時間數列分析之轉換函數模式在學生數預測上之應用

Abstract

本研究以二元時間數列分析（轉換函數模式）來預測國小學生數，國中學生數，及年中人口數。預期能有更準確的預測。在ω(B)與δ(B)之秩的決定上，本研究採s=0，1，2，3; r=0，1，2，3之組合，加上實際推理的考量，一一嘗試，以尋求最佳模式。選擇模式所用指標有：殘差的標準誤，AIC，SBC，殘差的自我相關，殘差的逆自我相關，殘差的偏自我相關，殘差與「白化後的自變數列」之交叉相關函數，及預測值與實際值之差。在嘗試錯誤過程中發現，b期（自變數列對依變數列的影響開始顯現的期）的決定不能光靠自變數列與依變數列的交叉相關，而應加上實際推理之考量。本研究顯示，在兩數列有高相關的前題下，轉換函數模式可有效的應用於教育計量上的預測，這對於教育計畫的科學化將有重大的貢獻。In order to improve the predictions made by the single-variate ARIMA time series analysis, the transfer function model is introduced to forecast the number of population, the student number of elementary schools as well as of junior high schools in the ROC. In deciding the optimal orders of δ(B) and w(B), all possible combinations of r=0,1, 2,3, s=0,1,2,3 and additionally the logical inference were considered and tried. The criteria used in checking the adequacy of different models were: standard error estimate, AIC, SBC, autocorrelation function of residuals, inverse autocorrelation function of residuals, partial autocorrelation function of residuals, cross correlation function of residuals with prewhitened input series, and the difference between the predicted value and the real value. It was found that, in determining the b period, which is that the effect of independent series on dependent series begins to appear, in addition to the cross correlation function between two Series, the logical inference should also be included in consideration. The results of the study show that with the prerequisition of high correlation between two series, the transfer function model can be fruitfully applied to quantitative predictions in the educational planning.