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

Mikko S. Pakkanen

Stochastic Processes and their Applications, 2014, vol. 124, issue 5, 1942-1973

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.

Keywords: Ambit field; Power variation; Law of large numbers; Central limit theorem; Chaos decomposition (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.spa.2014.01.005

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