本研究以台股指數為主要對象，其影響台股指數變動之主要因素，計有五大構面24個變數，包括一為總體經濟因素(含7個變數)，二為重要國外股價指數(含7個變數)，三為資金籌碼面(含4個變數)，四為企業獲利能力(含5個變數)，五為其他因素(含1個變數)。樣本期間為2011年1月至2022年12月，採用月資料(共有144個月)。

本研究方法包括三大部分，一為主成分分析，二為共線性檢定與逐步迴歸分析，三為建立三種研究模型(含複迴歸模型、ARIMA模型、VAR模型)之估計與預測，以模型誤差之大小來決定其優劣。有關建立三種模型來選取最佳模型，並做未來之預測，乃為本研究之特色或貢獻。

從主成分分析結果可知，本研究只萃取特徵值大於1的主成分，共有4個主成分。其中第一主成分對所有變數的解釋比例為55.70%，第二主成分為11.80%，第三主成分為8.56%，第四主成分為5.40%，合計已達 81. 46%。

將24個自變數再進行複迴歸分析，從五大構面影響台股指數之變動因素觀察，其影響最大者為企業獲利能力構面，其次(考量相關性)為重要國外股價指數構面，第三為總體經濟因素構面，至於資金籌碼面，其他因素構面似無影響性。

要建立ARIMA模型，須先作單根檢定，並依AIC訊息準則，可獲得其適當的ARIMA(2,1,2)模型，其估計結果4個變數[含AR(1)、AR(2)、MA(1)、MA(2)]均很顯著。F值亦顯著，D-W值(2.013475)接近於2，表示其殘差項無自我相關。惟R2判定係數為 0.096380係偏低。

關於三種模型之預測結果，每種模型均含樣本內估計(11年月資料)，樣本外預測(1年月資料)二部分。並作三種模型誤差之比較，以RMSE(均方根誤差)與MAE
(平均絕對誤差)來衡量，其數值越小者越佳。其中以縮減式VAR模型之RMSE與MAE均最小，排名第一；其次以複迴歸模型，其RMSE與MAE均名列第二；而ARIMA模型，其RMSE與MAE均居第三殿後。

本研究因採用三種模型，蒐集25個變數資料，並作深入探討，以獲得最佳預測模型，應可提供給主管機關、證劵業及投資者作為監理、經營及投資之參據。

This study takes the Taiwan stock index as the main object. The main factors affecting the changes of the Taiwan stock index include five dimensions and 24 variables, including one is the overall economic factor (including 7 variables), and the other is the important foreign stock price index (Including 7 variables), the third is the level of capital chips (including 4 variables), the fourth is the profitability of the enterprise (including 5 variables), and the fifth is other factors (including 1 variable). The sample period is from January 2011 to December 2022, using monthly data (144 months in total).

This research method includes three parts, one is principal component analysis, the other is collinearity test and stepwise regression analysis, the third is the estimation and prediction of three research models (including multiple regression model, ARIMA model, VAR model), and the model error. The size determines its pros and cons. It is the feature or contribution of this study to establish three models to select the best model and make future predictions.

From the results of principal component analysis, it can be seen that this study only extracts principal components with eigenvalues greater than 1, and there are 4 principal components in total. Among them, the first principal component explained 55.70% of all variables, the second principal component accounted for 11.80%, the third principal component accounted for 8.56%, and the fourth principal component accounted for 5.40%, totaling 81.46%.

Perform multiple regression analysis on the 24 independent variables, and observe the factors that affect the Taiwan stock index from the five aspects. The most influential factor is the dimension of corporate profitability, followed by (considering the correlation) the dimension of important foreign stock prices, the third dimension is the overall economic factor, as for the capital bargaining chip aspect, other factors seem to have no influence.

To establish an ARIMA model, a single root test must be done first, and the appropriate ARIMA(2,1,2) model can be obtained according to the AIC information criterion, and the estimated results have 4 variables [including AR(1), AR(2), MA(1), MA(2)] are all significant. The F value is also significant, and the D-W value (2.013475) is close to 2, indicating that the residuals have no self-correlation. But the coefficient of determination of R2 is 0.096380 which is low.

Regarding the prediction results of the three models, each model includes two parts: in-sample estimation (11-year-month data) and out-of-sample prediction (1-year-month data). And compare the errors of the three models, using RMSE (root mean square error) and MAE(mean absolute error), the smaller the value, the better. Among them, the RMSE and MAE of the reduced VAR model are the smallest, ranking first; followed by the multiple regression model, its RMSE and MAE are both ranked second; and the ARIMA model, its RMSE and MAE are both ranked third.

This study adopts three models, collects 25 variable data, and conducts in-depth discussions to obtain the best prediction model, which should be provided to the competent authorities, securities industry and investors as a reference for supervision, operation and investment.

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