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

Mikko S. Pakkanen ()
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Mikko S. Pakkanen: Aarhus University and CREATES, Postal: Department of Economics and Business, Fuglesangs Allé 4, 8210 Aarhus V, Denmark

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

Abstract: We study the asymptotic behavior of lattice power variations of two-parameter ambit fields that are driven by white noise. Our first result is a law of large numbers for such power variations. Under a constraint on the memory of the ambit field, normalized power variations are shown to converge to certain integral functionals of the volatility field associated to the ambit field, when the lattice spacing tends to zero. This law of large numbers holds also for thinned power variations that are computed by only including increments that are separated by gaps with a particular asympotic behavior. Our second result is a related stable central limit theorem for thinned power variations. Additionally, we provide concrete examples of ambit fields that satisfy the assumptions of our limit theorems.

Keywords: ambit field; power variation; law of large numbers; central limit theorem; chaos decomposition (search for similar items in EconPapers)
JEL-codes: C10 C14 (search for similar items in EconPapers)
Pages: 28
Date: 2013-10-01
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (1)

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