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Thick pen transformation for time series

Author

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  • Fryzlewicz, Piotr
  • Oh, H. S.

Abstract

Traditional visualization of time series data often consists of plotting the time series values against time and 'connecting the dots'. We propose an alternative, multiscale visualization technique, motivated by the scale-space approach in computer vision. In brief, our method also 'connects the dots' but uses a range of pens of varying thicknesses for this. The resulting multiscale map, which is termed the thick pen transform, corresponds to viewing the time series from a range of distances. We formally prove that the thick pen transform is a discriminatory statistic for two Gaussian time series with distinct correlation structures. Further, we show interesting possible applications of the thick pen transform to measuring cross-dependence in multivariate time series, classifying time series and testing for stationarity. In particular, we derive the asymptotic distribution of our test statistic and argue that the test is applicable to both linear and non-linear processes under low moment assumptions. Various other aspects of the methodology, including other possible applications, are also discussed.

Suggested Citation

  • Fryzlewicz, Piotr & Oh, H. S., 2011. "Thick pen transformation for time series," LSE Research Online Documents on Economics 37663, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:37663
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    File URL: http://eprints.lse.ac.uk/37663/
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    References listed on IDEAS

    as
    1. Elena Andreou & Eric Ghysels, 2002. "Detecting multiple breaks in financial market volatility dynamics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 579-600.
    2. Fryzlewicz, Piotr & Sapatinas, Theofanis & Subba Rao, Suhasini, 2008. "Normalized least-squares estimation in time-varying ARCH models," LSE Research Online Documents on Economics 25187, London School of Economics and Political Science, LSE Library.
    3. Cătălin Stărică & Clive Granger, 2005. "Nonstationarities in Stock Returns," The Review of Economics and Statistics, MIT Press, vol. 87(3), pages 503-522, August.
    4. Richard A. Davis & Thomas C. M. Lee & Gabriel A. Rodriguez‐Yam, 2008. "Break Detection for a Class of Nonlinear Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 834-867, September.
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    Cited by:

    1. Wadud, Sania & Gronwald, Marc & Durand, Robert B. & Lee, Seungho, 2023. "Co-movement between commodity and equity markets revisited—An application of the Thick Pen method," International Review of Financial Analysis, Elsevier, vol. 87(C).
    2. Tommaso Proietti, 2023. "Peaks, gaps, and time‐reversibility of economic time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(1), pages 43-68, January.
    3. Lasse Holmström & Leena Pasanen, 2017. "Statistical Scale Space Methods," International Statistical Review, International Statistical Institute, vol. 85(1), pages 1-30, April.
    4. Minji Kim & Hee-Seok Oh & Yaeji Lim, 2023. "Zero-Inflated Time Series Clustering Via Ensemble Thick-Pen Transform," Journal of Classification, Springer;The Classification Society, vol. 40(2), pages 407-431, July.
    5. Jach, Agnieszka, 2017. "International stock market comovement in time and scale outlined with a thick pen," Journal of Empirical Finance, Elsevier, vol. 43(C), pages 115-129.
    6. Marc Gronwald & Xin Jin, 2023. "Macroeconomics with a Thick Pen," CESifo Working Paper Series 10430, CESifo.

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    More about this item

    Keywords

    multiscale; non-stationary time series; testing for stationarity; time series dependence measures; time series visualization;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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