應用灰色理論於黃金價格之預測

Abstract

自古以來黃金一直是大家最喜愛的飾品，尤其是其本身具保值性、不易腐蝕性及對抗通膨之特性，其用途除作為裝飾用外，主要用於電子產品、半導體工業、牙醫業及工程方面。華麗的黃金飾品，一直是個人的社會地位和財富的象徵。當傳統金融市場趨向不穩定的時候，黃金市場是一個提供傳統金融市場投資者分散風險的保險市場，因此，投資人會把資金轉到可以避險或投機的市場。其次，美元的貶值、石油價格的上升和通貨膨脹的因素，都會造成黃金價格的上漲。近幾年來黃金在投資性的需求呈現大幅增加的趨勢，已成為重要的金融投資工具之一，它同時具有貨幣和貴金屬的性質，是一種相當特殊之投資商品，這也說明了黃金需求的轉變，正由實體現貨轉變為投資理財的重要工具。 本研究主要在預測黃金價格之未來趨勢，黃金價格之變動，大部份原因係來自於黃金本身供需之影響。因此藉由了解任何影響黃金供需之因素，並根據黃金過去之變動情形，針對黃金價格的未來走勢進行預測係為本研究之目的。研究方法係採取灰色理論中之GM(1,1)模型為建構模式，研究之內容係以世界黃金協會(World Gold Council,WGC)之黃金價格的歷史資料，樣本為1993年至2012年間之黃金價格均價。另保留2010年至2012年之年月季資料作為樣本外預測之用。 本研究採取GM(1，1)預測模型，並用MAPE來作預測之精確度，證明其預測能力。實證成果發現本文所採用之GM(1,1)模型之預測能力佳，其MAPE值皆小於10%~20%，具有良好之預測能力。

Since ancient times, gold has always been everyone 's favorite metal; especially with the stability of value against fluctuation, durability against most corrosive compounds, plus it is also a way to hedge against inflation. In addition to making decorations, gold is mainly used in electronic components, semiconductor industry, dentistry and engineering. Possessing gold is also a way to display an individual's social status and wealth. When investors are facing instability in general financial markets, the gold market provides a choice of risk diversification, where they are able to do hedging or speculation. Observation shows that the price of gold rises as the US dollar depreciates, or as the oil prices rise, and when inflation occurs. In recent years, a substantial increase of market demand for gold shows that gold has become one of the most important financial instruments. Since it’s a special article with natures of both currency and precious metal, the shape of market demand for gold has changed and transforms gold from a mere physical item into an important tool for investment. This study focuses on predicting the future trend of gold price, which is mostly affected by the market supply and demand itself. It applied the theory of grey GM (1,1) as a construction prediction model. Research is based on the historical data from World Gold Council (WGC), 2006. which includes the average gold price during a sampling period from 1993 to 2012. I reserve data ranging from 2010 to 2012 to conduct out-of-sample forecast。 I take the GM (1,1) prediction model to test the accuracy of the prediction, and use Mean Absolute Percentage Error (MAPE) test to prove its ability to forecast. The study found that, the MAPE values ranged between 10% and 20 % or less, thereby concluding that the GM (1,1) model has a good predictive ability for gold price.