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Some Bootstrap Tests for Non-linearity and Long Memory in Financial Time Series


  • Rodney C Wolff
  • Adrian G Barnett


Understanding and forecasting financial time series depend crucially on identifying any non-linearity which may be present. Recent developments in tests for non-linearity very commonly display low power, most likely because of over-smoothing and discarding pertinent information. In this presentation, we present some bootstrap tests for non-linearity in a time series, and explain how it can assist in identifying the form of non-linearity. Our methods are based on higher-order moments of the time series of interest, and its bispectrum, being the Fourier transform of the third-order moment. As a by-product of the proposed tests, we identify signature behaviour of long memory, and discuss this observation particularly in the context of high-frequency econometric measurements.

Suggested Citation

  • Rodney C Wolff & Adrian G Barnett, 2004. "Some Bootstrap Tests for Non-linearity and Long Memory in Financial Time Series," Econometric Society 2004 Australasian Meetings 350, Econometric Society.
  • Handle: RePEc:ecm:ausm04:350

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    More about this item


    Bispectrum; Bootstrap tests; Higher-order moments; Non-linearity; Time series.;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques


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