Wavelet-based detection of outliers in financial time series

Outliers in financial data can lead to model parameter estimation biases, invalid inferences and poor volatility forecasts. Therefore, their detection and correction should be taken seriously when modeling financial data. The present paper focuses on these issues and proposes a general detection and correction method based on wavelets that can be applied to a large class of volatility models. The effectiveness of the new proposal is tested by an intensive Monte Carlo study for six well-known volatility models and compared to alternative proposals in the literature, before it is applied to three daily stock market indices. The Monte Carlo experiments show that the new method is both very effective in detecting isolated outliers and outlier patches and much more reliable than other alternatives, since it detects a significantly smaller number of false outliers. Correcting the data of outliers reduces the skewness and the excess kurtosis of the return series distributions and allows for more accurate return prediction intervals compared to those obtained when the existence of outliers is ignored.

[1]  Lon-Mu Liu,et al.  Joint Estimation of Model Parameters and Outlier Effects in Time Series , 1993 .

[2]  M. Otto,et al.  Outliers in Time Series , 1972 .

[3]  Seth Greenblatt,et al.  Wavelets in Econometrics: An Application to Outlier Testing , 1994 .

[4]  I. Daubechies,et al.  Multiresolution analysis, wavelets and fast algorithms on an interval , 1993 .

[5]  L. Glosten,et al.  On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks , 1993 .

[6]  R. Tsay,et al.  Outlier Detection in Multivariate Time Series by Projection Pursuit , 2006 .

[7]  Ralph B. D'Agostino,et al.  Goodness-of-Fit-Techniques , 2020 .

[8]  J. Ledolter.  The effect of additive outliers on the forecasts from ARIMA models , 1989 .

[9]  Peter M. Summers.  What Caused the Great Moderation? Some Cross-Country Evidence , 2005 .

[10]  Daniel Peña,et al.  Effects of outliers on the identification and estimation of GARCH models , 2007 .

[11]  P. Franses,et al.  Additive outliers, GARCH and forecasting volatility , 1999 .

[12]  R. Baillie,et al.  The Message in Daily Exchange Rates , 1989 .

[13]  Mauro Gallegati,et al.  Wavelet Variance Analysis of Output in G-7 Countries , 2007 .

[14]  A. Walden,et al.  Wavelet Methods for Time Series Analysis , 2000 .

[15]  Francisco J. Prieto,et al.  Multivariate Outlier Detection and Robust Covariance Matrix Estimation , 2001, Technometrics.

[16]  Amélie Charles,et al.  Forecasting volatility with outliers in GARCH models , 2008 .

[17]  Canan Bilen,et al.  Wavelet-Based Detection of Outliers in Time Series , 2002 .

[18]  M. King,et al.  Influence Diagnostics in Generalized Autoregressive Conditional Heteroscedasticity Processes , 2005 .

[19]  I. Johnstone,et al.  Ideal spatial adaptation by wavelet shrinkage , 1994 .

[20]  Timo Teräsvirta,et al.  An Introduction to Univariate GARCH Models , 2006 .

[21]  S. Mallat.  Multiresolution approximations and wavelet orthonormal bases of L^2(R) , 1989 .

[22]  Lon-Mu Liu,et al.  Forecasting time series with outliers , 1993 .

[23]  Xibin Zhang,et al.  Assessment of Local Influence in GARCH Processes , 2004 .

[24]  T. Bollerslev,et al.  A CONDITIONALLY HETEROSKEDASTIC TIME SERIES MODEL FOR SPECULATIVE PRICES AND RATES OF RETURN , 1987 .

[25]  Ruey S. Tsay,et al.  Analysis of Financial Time Series , 2005 .

[26]  R. Ogden,et al.  Essential Wavelets for Statistical Applications and Data Analysis , 1996 .

[27]  N. Kiefer,et al.  Testing Normality in Econometric Models , 1982 .

[28]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

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

[30]  Marius Ooms,et al.  Outlier detection in GARCH models , 2005 .

[31]  Andre Lucas,et al.  Testing for ARCH in the presence of additive outliers , 1999 .

[32]  Luigi Grossi,et al.  A robust forward weighted Lagrange multiplier test for conditional heteroscedasticity , 2009, Comput. Stat. Data Anal..

[33]  Yazhen Wang.  Jump and sharp cusp detection by wavelets , 1995 .

[34]  Shinichi Sakata,et al.  HIGH BREAKDOWN POINT CONDITIONAL DISPERSION ESTIMATION WITH APPLICATION TO S&P 500 DAILY RETURNS VOLATILITY , 1998 .

[35]  Daniel Peña.  Outliers, Influential Observations, and Missing Data , 2011 .

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

[37]  Jin-Chuan Duan,et al.  Approximating the GJR-GARCH and EGARCH option pricing models analytically , 2006 .

[38]  Stephen L Taylor,et al.  Modelling Financial Time Series , 1987 .

[39]  Sébastien Laurent,et al.  G@RCH 2.2: An Ox Package for Estimating and Forecasting Various ARCH Models , 2001 .

[40]  T. Teräsvirta.  Two Stylized Facts and the Garch (1,1) Model , 1996 .