用，若變數為非定態(Non-stationary) ，則需差分成定態變數，不過會使變數失去長期關係或經濟意涵無意義，而後者為變數是非定態下使用，可包含變數之長短期關係，不過兩者均有一共同缺點，即模型內無法納入太多變數。
因此，本文採用Banerjee, Marcellino, and Masten (2014) 所提出之因子擴充誤差修正模型(Factor-Augmented Error Correction Models,FECM) ，是結合ECM 與動態因子模型(Dynamic Factor Model) ，即藉由大量變數資訊萃取出的因子與ECM作結合，使FECM 兼具共整合(cointegration)、誤差修正與容納大量變數資訊的優點。相較於ECM，FECM 裡的變數資訊可以更加全面，故採用FECM 來作預測之模型。而本文採用FECM 來預測五年期公債殖利率，十年期公債殖利率與台灣景氣領先指標，並探討是否會比ECM 預測力好，而研究的實證結果顯示，FECM預測力有比ECM 好。

Forecasting five-year treasury yield, ten-year treasury yield and Taiwan’s leading indicator is main discussion of this paper. Moreover, time series of multivariate variables commonly use Vector Autoregression (VAR) and Error Correction Model (ECM) as its predictive models. There are some differences between these two models. The former can only be used when variables are stationary, if the variables are non-stationary it will need to differentiate to stationary variables, but it will let variables lose its long-term relationship or the implications of the economy. The latter is used for non-stationary variables, it contains the long-term and short term’s relationships of its variables, nevertheless, those two models have a common drawbacks which is the models could not contain lots of variables.
Therefore, this paper use method of Banerjee et al. (2014) and they claimed that Factor-Augmented Error Correction Models (FECM) is combined ECM and Dynamic Factor Model. This model is working through factors that extract from big amount of variables assemble with ECM, it shows that FECM has benefit of cointegration, error correction and having a capacity of big amount of variables. Comparing ECM with FECM, FECM is better than ECM in the theorem, so FECM definitely would be the first choice to used as predictive model. Furthermore, in this paper, it uses FECM to forecast five-year treasury yield, ten-year treasury yield and leading indicator of Taiwan, and to examine if FECM is better than ECM. The result shows that the prediction’s ability of FECM has a higher quality then prediction’s ability of ECM.

誌謝----------------------------------------------------------------------------------iii
摘要----------------------------------------------------------------------------------iv
Abstract-----------------------------------------------------------------------------v
目錄----------------------------------------------------------------------------------vi
圖次----------------------------------------------------------------------------------viii
表次----------------------------------------------------------------------------------ix
1 緒論--------------------------------------------------------------------------------1
1.1 研究動機及目的-------------------------------------------------------------1
1.2 研究架構---------------------------------------------------------------------- 2
2 文獻回顧--------------------------------------------------------------------------3
2.1 債券殖利率相關理論之回顧---------------------------------------------3
2.2 實證文獻之回顧-------------------------------------------------------------5
3 研究方法--------------------------------------------------------------------------7
3.1 ADF 單根檢定----------------------------------------------------------------7
3.2 共整合檢定---------------------------------------------------------------------8
3.2.1 Engle-Granger 兩階段共整合檢定-----------------------------------9
3.2.2 Johanson 共整合檢定----------------------------------------------------9
3.3 擴充因子誤差修正模型-----------------------------------------------------11
3.4 萃取因子方法------------------------------------------------------------------13
3.5 因子個數選取方法-----------------------------------------------------------15
3.6 落後期的選擇------------------------------------------------------------------16
3.7 預測力指標---------------------------------------------------------------------16
3.8 Diebold Mariano 檢定-------------------------------------------------------17
4 實證分析與結果------------------------------------------------------------------18
4.1 資料來源與處理---------------------------------------------------------------18
4.2 因子數量之決定---------------------------------------------------------------19
4.3 決定落後期數-------------------------------------------------------------------19
4.4 共整合檢定----------------------------------------------------------------------20
4.5 估計因子擴充誤差修正模型-----------------------------------------------21
4.6 估計誤差修正模型------------------------------------------------------------22
4.7 樣本內預測力比較------------------------------------------------------------23
4.8 樣本外預測----------------------------------------------------------------------26
5 結論----------------------------------------------------------------------------------28
參考文獻------------------------------------------------------------------------------30
附錄一---------------------------------------------------------------------------------33

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