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

Mikkel Bennedsen ()
Additional contact information
Mikkel Bennedsen: Aarhus University and CREATES, Postal: Department of Economics and Business Economics, Fuglesangs Allé 4, 8210 Aarhus V, Denmark

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

Abstract: Using theory on (conditionally) Gaussian processes with stationary increments developed in Barndorff-Nielsen et al. (2009, 2011), this paper presents a general semiparametric approach to conducting inference on the fractal index, a, of a time series. Our setup encompasses a large class of Gaussian processes and we show how to extend it to a large class of non-Gaussian models as well. It is proved that the asymptotic distribution of the estimator of a does not depend on the specifics of the data generating process for the observations, but only on the value of a and a “heteroscedasticity” factor. Using this, we propose a simulation-based approach to inference, which is easily implemented and is valid more generally than asymptotic analysis. We detail how the methods can be applied to test whether a stochastic process is a non-semimartingale. Finally, the methods are illustrated in two empirical applications motivated from finance. We study time series of log-prices and log-volatility from 29 individual US stocks; no evidence of non-semimartingality in asset prices is found, but we do find evidence of non-semimartingality in volatility. This confirms a recently proposed conjecture that stochastic volatility processes of financial assets are rough (Gatheral et al., 2014).

Keywords: Fractal index; Monte Carlo simulation; roughness; semimartingality; fractional Brownian motion; stochastic volatility JEL Classification: C12; C22; C63; G12 MSC 2010 Classification: 60G10; 60G15; 60G17; 60G22; 62M07; 62M09; 65C05 (search for similar items in EconPapers)
Pages: 35
Date: 2016-08-04
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
https://repec.econ.au.dk/repec/creates/rp/16/rp16_21.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:aah:create:2016-21

Access Statistics for this paper

More papers in CREATES Research Papers from Department of Economics and Business Economics, Aarhus University
Bibliographic data for series maintained by ().