我國各級學校未來學生數之預測

Abstract

本研究嘗試以時間數列的方法來預測我國各級學校未來的學生數，以供教育計劃之素材。首先比較時間數列之ARIMA預測方法與其他預測方法之準確性。然後介紹時間數列預測方法之基本概念，並進行預測。預測之前必須先確定模式。模式辨認過程是先差分，以差分過的自我相關函數與偏自我相關函數達顯著的時差來判斷移動平均過程與自我迴歸過程的秩。如殘差的自我相關函數皆不達顯著，則表示模式適合。如同時有多個模式適合，則取殘差均方和最小的模式，另外加上常數，以建立另一方案。各以兩方案來預測。兩方案在未來實現的可能性，則以殘差均方和及教育政策之趨勢來研判。近年來由於人力規劃及教育計劃的實際需要，人力推估與預測技術逐漸被重視及應用，預測方法也不斷的推陳出新，以期能得到更精確的預測值。本文試圖比較時間數列預測方法與其他預測方法的準確性，之後應用時間數列預測方法來預測我國各學學校學生數，以供教育計劃之參考。This study applies the time series analysis to forecast the future student number of each school level. The predicted values might be used in the educational planning. At first, different forecasting methods were compared in view of their predicting precision, then the basic concepts of time series analysis were discussed. The forecasting procedure used in this study follows: (a) differencing, (b) identifying the orders of autoregressive process and moving average process according to the significant lags in "pacf" and "acf" of differenced time series respectively, (c) accepting the model whose "acf" of resifuals are all not significant and which has least residual mean squares, (d) constant component was added to the selected model to build an alternative model. The realizability of each alternative model was discussed according to their residual mean squares and trend of educational policies.