ICA-K-means Method For Stock Portfolio

With the rapid development of the global economy,the financial industry has entered a period of vigorous development,and various financial products and financial derivatives have emerged one after another.As an important tool in the field of quantitative investment,the portfolio theory is increasingly concerned by investors and plays a crucial role in the development of the financial investment.The essence of portfolio theory is to search for the optimal portfolio,that is,under the given conditions of profitability,the risks assumed by the investment activities are minimized or the investment profits are maximized under the condition of established investment activity risks.Time series clustering analysis is an important research on time series data mining.Due to the special structure of time series data,the general clustering algorithm are not likely to be directly applied to time series data.In this paper,we proposes a stock portfolio model based on independent component analysis and adapted K-means algorithm.This model first extract features of time series data by independent component analysis,and then applies adapted K-means clustering algorithm to cluster the time series data.According to the clustering analysis results,the Markowitz model with integer programming is presented to construct the investment portfolio.The numerical results shows its effectiveness and feasibility based on the authentic stock time series data.There are mainly two improvements in this article:Firstly,the classical K-means algorithm requires the user to specify the number of clusters in advance and select the initial point.Because of the randomness of the number of clusters and the initial point selection,the global optimal solution cannot be obtained.Inspired by the idea of DBSCAN algorithm,the adapted K-means algorithm is proposed to overcome the two shortcomings,which brings a higher accuracy and stability of the clustering.Secondly,the return sequence of most financial assets is not a Gaussian distribution,but a non-Gaussian distribution with features of leptokurtosis and fat-tail.ICA is the appropriate method of processing non-Gaussian distribution data.Here,ICA is used to extract time series features,the adapted K-means algorithm is applied for clustering and the Markowitz model with integer programming build a portfolio.This paper is organized as follows.Section 1 of this paper briefly reviews the development status of independent component analysis,cluster analysis and portfolio theory.The second section introduces the basic theory and method of independent component analysis.The third section describes the basic theory and algorithm of cluster analysis.In the fourth section,in view of the principles,advantages and disadvantages of K-means algorithm and DBSCAN algorithm,an adapted K-means algorithm is proposed.And then the ICA-K-means model is built.Numerical experiment shows its effectiveness and feasibility in fifth section.There are summaries and future works in the last section.