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Semiparametric estimation and inference on the fractal index of Gaussian and conditionally Gaussian time series data

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This paper studies the properties of a particular estimator of the fractal index of a time series with a view to applications in financial econometrics and mathematical finance. We show how measurement noise (e.g., microstructure noise) in the observations will bias the estimator, potentially resulting in the econometrician erroneously finding evidence of fractal characteristics in a time series. We propose a new estimator which is robust to such noise and construct a formal hypothesis test for the presence of noise in the observations. A number of simulation exercises are carried out, providing guidance for implementation of the theory. Finally, the methods are illustrated on two empirical data sets; one of turbulent velocity flows and one of financial prices.

Original languageEnglish
JournalEconometric Reviews
Pages (from-to)875-903
Number of pages29
Publication statusPublished - Oct 2020

    Research areas

  • 60G10, 60G15, 60G17, 60G22, 62M07, 62M09, 65C05, Estimation, fractal index, fractional Brownian motion, inference, roughness, stochastic volatility, BROWNIAN SEMISTATIONARY PROCESSES, ROUGHNESS, DIMENSION, LONG-MEMORY, VARIANCE, VOLATILITY

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