Journal
JOURNAL OF APPLIED PROBABILITY
Volume 41, Issue 4, Pages 1093-1103Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1239/jap/1101840554
Keywords
covariance; intrinsically stationary; long memory; positive definite; stationary; variogram
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This paper studies a class of stationary covariance models, in both the discrete- and the continuous-time domains, which possess a simple functional form gamma (tau +tau(0))+gamma(tau - tau(0))-2gamma (tau), where tau(0) is a fixed lag and gamma(tau) is an intrinsically stationary variogram, and include the fractional Gaussian noise of Kolmogorov (1940) and a stochastic volatility model of Barndorff-Nielsen and Shephard (2001), (2002) as special cases. Properties of the class, and interesting special cases with long memory, are studied. We also characterize the covariance function via the variogram.
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