Department of Economics and Business Economics

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

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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, α, 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 α does not depend on the specifics of the data generating process for the observations, but only on the value of α 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).
Original languageEnglish
Place of publicationAarhus
PublisherInstitut for Økonomi, Århus Universitet
Number of pages35
Publication statusPublished - 9 Aug 2016
SeriesCREATES Research Papers
Number2016-21

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