On Independent Component Analysis with Stochastic Volatility Models


  • Markus Matilainen University of Turku
  • Jari Miettinen University of Jyvaskyla
  • Klaus Nordhausen University of Turku
  • Hannu Oja University of Turku
  • Sara Taskinen University of Jyvaskyla




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.


Belouchrani A, Abed Meraim K, Cardoso JF, Moulines E (1997). A Blind Source Separation Technique Based on Second Order Statistics. IEEE Transactions on Signal Processing, 45, 434-444.

Bollerslev T (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31(3), 307-327.

Broda SA, Paolella MS (2009). CHICAGO: A Fast and Accurate Method for Portfolio Risk Calculation. Journal of Financial Econometrics, 7(4), 412-436.

Cardoso JF (1989). Source Separation Using Higher Order Moments. In International Conference on Acoustics, Speech, and Signal Processing, pp. 2109-2112.

Cardoso JF, Souloumiac A (1993). Blind Beamforming for Non-Gaussian Signals. In IEE Proceedings F, volume 140, pp. 362-370.

Chen Y, Härdle W, Spokoiny V (2007). Portfolio Value at Risk Based on Independent Component Analysis. Journal of Computational and Applied Mathematics, 205, 594-607.

García-Ferrer A, González-Prieto E, Peña D (2012). A Conditionally Heteroskedastic Independent Factor Model With an Application to Financial Stock Returns. International Journal of Forecasting, 28(1), 70-93.

Hyvärinen A (2001). Blind Source Separation by Nonstationarity of Variance: A Cumulantbased Approach. IEEE Transactions on Neural Networks, 12(6), 1471-1474.

Hyvärinen A, Oja E (1997). A Fast Fixed-Point Algorithm for Independent Component Analysis. Neural Computation, 9, 1483-1492.

Ilmonen P, Nordhausen K, Oja H, Ollila E (2010). A New Performance Index for ICA: Properties Computation and Asymptotic Analysis. In V Vigneron, V Zarzoso, E Moreau,

R Gribonval, E Vincent (eds.), "Latent Variable Analysis and Signal Separation", LNCS, volume 6365, pp. 229-236. Springer, Heidelberg.

Ilmonen P, Oja H, Sering R (2012). On Invariant Coordinate System (ICS) Functionals. International Statistical Review, 80, 93-110.

Kastner G (2016). Dealing with Stochastic Volatility in Time Series Using the R Package stochvol. Journal of Statistical software, 69(5), 1-30.

Lu CJ, Wu JY, Lee TS (2009). Application of Independent Component Analysis Preprocessing and Support Vector Regression in Time Series Prediction. In International Joint Conference on Computational Sciences and Optimization, volume 1, pp. 468-471.

Matilainen M, Miettinen J, Nordhausen K, Oja H, Taskinen S (2016). tsBSS: Tools for Blind Source Separation for Time Series. R package version 0.2, URL https://CRAN.R-project.org/package=tsBSS.

Matilainen M, Nordhausen K, Oja H (2015). New Independent Component Analysis Tools for Time Series. Statistics & Probability Letters, 105, 80-87.

Matteson D, Ruppert D (2011). Time-Series Models of Dynamic Volatility and Correlation. IEEE Signal Processing Magazine, 28(5), 72-82.

Miettinen J, Illner K, Nordhausen K, Oja H, Taskinen S, Theis F (2016). Separation of Uncorrelated Stationary Time Series Using Autocovariance Matrices. Journal of Time Series Analysis, 37(3), 337-354.

Miettinen J, Nordhausen K, Oja H, Taskinen S (2014). fICA: Classical, Reloaded and Adaptive FastICA Algorithms. R package version 1.0-2, URL http://CRAN.R-project.org/package=fICA.

Miettinen J, Nordhausen K, Oja H, Taskinen S, Virta J (2017a). The Squared Symmetric FastICA Estimator. Signal Processing, 131, 402-411.

Miettinen J, Nordhausen K, Taskinen S (2017b). Blind Source Separation Based on Joint Diagonalization in R: The Packages JADE and BSSasymp. Journal of Statistical Software, 76(2). URL http://dx.doi.org/10.18637/jss.v076.i02.

Miettinen J, Taskinen S, Nordhausen K, Oja H (2015). Fourth Moments and Independent Component Analysis. Statistical Science, 30, 372-390.

Oja E, Kiviluoto K, Malaroiu S (2000). Independent Component Analysis for Financial Time Series. In Adaptive Systems for Signal Processing, Communications, and Control Symposium, pp. 111-116.

R Core Team (2016). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. R version 3.2.4, URL http://www.R-project.org/.

Shi Z, Jiang Z, Zhou F (2009). Blind Source Separation with Nonlinear Autocorrelation and Non-Gaussianity. Journal of Computational and Applied Mathematics, 223(1), 908-915.

Taskinen S, Miettinen J, Nordhausen K (2016). A More Efficient Second Order Blind Identification Method for Separation of Uncorrelated Stationary Time Series. Statistics & Probability Letters, 116, 21-26.

Taylor SJ (1982). Financial Returns Modelled by the Product of Two Stochastic Processes - A Study of Daily Sugar Prices 1961-79. In OD Anderson (ed.), Time Series Analysis: Theory and Practice 1, pp. 203-216. Springer, North-Holland, Amsterdam.

Wuertz W, Rmetrics Core Team (2013). fGarch: Rmetrics - Autoregressive Conditional Heteroskedastic Modelling. R package version 3010.82, URL http://CRAN.R-project.org/package=fGarch.




How to Cite

Matilainen, M., Miettinen, J., Nordhausen, K., Oja, H., & Taskinen, S. (2017). On Independent Component Analysis with Stochastic Volatility Models. Austrian Journal of Statistics, 46(3-4), 57–66. https://doi.org/10.17713/ajs.v46i3-4.671