基于主成分分析与Fourier变换的动态投资组合

武  丹; 李星野

基于主成分分析与Fourier变换的动态投资组合

引用本文：武丹，李星野.基于主成分分析与Fourier变换的动态投资组合[J].经济数学,2019,(4):20-26

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作者	单位
武丹，李星野	（上海理工大学管理学院，上海 200093）

中文摘要:提出了一种将主成分分析与Fourier变换组合的资产投资组合方法.对于N个资产，首先利用主成分分析中第一主成分确定各资产的组合权重并建立投资组合，利用Fourier变换获得该组合残差的复合周期趋势，最后利用ARMA模型对趋势残差进行区间预测.为使资产保值，当组合股价达到最低点时，各资产以第一主成分对应权重进行组合建仓；当组合股价反向上升达到最高点时，则以第N主成分对应权重进行组合并调仓.在实证模拟方面，选取2016年1月4日-2018年6月8日全球股票主要指数的收盘价数据进行实证分析.模拟结果表明：基于主成分分析的投资组合在收益及资产保值方面表现更佳.

中文关键词:主成分分析投资组合 Fourier变换 ARMA模型

Dynamic Portfolio Based on Principal Component Analysis and Fourier Transform

Abstract:This paper proposes a method for the portfolio of assets based on the principal component analysis and Fourier transform. For the N assets, the first principal component in principal component analysis is used to determine the portfolio weight of each asset and to establish the investment portfolio. The Fourier transform is used to obtain the complex periodic trend of the residual. Finally, the residuals of the trend are modeled by ARMA model to obtain the prediction interval. In order to maintain the value of assets, when the portfolio stock price reaches the lowest point, the first principal component of each asset corresponds to the weight of the portfolio. When the reverse rise of the portfolio stock price reaches the highest point, the corresponding weight of the N principal component will be combined and adjusted. In terms of empirical, this paper selected the closing prices of major global stock indexes from January 4, 2016 to June 8, 2018 for empirical analysis. The results show that the portfolio based on principal component analysis performs better in terms of return and asset preservation.

keywords:principal component analysis portfolio Fourier transform ARMA model

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