臺灣地區汽車持有預測模式之建構與評估：ARMAX之應用

Construction and Evaluation of A Forecasting Model for Automobile Ownership in Taiwan: An Application ARMAX

臺灣地區汽車持有數的逐年成長反映出臺灣正無法避免地逐漸邁向高機動車輛依存性，而此現象會附加產生經濟、社會與環境上的成本，加上國家地區內汽車持有數量的預測對於國家經濟、未來能源需求與污染排放預測有其關鍵性，因此掌握未來的汽車持有數量便顯得尤其重要。本研究有別於傳統預測之迴歸模型，使用結合迴歸模式與時間數列模式之ARMAX動態迴歸模式建立汽車持有預測模式。模式估計結果顯示汽車持有數量可以透過一階自我迴歸、落後一期之移動平均與國內生產毛額、交通類消費者物價指數兩經濟變數加以解釋，且加入經濟解釋變數的ARMAX（1,1）模式具有高預測精確度，其樣本內、樣本外之評估結果均優於不含解釋變數之AR（2）與ARMA（1,1）模式，ARMAX（1,1）模式確實能解釋與萃取汽車持有數的訊息。最後本研究應用ARMAX（1,1）模式，預測未來民國96年至民國101年之汽車持有數量。

The continuous increment in automobile ownership in Taiwan reflects the fact that the Taiwan society has been increasing its reliance on motor vehicles, which in turn increase the economic, social, and environmental cost. In addition, the prediction of domestic automobile ownership is critical to the projection of a nation's economy, energy needs, and pollution production. Therefore, an accurate prediction of automobile ownership becomes extremely important. Different from traditional regression approaches, this research combines regression models and time-series models as an ARMAX dynamic regression model to predict automobile ownership. The results indicated that the quantity of automobile ownership can be estimated by the GDP and transportation and communication CPI with a first-order autoregressive and a stochastic moving average filter at lag 1 with a high level of accuracy. The model ARMAX(1,1) with economic variables outperforms the models without any explanatory variables such as AR(2) and ARMA(1,1). This result demonstrates the excellent ability of the proposed model ARMAX(1,1) to explain and extract the information of automobile ownership. Finally, this research applied the model ARMAX(1,1) to predict the automobile ownerships from 2007 to 2012 in Taiwan.