利用局部赫斯特指數預測國內股票市場

Abstract

水文學家Hurst被稱為「尼羅河之父」，其所發展的R/S分析法用於研究河水流量的長期變化，藉之建造合適規模之水壩，衡量時間序列持續性的赫斯特指數便因其而得名。 金融市場大規模崩盤一直是備受關注的研究主題，由於無法被效率市場假說所解釋，因此學者轉而尋求建構在其它理論基礎上的方法作為研究工具，R/S分析法即為一例。Mandelbrot(1975)首次將R/S分析法運用於股票市場，並根據研究結果建構出碎形市場假說。近年來，也有越來越多學者將赫斯特指數用來衡量正向持續性的概念，套用到短期的趨勢預測上，並證實也有一定的預測能力。 本研究以R/S分析法衡量臺灣股票市場過去32年來的長記憶現象，透過文獻探討、分析比較計算過程的各項參數，建構出適當的局部赫斯特指數求算方式，並進一步探討其預測效力，特別是市場大規模崩盤的預警效果。最終，我們將時間窗長度設定為160天，計算過程的子序列長度範圍介於10到80天之間。將局部赫斯特指數之時間序列與臺灣發行量加權股價指數進行比較後，我們有以下幾點結論： 1.長期來看，台灣的局部赫斯特指數有下降趨勢，正向持續性逐漸削弱。 2.局部赫斯特指數的短期波動相當大，若單就某一特定時點之局部赫斯特指數進行預測，其解釋力不佳，移動平均具有較佳之解釋力。 3.局部赫斯特指數雖然具有一定之預警效果，但其訊號出現到實際市場崩盤之間存在一段約為半年的延遲時間，對於未來9個月的報酬有最佳之預測效力。

Harold E. Hurst, “Father of the Nile”, is a hydrologist who was devoted to the research of long-term persistency for river flow, and he developed Rescaled Range Analysis(R/S analysis), which is still an useful statistical tool today. The famous “Hurst exponent”, as a measurement of persistency, was named after him. Sharp crashes in financial market, which cannot be explained by Efficient Market Hypothesis, is always one of the most popular topics, and researchers have used methods structured on other thesis as a tool to measure it. Mandelbrot(1975) was the one who brought R/S analysis to the stock market, and he constructed Fractal Market Hypothesis based on his research. Nowadays, more and more papers discussed about using Hurst exponent as a tool for short-term technical analysis to predict future price, and the predictive power has been proved. I used R/S analysis to measure the long memory in Taiwan stock market for the past 32 years, and constructed appropriate methodology to build the local Hurst exponent time series through paper review and discussing parameter settings. I tried to find out whether the local Hurst exponent, built with R/S analysis, is good at prediction or not. Finally, I decided to set 160 days as the time-window length, and use the subseries length ranges from 10 to 80 in the calculation. After comparing the local Hurst exponent time series with TAIEX, here are my conclusions： 1.According to the local Hurst exponent time series data I derived, the value of Hurst exponent keeps dropping over past 32 years at a slow pace, and the market seems to be more efficient. 2.The short-term volatility for local Hurst exponent is large, and it predicts badly if we only use a single point instead of a series pattern. Moreover, the moving average of the local Hurst exponent, which is less volatile in short term, has better predictive power. 3.Although the local Hurst exponent has predictive power, there is a time lag, about six months, between the warning signal and the time crash happened. As a result, the local Hurst exponent has the best predictive power toward nine-month yields.