We develop the asymptotic theory for the realised power variation of the processes X = f • G, where G is a Gaussian process with stationary increments. More specifically, under some mild assumptions on the variance function of the increments of G and certain regularity condition on the path of the process f we prove the convergence in probability for the properly normalised realised power variation. Moreover, under a further assumption on the H¨older index of the path of f, we show an associated stable central limit theorem. The main tool is a general central limit theorem, due essentially to Hu & Nualart (2005), Nualart & Peccati (2005) and Peccati & Tudor (2005), for sequences of random variables which admit a chaos representation.
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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number
2007-42.
Find related papers by JEL classification: C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - General C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
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