Dynamic Models for Climate Extremes

Data on maxima and minima arise in climate and environment, as well as in economics and finance. Specific examples include rainfall, river level and air quality. This article proposes a new score-driven time series model for dealing with such data. A modification, called the composite score, is used to guarantee invertibility. The statistical properties of the maximum likelihood estimator are investigated and applications to river flow and temperature shows that the model works well in practice. The composite score technique may well prove useful in other situations.