
on Econometric Time Series 
By:  Mikkel Bennedsen 
Abstract:  Using theory on (conditionally) Gaussian processes with stationary increments developed in BarndorffNielsen et al. (2009, 2011), this paper presents a general semiparametric approach to conducting inference on the fractal index, $\alpha$, 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 nonGaussian models as well. It is proved that the asymptotic distribution of the estimator of $\alpha$ does not depend on the specifics of the data generating process for the observations, but only on the value of $\alpha$ and a "heteroskedasticity" factor. Using this, we propose a simulationbased 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 nonsemimartingale. Finally, the methods are illustrated in two empirical applications motivated from finance. We study time series of logprices and logvolatility from $29$ individual US stocks; no evidence of nonsemimartingality in asset prices is found, but we do find evidence of nonsemimartingality in volatility. This confirms a recently proposed conjecture that stochastic volatility processes of financial assets are rough (Gatheral et al., 2014). 
Date:  2016–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1608.01895&r=ets 
By:  Søren Johansen (University of Copenhagen and CREATES); Morten Ørregaard Nielsen (Queen?s University and CREATES) 
Abstract:  In the cointegrated vector autoregression (CVAR) literature, deterministic terms have until now been analyzed on a casebycase, or asneeded basis. We give a comprehensive unified treatment of deterministic terms in the additive model X(t)= Z(t) + Y(t), where Z(t) belongs to a large class of deterministic regressors and Y(t) is a zeromean CVAR. We suggest an extended model that can be estimated by reduced rank regression and give a condition for when the additive and extended models are asymptotically equivalent, as well as an algorithm for deriving the additive model parameters from the extended model parameters. We derive asymptotic properties of the maximum likelihood estimators and discuss tests for rank and tests on the deterministic terms. In particular, we give conditions under which the estimators are asymptotically (mixed) Gaussian, such that associated tests are khi squared distributed. 
Keywords:  Additive formulation, cointegration, deterministic terms, extended model, likelihood inference, VAR model 
JEL:  C32 
Date:  2016–07–24 
URL:  http://d.repec.org/n?u=RePEc:aah:create:201622&r=ets 