股票价格技术分析的数学原理及超前预测方法  

Mathematical Principles of Technical Analysis of Stock Prices and Methods of Forward Forecasting

作　　者：高宏[1] GAO Hong(Tsinghua University,Beijing 100084)

机构地区：[1]清华大学,北京100084

出　　处：《中国商论》2023年第12期121-125,共5页China Journal of Commerce

摘　　要：传统技术分析方法无法在数学上证明其有效性,使用古老而原始的图形和指标分析手段来获取股票价格中的基本波动信息,其分析结果不仅大大滞后于实际的股票价格变化趋势,还受随机噪声的严重干扰,具有很大的不确定性。本文根据《数理金融学》的实证研究结果建立了股票价格数学模型,从数学上证明了在微观尺度上表现出随机性和不可预测性的股票价格波动,在宏观尺度上具有总体的确定性和可预测性,并设计出LPD数字低通差分滤波器,可从股票价格数据中分离出相位超前的基本波动微分信号,提前预测基本波动的运动状态,以期为股票投资者提供及时有效的科学决策依据。Traditional technical analysis methods cannot be mathematically proven to be effective;using old and primitive graphical and indicator analysis tools to obtain information on fundamental fluctuations in stock prices,and their analytical results not only lag significantly behind actual stock prices,but are also subject to severe interference from stochastic noise and are highly uncertain.This paper establishes a mathematical model of stock prices based on the results of the empirical study of Mathematical Finance,demonstrating mathematically that stock price fluctuations,which exhibit randomness and unpredictability on the microscopic scale,have overall certainty and predictability.The digital low-pass differential(LPD)filter is designed to separate the phase ahead fundamental volatility differential signals from stock price data,predict the movement state of fundamental volatility in advance to provide stock investors with a timely and effective basis for scientific decision-making.

关 键 词：技术分析 股票价格数学模型 布朗噪声 微分超前预测 LPD低通差分滤波器 

分 类 号：F830.91[经济管理—金融学]