On Independent Component Analysis with Stochastic Volatility Models

Consider a multivariate time series where each component series is assumed to be a linear mixture of latent mutually independent stationary time series. Classical independent component analysis (ICA) tools, such as fastICA, are often used to extract latent series, but they don't utilize any information on temporal dependence. Also financial time series often have periods of low and high volatility. In such settings second order source separation methods, such as SOBI, fail. We review here some classical methods used for time series with stochastic volatility, and suggest modifications of them by proposing a family of vSOBI estimators. These estimators use different nonlinearity functions to capture nonlinear autocorrelation of the time series and extract the independent components. Simulation study shows that the proposed method outperforms the existing methods when latent components follow GARCH and SV models. This paper is an invited extended version of the paper presented at the CDAM 2016 conference.

[1]  Joni Virta,et al.  The squared symmetric FastICA estimator , 2015, Signal Process..

[2]  Simon A. Broda,et al.  Financial Valuation and Risk Management Working Paper No . 454 CHICAGO : A Fast and Accurate Method for Portfolio Risk Calculation , 2008 .

[3]  J. Cardoso,et al.  Blind beamforming for non-gaussian signals , 1993 .

[4]  Klaus Nordhausen,et al.  Blind Source Separation Based on Joint Diagonalization in R: The Packages JADE and BSSasymp , 2017 .

[5]  Daniel Peña,et al.  A conditionally heteroskedastic independent factor model with an application to financial stock returns , 2012 .

[6]  R. Serfling,et al.  On Invariant Coordinate System (ICS) Functionals , 2012 .

[7]  K. Nordhausen,et al.  A more efficient second order blind identification method for separation of uncorrelated stationary time series , 2016 .

[8]  K. Nordhausen,et al.  New independent component analysis tools for time series , 2015 .

[9]  E. Oja,et al.  Independent component analysis for financial time series , 2000, Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373).

[10]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[11]  Klaus Nordhausen,et al.  Separation of Uncorrelated Stationary time series using Autocovariance Matrices , 2014, Journal of Time Series Analysis.

[12]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[13]  David S. Matteson,et al.  Time-Series Models of Dynamic Volatility and Correlation , 2011, IEEE Signal Processing Magazine.

[14]  W. Härdle,et al.  Portfolio value at risk based on independent component analysis , 2007 .

[15]  Aapo Hyvärinen,et al.  Blind source separation by nonstationarity of variance: a cumulant-based approach , 2001, IEEE Trans. Neural Networks.

[16]  Jean-Francois Cardoso,et al.  Source separation using higher order moments , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[17]  K. Nordhausen,et al.  Fourth Moments and Independent Component Analysis , 2014, 1406.4765.

[18]  Klaus Nordhausen,et al.  A New Performance Index for ICA: Properties, Computation and Asymptotic Analysis , 2010, LVA/ICA.

[19]  Tian-Shyug Lee,et al.  Application of Independent Component Analysis Preprocessing and Support Vector Regression in Time Series Prediction , 2009, 2009 International Joint Conference on Computational Sciences and Optimization.

[20]  S. Taylor Financial Returns Modelled by the Product of Two Stochastic Processes , 1961 .

[21]  D. Chakrabarti,et al.  A fast fixed - point algorithm for independent component analysis , 1997 .

[22]  Zhiguo Jiang,et al.  Blind source separation with nonlinear autocorrelation and non-Gaussianity , 2009 .

[23]  Gregor Kastner,et al.  Dealing with Stochastic Volatility in Time Series Using the R Package stochvol , 2016, 1906.12134.