Estimation of Time Series Models via Robust Wavelet Variance

A robust approach to the estimation of time series models is proposed. Taking from a new estimation method called the Generalized Method of Wavelet Moments (GMWM) which is an indirect method based on the Wavelet Variance (WV), we replace the classical estimator of the WV with a recently proposed robust M-estimator to obtain a robust version of the GMWM. The simulation results show that the proposed approach can be considered as a valid robust approach to the estimation of time series and state-space models.

[1]  Jan Skaloud,et al.  Wavelet-Variance-Based Estimation for Composite Stochastic Processes , 2013 .

[2]  H. Künsch Infinitesimal Robustness for Autoregressive Processes , 1984 .

[3]  Henry W. Loescher,et al.  Comparison of temperature and wind statistics in contrasting environments among different sonic anemometer–thermometers , 2005 .

[4]  L. Denby,et al.  Robust Estimation of the First-Order Autoregressive Parameter , 1979 .

[5]  E. Ronchetti,et al.  Robust inference with GMM estimators , 2001 .

[6]  Yannick Stebler,et al.  Limits of the Allan Variance and Optimal Tuning of Wavelet Variance based Estimators , 2013 .

[7]  L. Hansen Large Sample Properties of Generalized Method of Moments Estimators , 1982 .

[8]  C. Kramer,et al.  Optimization of heterodyne observations using Allan variance measurements , 2001, astro-ph/0105071.

[9]  Peter Guttorp,et al.  Long-Memory Processes, the Allan Variance and Wavelets , 1994 .

[10]  Elvezio Ronchetti,et al.  Robust Indirect Inference , 2003 .

[11]  Nien Fan Zhang,et al.  Allan variance of time series models for measurement data , 2008 .

[12]  Oscar H. Bustos,et al.  Robust Estimates for ARMA Models , 1986 .

[13]  D. W. Allan,et al.  Time and Frequency (Time-Domain) Characterization, Estimation, and Prediction of Precision Clocks and Oscillators , 1987, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[14]  Maki Tachikawa,et al.  Allan-variance measurements of diode laser frequency-stabilized with a thin vapor cell , 2003 .

[15]  Xiaoji Niu,et al.  Analysis and Modeling of Inertial Sensors Using Allan Variance , 2008, IEEE Transactions on Instrumentation and Measurement.

[16]  A. M. Hilliard AFFILIATION , 1910 .

[17]  P. Fadel,et al.  Fractal properties of human muscle sympathetic nerve activity. , 2004, American journal of physiology. Heart and circulatory physiology.

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

[19]  Brandon J. Whitcher,et al.  Wavelet-Based Estimation for Seasonal Long-Memory Processes , 2004, Technometrics.

[20]  S. Herndon,et al.  Detection of nitrogen dioxide by cavity attenuated phase shift spectroscopy. , 2005, Analytical chemistry.

[21]  R. Martin,et al.  Robust bayesian estimation for the linear model and robustifying the Kalman filter , 1977 .

[22]  D. Percival,et al.  M-estimation of wavelet variance , 2012 .

[23]  Donald P. Percival,et al.  On estimation of the wavelet variance , 1995 .

[24]  F. Hampel The Influence Curve and Its Role in Robust Estimation , 1974 .

[25]  A. Walden,et al.  Statistical Properties and Uses of the Wavelet Variance Estimator for the Scale Analysis of Time Series , 2000 .

[26]  C. Greenhall Recipes for degrees of freedom of frequency stability estimators , 1991 .

[27]  P. Werle,et al.  The limits of signal averaging in atmospheric trace-gas monitoring by tunable diode-laser absorption spectroscopy (TDLAS) , 1993 .

[28]  V. Yohai,et al.  Robust Statistics: Theory and Methods , 2006 .

[29]  Gerard L Gebber,et al.  Fractal noises and motions in time series of presympathetic and sympathetic neural activities. , 2006, Journal of neurophysiology.

[30]  Steven D. Sargent,et al.  Tunable diode laser absorption spectroscopy for stable isotope studies of ecosystem–atmosphere CO2 exchange , 2003 .

[31]  Stéphane Guerrier,et al.  Improving Accuracy with Multiple Sensors: Study of Redundant MEMS-IMU/GPS Configurations , 2009 .