Limit theorems for power variations of ambit fields driven by white noise

Authors :: Pakkanen, Mikko S.
Source :: Stochastic Processes and their Applications 2014, Vol. 124, No. 5, 1942-1973
Publication Year :: 2013
Abstract: We study the asymptotics of lattice power variations of two-parameter ambit fields driven by white noise. Our first result is a law of large numbers for power variations. Under a constraint on the memory of the ambit field, normalized power variations converge to certain integral functionals of the volatility field associated to the ambit field, when the lattice spacing tends to zero. This result holds also for thinned power variations that are computed by only including increments that are separated by gaps with a particular asymptotic behavior. Our second result is a stable central limit theorem for thinned power variations.<br />Comment: 31 pages, 2 figures, v4: several improvements, including new remarks on the underlying ambit field and on a more general observation scheme

Database :: arXiv
Journal :: Stochastic Processes and their Applications 2014, Vol. 124, No. 5, 1942-1973
Publication Type :: Report
Accession number :: edsarx.1301.2107
Document Type :: Working Paper
Full Text :: https://doi.org/10.1016/j.spa.2014.01.005