Local normalization: Uncovering correlations in non-stationary financial time series

The measurement of correlations between financial time series is of vital importance for risk management. In this paper we address an estimation error that stems from the non-stationarity of the time series. We put forward a method to rid the time series of local trends and variable volatility, while preserving cross-correlations. We test this method in a Monte Carlo simulation, and apply it to empirical data for the S&P 500 stocks.

[1]  C. Peng,et al.  Mosaic organization of DNA nucleotides. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  V. Plerou,et al.  Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series , 1999, cond-mat/9902283.

[3]  Thomas Guhr,et al.  Power mapping with dynamical adjustment for improved portfolio optimization , 2010 .

[4]  W. Sharpe.  CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK* , 1964 .

[5]  T. Guhr,et al.  RANDOM-MATRIX THEORIES IN QUANTUM PHYSICS : COMMON CONCEPTS , 1997, cond-mat/9707301.

[6]  V. Plerou,et al.  Random matrix approach to cross correlations in financial data. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  H. Stanley,et al.  Detrended cross-correlation analysis: a new method for analyzing two nonstationary time series. , 2007, Physical review letters.

[8]  Testing for strict stationarity in financial variables , 2009 .

[9]  I. Kondor,et al.  Noisy Covariance Matrices and Portfolio Optimization II , 2002, cond-mat/0205119.

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

[11]  J. Durbin,et al.  Techniques for Testing the Constancy of Regression Relationships Over Time , 1975 .

[12]  J. Bouchaud,et al.  Noise Dressing of Financial Correlation Matrices , 1998, cond-mat/9810255.

[13]  H. Stöckmann,et al.  Quantum Chaos: An Introduction , 1999 .

[14]  Imre Kondor,et al.  Estimated correlation matrices and portfolio optimization , 2003, cond-mat/0305475.

[15]  R. C. Merton,et al.  Theory of Rational Option Pricing , 2015, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[16]  Matteo Marsili,et al.  Algorithms of maximum likelihood data clustering with applications , 2002 .

[17]  Olivier Ledoit,et al.  Improved estimation of the covariance matrix of stock returns with an application to portfolio selection , 2003 .

[18]  H. Stanley,et al.  Cross-correlations between volume change and price change , 2009, Proceedings of the National Academy of Sciences.

[19]  H. Stanley,et al.  Effect of trends on detrended fluctuation analysis. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Heidelberg,et al.  A New Method to Estimate the Noise in Financial Correlation Matrices , 2002, cond-mat/0206577.

[21]  G. Chow.  Tests of equality between sets of coefficients in two linear regressions (econometrics voi 28 , 1960 .

[22]  Walter Krämer,et al.  The CUSUM test for OLS residuals , 1992 .

[23]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[24]  F. Haake.  Quantum signatures of chaos , 1991 .

[25]  M Marsili,et al.  Data clustering and noise undressing of correlation matrices. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[27]  H. Stanley,et al.  Quantifying cross-correlations using local and global detrending approaches , 2009 .