Random discretization of stationary continuous time processes

Anne Philippe (), Caroline Robet and Marie-Claude Viano
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Anne Philippe: Université de Nantes
Caroline Robet: Université de Nantes
Marie-Claude Viano: Université de Lille 1

Metrika: International Journal for Theoretical and Applied Statistics, 2021, vol. 84, issue 3, No 4, 375-400

Abstract: Abstract This paper investigates second order properties of a stationary continuous time process after random sampling. While a short memory process always gives rise to a short memory one, we prove that long-memory can disappear when the sampling law has very heavy tails. Despite the fact that the normality of the process is not maintained by random sampling, the normalized partial sum process converges to the fractional Brownian motion, at least when the long memory parameter is preserved.

Keywords: Gaussian process; Long memory; Partial sum; Random sampling; Regularly varying covariance (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00184-020-00783-1

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