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Outlier detection in multivariate time series via projection pursuit

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  • Galeano, Pedro
  • Peña, Daniel
  • Tsay, Ruey S.

Abstract

This article uses Projection Pursuit methods to develop a procedure for detecting outliers in a multivariate time series. We show that testing for outliers in some projection directions could be more powerful than testing the multivariate series directly. The optimal directions for detecting outliers are found by numerical optimization of the kurtosis coefficient of the projected series. We propose an iterative procedure to detect and handle multiple outliers based on univariate search in these optimal directions. In contrast with the existing methods, the proposed procedure can identify outliers without pre-specifying a vector ARMA model for the data. The good performance of the proposed method is verified in a Monte Carlo study and in a real data analysis.

Suggested Citation

  • Galeano, Pedro & Peña, Daniel & Tsay, Ruey S., 2004. "Outlier detection in multivariate time series via projection pursuit," DES - Working Papers. Statistics and Econometrics. WS ws044211, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws044211
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    References listed on IDEAS

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    1. Bianco, Ana Maria, et al, 2001. "Outlier Detection in Regression Models with ARIMA Errors Using Robust Estimates," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(8), pages 565-579, December.
    2. Jushan Bai, 1994. "Least Squares Estimation Of A Shift In Linear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(5), pages 453-472, September.
    3. Carnero, María Ángeles & Peña, Daniel & Ruiz Ortega, Esther, 2003. "Detecting level shifts in the presence of conditional heteroscedasticity," DES - Working Papers. Statistics and Econometrics. WS ws036313, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Pena D. & Prieto F.J., 2001. "Cluster Identification Using Projections," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1433-1445, December.
    5. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    6. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    7. Balke, Nathan S, 1993. "Detecting Level Shifts in Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 81-92, January.
    8. Maravall, Agustin & Mathis, Alexandre, 1994. "Encompassing univariate models in multivariate time series : A case study," Journal of Econometrics, Elsevier, vol. 61(2), pages 197-233, April.
    9. Robert E. McCulloch & Ruey S. Tsay, 1994. "Bayesian Analysis Of Autoregressive Time Series Via The Gibbs Sampler," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(2), pages 235-250, March.
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    Cited by:

    1. Galeano, Pedro, 2007. "The use of cumulative sums for detection of changepoints in the rate parameter of a Poisson Process," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6151-6165, August.

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