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Dependent SiZer: Goodness-of-Fit Tests for Time Series Models

Author

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  • Cheolwoo Park
  • J. S. Marron
  • Vitaliana Rondonotti

Abstract

In this paper, we extend SiZer (SIgnificant ZERo crossing of the derivatives) to dependent data for the purpose of goodness-of-fit tests for time series models. Dependent SiZer compares the observed data with a specific null model being tested by adjusting the statistical inference using an assumed autocovariance function. This new approach uses a SiZer type visualization to flag statistically significant differences between the data and a given null model. The power of this approach is demonstrated through some examples of time series of Internet traffic data. It is seen that such time series can have even more burstiness than is predicted by the popular, long- range dependent, Fractional Gaussian Noise model.

Suggested Citation

  • Cheolwoo Park & J. S. Marron & Vitaliana Rondonotti, 2004. "Dependent SiZer: Goodness-of-Fit Tests for Time Series Models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(8), pages 999-1017.
    • Handle: RePEc:taf:japsta:v:31:y:2004:i:8:p:999-1017
    DOI: 10.1080/0266476042000270554
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    Citations

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    Cited by:

    1. Park, Cheolwoo & Kang, Kee-Hoon, 2008. "SiZer analysis for the comparison of regression curves," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 3954-3970, April.
    2. Cheolwoo Park & Yongho Jeon & Kee-Hoon Kang, 2016. "An exploratory data analysis in scale-space for interval-valued data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(14), pages 2643-2660, October.
    3. Park, Cheolwoo & Huh, Jib, 2013. "Statistical inference and visualization in scale-space using local likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 336-348.
    4. Park, Cheolwoo & Godtliebsen, Fred & Taqqu, Murad & Stoev, Stilian & Marron, J.S., 2007. "Visualization and inference based on wavelet coefficients, SiZer and SiNos," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5994-6012, August.
    5. Olsen, Lena Ringstad & Chaudhuri, Probal & Godtliebsen, Fred, 2008. "Multiscale spectral analysis for detecting short and long range change points in time series," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3310-3330, March.
    6. Huh, Jib & Park, Cheolwoo, 2015. "Theoretical investigation of an exploratory approach for log-density in scale-space," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 272-279.
    7. Lasse Holmström & Leena Pasanen, 2017. "Statistical Scale Space Methods," International Statistical Review, International Statistical Institute, vol. 85(1), pages 1-30, April.

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