灰色GM(1,1)模型於人口預測模式之應用－以彰化縣為例

The Concept of GM (1,1) Model and Its Application in the Population Prediction in Changhua County

賴家瑞(Chia-Jui Lai) ； 溫坤禮(Kun-Li Wen)

《智慧科技與應用統計學報》 2卷1期 (2004/06) Pp. 91-108

https://doi.org/10.29807/JTITAS.200406.0006

摘要

本研究主要目的在於探討灰色GM(1,1)模型應用於人口預測問題中的適用性。文中以彰化地區歷年資料為基礎，以灰色GM(1,1)模型進行實證研究，並將所得結果與傳統之人口預測方法（如算術級數法、簡單線型模式、指數曲線預測模式以及ARIMA模式等）所得之結果，進行比較分析。由於灰色預測模型具有建模樣本少、計算簡便等特性；因此，研究中亦探討在不同的等距取樣點下，灰色GM(1,1)模型的預測表現。實證結果顯示：針對彰化縣人口資料，在上述各預測模式中，以ARIMA模型在樣本內配適及樣本外預測表現較佳。然而，在建模數據僅有四點的情況下，灰色GM(1,1)模型亦有不錯的預測能力表現。研究結果可作為相關部門在考量精度及建模成本等因素下，選擇預測模型時的參考依據。

關鍵字

灰色GM 1,1模型 ； 人口預測 ； ARIMA模式

並列摘要

This article discusses the forecasting performance of grey GM (1,1) model in population prediction problem. Several traditional methods such as arithmetic progression method, linear regression model, exponential model and ARIMA model are also applied to the case of population predicting of Changhua County, Taiwan.
There are several advantages of Grey model such as easily computing and small data needed for model construction. We also discuss the forecasting performances of grey models in different sample sizes. Results indicate that the ARIMA model is the best one while predicting of Changhua County, Taiwan among all models. However, Grey model also performs well even the sample size is 4, which demonstrates the applications and efficiency of Grey model in practice.

並列關鍵字

GM 1,1 model ； Population Prediction ； ARIMA model