Wavelet-Based Detection of Outliers in Time Series

This article considers the problem of detecting outliers in time series data and proposes a general detection method based on wavelets. Unlike other detection procedures found in the literature, our method does not require that a model be specified for the data. Also, use of our method is not restricted to data generated from ARIMA processes. The effectiveness of the proposed method is compared with existing outlier detection procedures. Comparisons based on various models, sample sizes, and parameter values illustrate the effectiveness of the proposed method.

[1]  Ravi Mazumdar,et al.  On the correlation structure of the wavelet coefficients of fractional Brownian motion , 1994, IEEE Trans. Inf. Theory.

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

[3]  J. Durbin,et al.  Exact Tests of Serial Correlation using Noncircular Statistics , 1951 .

[4]  Chris Chatfield,et al.  Introduction to Statistical Time Series. , 1976 .

[5]  R. Tsay.  Outliers, Level Shifts, and Variance Changes in Time Series , 1988 .

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

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

[8]  A. Prest,et al.  Some Experiments in Demand Analysis , 1949 .

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

[10]  G. C. Tiao,et al.  Consistent Estimates of Autoregressive Parameters and Extended Sample Autocorrelation Function for Stationary and Nonstationary ARMA Models , 1984 .

[11]  Johannes Ledolter,et al.  OUTLIER DIAGNOSTICS IN TIME SERIES ANALYSIS , 1990 .

[12]  C. Muirhead.  Distinguishing Outlier Types in Time Series , 1986 .

[13]  R. Tsay.  Time Series Model Specification in the Presence of Outliers , 1986 .

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

[15]  I. Johnstone,et al.  Wavelet Threshold Estimators for Data with Correlated Noise , 1997 .

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

[17]  M. Frankenhaeuser,et al.  Estimation of time , 1959 .

[18]  Sujit K. Ghosh,et al.  Essential Wavelets for Statistical Applications and Data Analysis , 2001, Technometrics.

[19]  G. C. Tiao,et al.  Estimation of time series parameters in the presence of outliers , 1988 .

[20]  A. Tsybakov,et al.  Wavelets, approximation, and statistical applications , 1998 .

[21]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[22]  Amara Lynn Graps,et al.  An introduction to wavelets , 1995 .

[23]  A.H. Tewfik,et al.  Correlation structure of the discrete wavelet coefficients of fractional Brownian motion , 1992, IEEE Trans. Inf. Theory.