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The increment ratio statistic

Författare och institution:
Donatas Surgailis (-); Glles Teyssière (Centrum för finans & Institutionen för nationalekonomi med statistik); M Vaičiulis (-)
Publicerad i:
Journal of Multivariate Analysis, 99 ( 3 ) s. 510-541
Artikel, refereegranskad vetenskaplig
Sammanfattning (abstract):
We introduce a new statistic written as a sum of certain ratios of second-order increments of partial sums process View the MathML source of observations, which we call the increment ratio (IR) statistic. The IR statistic can be used for testing nonparametric hypotheses for d-integrated (View the MathML source) behavior of time series Xt, including short memory (d=0), (stationary) long-memory View the MathML source and unit roots (d=1). If Sn behaves asymptotically as an (integrated) fractional Brownian motion with parameter View the MathML source, the IR statistic converges to a monotone function Λ(d) of View the MathML source as both the sample size N and the window parameter m increase so that N/m→∞. For Gaussian observations Xt, we obtain a rate of decay of the bias EIR-Λ(d) and a central limit theorem View the MathML source, in the region View the MathML source. Graphs of the functions Λ(d) and σ(d) are included. A simulation study shows that the IR test for short memory (d=0) against stationary long-memory alternatives View the MathML source has good size and power properties and is robust against changes in mean, slowly varying trends and nonstationarities. We apply this statistic to sequences of squares of returns on financial assets and obtain a nuanced picture of the presence of long-memory in asset price volatility.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
Ekonomi och näringsliv
Ytterligare information:
Mathematical subject codes: 62F03; 62M10
Postens nummer:
Posten skapad:
2009-01-14 10:23
Posten ändrad:
2013-06-28 09:44

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