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No abstract

This article shows that multiple independent time series from the same ARMA process can be represented by a single univariate ARMA time series through an interleaving of the original series. Using this result, existing univariate modelling software can be used to fit a single ARMA time series model simultaneously to multiple independent realizations of the same ARMA process. The interleaving approach and its properties will be presented and compared with alternative estimation options. It will be applied to the modelling of 66 years of daily maximum temperatures for Perth, Western Australia and to other time series models.

Summary Long‐term historical daily temperatures are used in electricity forecasting to simulate the probability distribution of future demand but can be affected by changes in recording site and climate. This paper presents a method of adjusting for the effect of these changes on daily maximum and minimum temperatures. The adjustment technique accommodates the autocorrelated and bivariate nature of the temperature data which has not previously been taken into account. The data are from Perth, Western Australia, the main electricity demand centre for the South‐West of Western Australia. The statistical modelling involves a multivariate extension of the univariate time series ‘interleaving method’, which allows fully efficient simultaneous estimation of the parameters of replicated Vector Autoregressive Moving Average processes. Temperatures at the most recent weather recording location in Perth are shown to be significantly lower compared to previous sites. There is also evidence of long‐term heating due to climate change especially for minimum temperatures.