應用灰色理論預測臺灣地區房地產價格之研究

Applying Gray Theory to Forecast the Real Estate Price in Taiwan

灰色理論具有預測不確定訊息及數學基礎簡單的特性，本研究依據內政部不動產資訊平台公告之建物住宅買賣契約價格資料，試以灰色預測GM（1,1）模型分析步驟來預測房地產價格趨勢之可行性。本研究以全國及五大都市為預測標的獲得之成果顯示，年度平均及季平均的建物住宅買賣契約價格平均單價之預測值平均誤差百分比分別約在.05%~1.36%以及0.30%~1.24%之間，皆屬於優良的預測水準，具相當高的參考價。另以民國103年四季的住宅平均單價來預測民國104年Q1及Q2的價格時，顯示以季時段的近期數據來預測未來房地產價格時，相較於以年度別的長期數據來預測出的結果，更能符合近期房地產價格波動的趨勢。經與104年Q1之實際登錄價格比對結果預測值與真實值之誤差百分比分別為全國5.3%、新北市2.51%、臺北市0.88%、臺中市0.11%、臺南市1.55%以及高雄市的2.79%，均具有良好的預測精確度，研究成果顯示灰色理論GM（1,1）預測模型具有相當可靠度的預測可行性。

Grey theory can predict uncertain message with the feature of a simple mathematical basis. According to the building contracts of sold price announced in official real estate information platform in Taiwan, this study tried to use Gray model GM(1,1) to predict the feasibility of the real estate price trends. By investigating the whole country and five cities in Taiwan as predicted subjects, the obtained results show that the predicted error value for contract prices of residential building in annual average unit price was between 0.05% to 1.36%. And the predicted error value of quarterly average unit price is between 0.30% to 1.24%. All the predicted data are belonging to the excellent forecast level with very high reference value. Furthermore, applying the seasonal data of 2014 to predict the average price of residential transaction in 2015 Q1 and Q2, it shows that the predict value by seasonal data is more accurate than that forecasted by the annual value, and more consistent to the recent trend of price fluctuations. After comparing with the actually registered price in Q1 of 2015, the error is 5.3 percent nationwide, 2.51% in New Taipei, 0.88% in Taipei, 0.11% in Taichung, 1.55% in Kaohsiung, and 2.79% in Tainan. All of these data show high accuracy of prediction. Therefore, this research reveals that Gray Model GM(1,1) have quite reliable feasibility to predict the trends of real estate price in Taiwan.