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Wavelets in Time Series Analysis

Author

Listed:
  • Nason, G.P.
  • von Sachs, R.

Abstract

This article reviews the role of wavelets in statistical time series analysis. We survey work that emphasises scale such as estimation of variance and the scale exponent of a process with a specific scale behaviour such as 1/f processes. We present some of our own work on locally stationary wavelet (LSW) processes which model both stationary and some kinds of non-stationary processes. Analysis of time series assuming the LSW model permits identification of an evolutionary wavelet spectrum (EWS) that quantifies the variation in a time series over a particualr state and at a particular time. We address estimation of the EWS and show how our methodology reveals phenomena of interest in an infant electrocardiogram series.

Suggested Citation

  • Nason, G.P. & von Sachs, R., 1999. "Wavelets in Time Series Analysis," Papers 9901, Catholique de Louvain - Institut de statistique.
  • Handle: RePEc:fth:louvis:9901
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    References listed on IDEAS

    as
    1. GIJBELS, Irène & MAMMEN, Enno & PARK, Byeong U. & SIMAR, Léopold, 1997. "On estimation of monotone and concave frontier functions," CORE Discussion Papers 1997031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Fare,Rolf & Grosskopf,Shawna & Lovell,C. A. Knox, 2008. "Production Frontiers," Cambridge Books, Cambridge University Press, number 9780521072069, March.
    3. Tsybakov, A.B. & Korostelev, A.P. & Simar, L., 1992. "Efficient Estimation of Monotone Boundaries," Papers 9209, Catholique de Louvain - Institut de statistique.
    4. Kneip, A & Park, B-U & Simar, L, 1996. "A Note on the Convergence of Nonparametric DEA Efficiency Measures," Papers 9603, Catholique de Louvain - Institut de statistique.
    5. repec:cor:louvrp:-1139 is not listed on IDEAS
    6. SIMAR , Léopold, 1995. "Aspects of Statistical Analysis in DEA-Type Frontier Models," CORE Discussion Papers 1995061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Simar, Leopold & Wilson, Paul W., 1999. "Estimating and bootstrapping Malmquist indices," European Journal of Operational Research, Elsevier, vol. 115(3), pages 459-471, June.
    8. KNEIP, Alois & SIMAR, Léopold, 1995. "A General Framework for Frontier Estimation with Panel Data," CORE Discussion Papers 1995060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Léopold Simar & Paul W. Wilson, 1998. "Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models," Management Science, INFORMS, vol. 44(1), pages 49-61, January.
    10. Wilson, Paul W, 1993. "Detecting Outliers in Deterministic Nonparametric Frontier Models with Multiple Outputs," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 319-323, July.
    11. repec:cor:louvrp:-571 is not listed on IDEAS
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    Citations

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    Cited by:

    1. Debashis Mondal & Donald Percival, 2010. "Wavelet variance analysis for gappy time series," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(5), pages 943-966, October.
    2. Jammazi, Rania & Aloui, Chaker, 2012. "Crude oil price forecasting: Experimental evidence from wavelet decomposition and neural network modeling," Energy Economics, Elsevier, vol. 34(3), pages 828-841.
    3. Alper Ozun & Atilla Cifter, 2008. "Modeling long-term memory effect in stock prices: A comparative analysis with GPH test and Daubechies wavelets," Studies in Economics and Finance, Emerald Group Publishing, vol. 25(1), pages 38-48, March.
    4. Piotr Fryzlewicz & Sébastien Bellegem & Rainer Sachs, 2003. "Forecasting non-stationary time series by wavelet process modelling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(4), pages 737-764, December.
    5. Stephen Pollock & Iolanda Lo Cascio, 2005. "Orthogonality Conditions for Non-Dyadic Wavelet Analysis," Working Papers 529, Queen Mary University of London, School of Economics and Finance.
    6. Christoph Schleicher, 2002. "An Introduction to Wavelets for Economists," Staff Working Papers 02-3, Bank of Canada.
    7. repec:spr:waterr:v:32:y:2018:i:1:d:10.1007_s11269-017-1796-1 is not listed on IDEAS
    8. Cao, Guangxi & Xu, Wei, 2016. "Nonlinear structure analysis of carbon and energy markets with MFDCCA based on maximum overlap wavelet transform," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 505-523.
    9. Christian M. Hafner, 2012. "Cross-correlating wavelet coefficients with applications to high-frequency financial time series," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(6), pages 1363-1379, December.
    10. Amato, U. & Antoniadis, A. & De Feis, I., 2006. "Dimension reduction in functional regression with applications," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2422-2446, May.
    11. Jammazi, Rania & Aloui, Chaker, 2010. "Wavelet decomposition and regime shifts: Assessing the effects of crude oil shocks on stock market returns," Energy Policy, Elsevier, vol. 38(3), pages 1415-1435, March.
    12. repec:bla:jtsera:v:38:y:2017:i:2:p:151-174 is not listed on IDEAS
    13. Fryzlewicz, Piotr & Ombao, Hernando, 2009. "Consistent classification of non-stationary time series using stochastic wavelet representations," LSE Research Online Documents on Economics 25162, London School of Economics and Political Science, LSE Library.

    More about this item

    Keywords

    TIME SERIES ; STATISTICAL ANALYSIS ; ESTIMATION OF PARAMETERS;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General

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