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Discrete Dynamics in Nature and Society
Volume 2014, Article ID 365204, 7 pages
http://dx.doi.org/10.1155/2014/365204
Research Article

Functional Principal Components Analysis of Shanghai Stock Exchange 50 Index

College of Mathematics and Informatics, North China University of Water Conservancy and Hydroelectric Power, Zhengzhou 450000, China

Received 28 February 2014; Revised 23 May 2014; Accepted 4 July 2014; Published 22 July 2014

Academic Editor: Seenith Sivasundaram

Copyright © 2014 Zhiliang Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The main purpose of this paper is to explore the principle components of Shanghai stock exchange 50 index by means of functional principal component analysis (FPCA). Functional data analysis (FDA) deals with random variables (or process) with realizations in the smooth functional space. One of the most popular FDA techniques is functional principal component analysis, which was introduced for the statistical analysis of a set of financial time series from an explorative point of view. FPCA is the functional analogue of the well-known dimension reduction technique in the multivariate statistical analysis, searching for linear transformations of the random vector with the maximal variance. In this paper, we studied the monthly return volatility of Shanghai stock exchange 50 index (SSE50). Using FPCA to reduce dimension to a finite level, we extracted the most significant components of the data and some relevant statistical features of such related datasets. The calculated results show that regarding the samples as random functions is rational. Compared with the ordinary principle component analysis, FPCA can solve the problem of different dimensions in the samples. And FPCA is a convenient approach to extract the main variance factors.