Extremal analysis of processes sampled at different frequencies

• Published in: Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 62; no. 1; pp. 117 - 135
• Main Authors: Robinson, M. E., Tawn, J. A.
• Format: Journal Article
• Language: English
• Published: Oxford, UK and Boston, USA Blackwell Publishers Ltd 2000; Blackwell Publishers; Blackwell; Royal Statistical Society
• Series: Journal of the Royal Statistical Society Series B
• Subjects: Approximation; Data analysis; Data sampling; Distribution; Distribution functions; Exact sciences and technology; Extremal index; Extreme value theory; Generalized extreme value distribution; Mathematical analysis; Mathematical maxima; Mathematics; Probability and statistics; Probability theory and stochastic processes; Rain; Rainfall; Samples; Sampling frequency; Sampling rates; Sciences and techniques of general use; Series convergence; Stochastic processes; Tidal waves; Time dependence; Time series; Values; Waves; Markov process; Extreme search; Extreme value distribution; Time series; Geometric distribution; Stochastic process; Moving maxima process; Sampling frequency; Upper bound; Rain; Extreme value theory; Extreme value; Ocean wave
• ISSN: 1369-7412; 1467-9868
• DOI: 10.1111/1467-9868.00223

The observed extremes of a discrete time process depend on the process itself and the sampling frequency. We develop theoretical results which show how to account for the effect of sampling frequency on extreme values, thus enabling us to analyse systematically extremal data from series with different sampling rates. We present statistical methodology based on these results which we illustrate though simulations and by applications to sea-waves and rainfall data.