Correcting outliers in GARCH models: a weighted forward approach

In this paper we develop a weighted forward search (WFS) approach to the correction of outliers in GARCH(1,1) models relying on the foward search (FS) method introduced by Atkinson and Riani (Robust diagnostic regression analysis. Springer, New York, 2000). The WFS is based on a weighting system of each unit and is an extension of the FS from independent to dependent observations. We propose a WFS test for the detection of outliers in GARCH(1,1) models and a WFS estimator of GARCH(1,1) coefficients which automatically corrects outliers. Extensive Monte Carlo simulations show the good performance of the WFS test with respect to other methods of outlier detection for the same models. The marked similarity between the distribution of MLE before strong contamination of the time series and after decontamination through the WFS proves the reliability of the WFS estimator. Finally, the application of the WFS procedure to several financial time series of the NYSE reveals the effectiveness of the method when extreme returns are observed.

[1]  Helena Veiga,et al.  Wavelet-based detection of outliers in financial time series , 2010, Comput. Stat. Data Anal..

[2]  B. Hérault,et al.  entropart : An R Package to Measure and Partition Diversity , 2015 .

[3]  Alessio Farcomeni,et al.  Strong consistency and robustness of the Forward Search estimator of multivariate location and scatter , 2014, J. Multivar. Anal..

[4]  K. Carstensen.  The finite-sample performance of robust unit root tests , 2003 .

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

[6]  Sebastián Ossandón,et al.  On the Nonlinear Estimation of GARCH Models Using an Extended Kalman Filter , 2011 .

[7]  Kuldeep Kumar,et al.  Robust Statistics, 2nd edn , 2011 .

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

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

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

[11]  Daniel Peña,et al.  Missing observations in ARIMA models: Skipping approach versus additive outlier approach , 1999 .

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

[13]  Philip Hans Franses,et al.  Non-Linear Time Series Models in Empirical Finance , 2000 .

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

[15]  Olivier Darné,et al.  Outliers and GARCH models in financial data , 2005 .

[16]  Anthony C. Atkinson,et al.  Monitoring robust regression , 2014 .

[17]  Helena Veiga,et al.  Outliers, GARCH-type models and risk measures: A comparison of several approaches ☆ , 2014 .

[18]  Silvia Salini,et al.  Reliable Robust Regression Diagnostics , 2016 .

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

[20]  L. Grossi.  Analyzing Financial Time Series through Robust Estimators , 2004 .

[21]  Marco Riani,et al.  Extensions of the Forward Search to Time Series , 2004 .

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

[23]  Franz C. Palm,et al.  Testing for jumps in conditionally Gaussian ARMA-GARCH models, a robust approach , 2016, Comput. Stat. Data Anal..

[24]  Nora Muler,et al.  Robust estimates for GARCH models , 2008 .

[25]  Marco Riani,et al.  Robust methods for the analysis of spatially autocorrelated data , 2002 .

[26]  Wanbo Lu,et al.  A generalized least squares estimation method for the autoregressive conditional duration model , 2019 .

[27]  Helena Veiga,et al.  A robust closed-form estimator for the GARCH(1,1) model , 2016 .

[28]  Stefan Van Aelst,et al.  The minimum weighted covariance determinant estimator , 2008 .

[29]  Anthony C. Atkinson,et al.  Robust Diagnostic Regression Analysis , 2000 .

[30]  Jonathan B. Hill,et al.  Supplemental Material for GEL Estimation for Heavy-Tailed GARCH Models with Robust Empirical Likelihood Inference , 2015 .

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

[32]  Patrick J. Heagerty,et al.  Window Subsampling of Estimating Functions with Application to Regression Models , 2000 .

[33]  Peter J. Rousseeuw,et al.  Robust Regression and Outlier Detection , 2005, Wiley Series in Probability and Statistics.

[34]  Werner A. Stahel,et al.  Robust Statistics: The Approach Based on Influence Functions , 1987 .

[35]  H. Guirguis,et al.  Extreme observations and non-normality in ARCH and GARCH , 2007 .

[36]  Tommaso Proietti.  Missing data in time series: A note on the equivalence of the dummy variable and the skipping approaches , 2008 .

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

[38]  Pascal Bondon,et al.  Least squares estimation of ARCH models with missing observations , 2012 .

[39]  B. Mendes,et al.  Assessing the bias of maximum likelihood estimates of contaminated garch models , 2000 .

[40]  Jonathan B. Hill.  Robust Estimation and Inference for Heavy Tailed GARCH , 2014, 1507.07653.

[41]  Domenico Perrotta,et al.  The Forward Search for Very Large Datasets , 2015 .

[42]  Pedro L. Valls Pereira,et al.  Small sample properties of GARCH estimates and persistence , 2006 .

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

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

[45]  Peter J. Rousseeuw,et al.  Robust regression and outlier detection , 1987 .

[46]  A. Atkinson.  Fast Very Robust Methods for the Detection of Multiple Outliers , 1994 .

[47]  F. Javier Trívez,et al.  Forecasting volatility in GARCH models with additive outliers , 2007 .

[48]  Pedro Galeano,et al.  Shifts in Individual Parameters of a GARCH Model , 2010 .

[49]  M. Hubert,et al.  High-Breakdown Robust Multivariate Methods , 2008, 0808.0657.