台灣加權股價指數漲跌方向之Probit模型預測

2019年末，新冠疫情在中國大爆發，隨即蔓延至全球，在最初的一年多里，因著對病毒的認識不足以及疫苗資源的匱乏，各國雖然防疫政策、醫療水平雖不盡相同，但實體經濟均受到了非常大的衝擊，全球經濟一度停擺。各國為了刺激經濟，紛紛調降利率，這導致了股市的大漲，連加密貨幣這種虛擬資產價格也節節攀升。2021年後，許多國家從疫情陰霾中走出來，出現了報復性消費、旅遊，但此時全球供應鏈並未及時恢復，通膨開始蔓延並受到广泛關注。2022年4月24日，俄烏戰爭正式打響，戰爭造成了全球糧食價格和能源價格的上漲，國際關係和地緣政治成為影響經濟發展的主旋律，通膨繼續飆升。根據美國勞工部勞動統計局（BLS）資料顯示，2022年6月，美國CPI年增率為9.1%，創下40年新高，從台灣行政院主計處的資料來看，台灣的CPI也在緩步上升，3月衝破3%，六月更是達到了3.59%，創下14年新高。在這樣高通膨的時代背景下，人們開始尋求定存以外的投資工具，試圖戰勝通膨。然而股票、選擇權、期貨這些高收益投資工具的背後往往也伴隨著較高的風險，本研究將重點放在了台灣加權股價指數的漲跌方向的預測上，試圖通過整合各類指數的歷史資料並找到一個趨勢，預測未來台指的漲跌，進而幫助投資人投資股票、選擇權與期貨。此研究蒐集民國106年10月20日至111年10月19日共計5年之交易日之資料，包括了文獻中常常被討論並認為對於台指有比較重大影響力的一些變數：台股成交值、美國道瓊斯工業指數平均值（DJI）、美國標準普爾500指數、美國納斯達克綜合指數。利用計量中的Probit模型，算出每日漲跌的機率，以此推斷隔日台指的漲跌。研究結果顯示：採用Probit模型，利用過去資訊預測隔日台指漲跌在特定條件下能得到比較好的結果，其中成交值與標普500的組合、成交值與道瓊斯與納斯達克的組合、成交值與標普500與納斯達克的組合、成交值與道瓊斯與標普500與納斯達克的組合均達到了74%的綜合預測準確率。單一變數的預測能力總體弱於多變數組合，這些變數對於隔日台指下跌的預測準確率是遠遠高於隔日台指漲的預測率的，模型結果整體優於隨機預測，模型具有一定的適用性。

關鍵字

台灣加權股價指數；股市漲跌預測；台指成交值；美國三大指數； Probit模型

並列摘要

In late 2019, COVID-19 epidemic broke out in China and then spread around the world. For the first year or so, due to the lack of knowledge about the virus and the lack of vaccine resources, the real economy was hit very hard and the global economy came to a halt, despite the different policies on pandemic prevention and the level of medical care in different countries. In order to stimulate the economy, all counties cut their interest rates, which led to a surge in the stock market, and the price of virtual assets such as cryptocurrencies was also rising. After 2021, many countries recovered from the pandemic and experienced compensatory consumption and travel, but the global supply chain did not recover in time and inflation became a widespread concern. The Russia-Ukraine war caused global food and energy prices to rise, and international relations and geopolitics became the main factors affecting economic development, and inflation continued to soar. According to the U.S. Department of Labor's Bureau of Labor Statistics (BLS), in June 2022, the U.S. CPI increased at an annual rate of 9.1%, a 40-year high. From the data of the Office of the Comptroller of the Executive Yuan in Taiwan, Taiwan's CPI is also rising slowly, surpassing 3% in March and reaching 3.59% in June, a 14-year high. Against this backdrop of high inflation, people are seeking investment tools other than fixed deposits to try to beat inflation. However, high yield investment tools such as stocks, options and futures were often with higher risks. This study focuses on the prediction of the rise and fall of Taiwan's weighted stock indices, trying to find a trend by integrating the historical data of various indices to predict the future rise and fall of Taiwan Stock Exchange Capitalization Weighed Stock Index (TAIEX) , and then help investors to invest in stocks, options and futures. This study collected data for five years from October 20,2017 to October 19, 2022, and included some variables that were considered to be important for the TAIEX: Taiwan stock turnover value, Dow Jones Industrial Average (DJI), S&P 500, and NASDAQ Composite Index. The Probit model was used to calculate the daily odds of rise and fall, and to infer the rise and fall of the index on the next day. The results of the study were that the Probit model, which used past information to predict the rise and fall of the TAIEX on the next day, could achieve relatively better results under certain conditions, with the combination of trading volume and S&P 500, trading volume and Dow Jones and NASDAQ, trading volume and S&P 500 and NASDAQ, and trading volume and Dow Jones and S&P 500 and NASDAQ all achieving a combined accuracy of 74%. The predictive power of a single variable was generally weaker than that of a multivariate combination. The predictive accuracy of these variables for the next day's TAIEX fall was much higher than that for the next day's TAIEX rise and the model results was generally better than the stochastic prediction. The model has certain applicability.