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

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Semiparametric estimation and inference on the fractal index of Gaussian and conditionally Gaussian time series data. / Bennedsen, Mikkel.

In: Econometric Reviews, Vol. 39, No. 9, 10.2020, p. 875-903.

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@article{605bc9816e694c51a6475c7dff91e764,
title = "Semiparametric estimation and inference on the fractal index of Gaussian and conditionally Gaussian time series data",
abstract = "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.",
keywords = "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",
author = "Mikkel Bennedsen",
year = "2020",
month = oct,
doi = "10.1080/07474938.2020.1721832",
language = "English",
volume = "39",
pages = "875--903",
journal = "Econometric Reviews",
issn = "0747-4938",
publisher = "Taylor & Francis Inc.",
number = "9",

}

RIS

TY - JOUR

T1 - Semiparametric estimation and inference on the fractal index of Gaussian and conditionally Gaussian time series data

AU - Bennedsen, Mikkel

PY - 2020/10

Y1 - 2020/10

N2 - 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.

AB - 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.

KW - 60G10

KW - 60G15

KW - 60G17

KW - 60G22

KW - 62M07

KW - 62M09

KW - 65C05

KW - Estimation

KW - fractal index

KW - fractional Brownian motion

KW - inference

KW - roughness

KW - stochastic volatility

KW - BROWNIAN SEMISTATIONARY PROCESSES

KW - ROUGHNESS

KW - DIMENSION

KW - LONG-MEMORY

KW - VARIANCE

KW - VOLATILITY

UR - http://www.scopus.com/inward/record.url?scp=85079407990&partnerID=8YFLogxK

U2 - 10.1080/07474938.2020.1721832

DO - 10.1080/07474938.2020.1721832

M3 - Journal article

AN - SCOPUS:85079407990

VL - 39

SP - 875

EP - 903

JO - Econometric Reviews

JF - Econometric Reviews

SN - 0747-4938

IS - 9

ER -