Statistical Analysis of Heat Waves in the State of Victoria in Australia

The recent blistering heat waves of 2009 in the state of Victoria in Australia were so unprecedented in terms of duration and intensity that society was largely unprepared. These heat waves caused serious health, social and economic problems. In this paper, the daily maximum temperatures at ten selected stations are studied. Auto‐regressive integrated moving‐average models are used to prewhiten the time series. Uncorrelated, non‐normal and heavy‐tailed residuals are analyzed by means of a new skew t‐mixture distribution. The number of mixture components is effectively determined by an innovative penalisation procedure. It is shown that the resulting skew t‐mixture models provide an acceptable fit in all cases. Possible future temperature patterns are obtained through simulation. It is forecast that the average duration of high temperature episodes will increase by two to three days per year and a new eight‐year high temperature level is very likely in the coming few years. The relationship between heavy tail behaviour of the fitted distribution and heat waves is noteworthy.