Extreme values from a nonstationary stochastic process: An application to air quality analysis

A procedure for using air quality data to estimate the mean value of the maximum concentration in a year-long sequence of lognormally distributed air pollutant concentrations has been described by Larsen. This procedure and analogous procedures for non-lognormal concentrations implicitly assume that sequences of pollutant concentrations are stationary. However, air pollutant concentrations often vary systematically in response to seasonal and other factors and, therefore, are nonstationary. In this paper it is shown that application of procedures, such as Larsen's, that assume stationarity to a nonstationary sequence of concentrations can produce seriously erroneous results. Two methods for using air quality data to estimate the distributional properties of maxima of nonstationary sequences of concentrations are illustrated. One method involves identifying a nonstationary stochastic process that explains the data and computing the probability distributions of maxima of sequences generated by this stochastic process. The other involves applying the Larsen procedure to a suitably selected subsequence of the data.