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Outliers in functional autoregressive time series

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  • Battaglia, Francesco

Abstract

A method for identifying and estimating outliers in a time series is proposed, based on fitting functional autoregressive models. Both additive and innovation outliers may be defined. A simulation experiment and the analysis of some real data sets suggest that the proposed method is effective both for series following some nonlinear models, such as self-exciting threshold autoregressive or exponential autoregressive, and for linear series generated by autoregressive moving average processes.

Suggested Citation

  • Battaglia, Francesco, 2005. "Outliers in functional autoregressive time series," Statistics & Probability Letters, Elsevier, vol. 72(4), pages 323-332, May.
  • Handle: RePEc:eee:stapro:v:72:y:2005:i:4:p:323-332
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    References listed on IDEAS

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    1. Chen, Cathy W. S., 1997. "Detection of additive outliers in bilinear time series," Computational Statistics & Data Analysis, Elsevier, vol. 24(3), pages 283-294, May.
    2. Jianqing Fan & Qiwei Yao & Zongwu Cai, 2003. "Adaptive varying-coefficient linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 57-80.
    3. Francesco Battaglia & Lia Orfei, 2005. "Outlier Detection And Estimation In NonLinear Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(1), pages 107-121, January.
    4. Cai, Zongwu & Fan, Jianqing & Yao, Qiwei, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
    5. R. Dahlhaus & M. Neumann & R. von Sachs, 1997. "Nonlinear Wavelet Estimation of Time-Varying Autoregressive Processes," SFB 373 Discussion Papers 1997,34, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    6. Cai, Zongwu & Ould-Saïd, Elias, 2003. "Local M-estimator for nonparametric time series," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 433-449, December.
    7. van Dijk, Dick & Franses, Philip Hans & Lucas, Andre, 1999. "Testing for ARCH in the Presence of Additive Outliers," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 539-562, Sept.-Oct.
    8. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
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    Cited by:

    1. Romo Urroz, Juan & Lillo Rodríguez, Rosa Elvira & Mingotti, Nicola, 2015. "A Random Walk Test for Functional Time Series," DES - Working Papers. Statistics and Econometrics. WS ws1506, Universidad Carlos III de Madrid. Departamento de Estadística.

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