CLT for quadratic variation of Gaussian processes and its application to the estimation of the Orey index

K. Kubilius

Statistics & Probability Letters, 2020, vol. 165, issue C

Abstract: We give a two-dimensional central limit theorem (CLT) for the second-order quadratic variation of the centered Gaussian processes on [0,T]. Though the approach we use is well known in the literature, the conditions under which the CLT holds are usually based on differentiability of the corresponding covariance function. In our case, we replace differentiability conditions by the convergence of the scaled sums of the second-order moments. To illustrate the usefulness and easiness of use of the approach, we apply the obtained CLT to proving the asymptotic normality of the estimator of the Orey index of a subfractional Brownian motion.

Keywords: Quadratic variation; Central limit theorem; Gaussian process; Orey index (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spl.2020.108845

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