Level change detection in time series using higher order statistics

Changes in the level of a time series are usually attributed to an intervention that interrupts its evolution. The resulting time series are referred to as interrupted time series and they are studied in order to measure, e.g. the impact of new laws or medical treatments. In the present paper a heuristic method for level change detection in non-stationary time series is presented. The method uses higher order statistics, namely the skewness and the kurtosis, and can identify both the existence of a change in the level of the time series as well as the time point it has happened. The technique is tested with both simulated and real world data and is straightforward applicable to the detection of outliers in time series.

[1]  W. Velicer,et al.  A Comparison of Alternative Approaches to the Analysis of Interrupted Time-Series. , 1985, Multivariate behavioral research.

[2]  Takashi Matsumoto,et al.  Adaptation and Change Detection With a Sequential Monte Carlo Scheme , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[3]  T. J. Breen,et al.  Biostatistical Analysis (2nd ed.). , 1986 .

[4]  J. Kenney.  Mathematics of statistics , 1940 .

[5]  Stavros M. Panas,et al.  Automatic P phase picking using maximum kurtosis and κ-statistics criteria , 2004, IEEE Geosci. Remote. Sens. Lett..

[6]  Dean Keith Simonton,et al.  Cross-sectional time-series experiments: Some suggested statistical analyses , 1977 .

[7]  Kenji Yamanishi,et al.  A unifying framework for detecting outliers and change points from non-stationary time series data , 2002, KDD.

[8]  Douglas M. Hawkins,et al.  The Changepoint Model for Statistical Process Control , 2003 .

[9]  Vice President,et al.  Fraud Detection using Autobox's Automatic Intervention Detection , 2002 .

[10]  D. McDowall,et al.  Interrupted Time Series Analysis , 1980 .

[11]  G. C. Tiao,et al.  A CHANGE IN LEVEL OF A NON-STATIONARY TIME SERIES. , 1965 .

[12]  Stavros M. Panas,et al.  ECG data compression using wavelets and higher order statistics methods , 2001, IEEE Transactions on Information Technology in Biomedicine.

[13]  J. H. Zar,et al.  Biostatistical Analysis (5th Edition) , 1984 .

[14]  Jeffrey E. Jarrett,et al.  Improving forecasting for telemarketing centers by ARIMA modeling with intervention , 1998 .