A First Application of Independent Component Analysis to Extracting Structure from Stock Returns

Abstract

Abstract. This paper discusses the application of a modern signal processing technique known as independent component analysis (ICA) or blind source separation to multivariate financial time series such as a portfolio of stocks. The key idea of ICA is t o linearly map the observed multivariate time series into a new space of statistically independent components (ICs). This can be viewed as a factorization of the portfolio since joint probabilities become simple products in the coordinate system of the ICs. We apply ICA to three years of daily returns of the 28 largest Japanese stocks and compare the results with those obtained using principal component analysis. The results indicate that the estimated ICs fall into two categories, (i) infrequent but large shocks (responsible for the major changes in the stock prices), and (ii) frequent smaller fluctuations (contributing little to the overall level of the stocks). We show that the overall stock price can be reconstructed surprisingly well by using a small number of thresholded weighted ICs. In contrast, when using shocks derived from principal components instead of independent components, the reconstructed price is less similar to the original one. Independent component analysis is a potentially powerful method of analyzing and understanding driving mechanisms in financial markets. There are further promising applications to risk management since ICA focuses on higher-order statistics.

Portfolio Value at Risk Based on Independent Components Analysis

“…Pro-moted by the success in engineering, ICA has been applied in different areas such as brain imaging (Duann, Jung, Kuo, Yeh, Makeig, Hsieh and Sejnowski, 2002) and telecommunication study (Ristaniemi, Raju and Karhunen, 2002). An early implementation of ICA in financial time series is given in Back and Weigend (1998), drawing comparisons of ICs and principal components (PCs) applied to 28 Japanese stocks from 1986 to 1989. Few contributions however exist for the application of ICA in risk management.…”

Independent Multiresolution Component Analysis and Matching Pursuit

“…We then form a temporally aggregated time series of correspondent ve-minute 5m data from the original one; thus, they are simply given by the average of components sampled at the time interval of one minute. The aggregated sample consists of 7092 observations 8 . Model design tasks involve the representation of features such as short and long range dependence, hidden periodicities, external shocks, surprise variable e ects and other factors with impact on prices and returns Andersen & Bollerslev, 1997.…”

Eliminating indeterminacy in ICA

“…The ICA is often used as a preprocessing stage in applications that identify, process or further analyse the separated signals, e.g. pattern recognition, speech coding and compression [25,6]. Eliminating the ICA indeterminacy has a great in uence to the subsequent processes.…”