A single series representation of multiple independent ARMA processes

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.

Using multivariate time series methods to estimate location and climate change effects on temperature readings employed in electricity demand simulation

“…In this paper the effects of location shift and climate change on historical temperature recordings for Perth, Western Australia, (as employed in electricity demand simulation) are estimated. The analysis uses multivariate time series models and incorporates a multivariate extension of the univariate interleaving method (Bowden & Clarke ). The interleaving approach allows replicated realisations of the same VARMA process to be modelled as a single VARMA series of the same dimension as each of the original series but with extended length.…”

“…Interleaving allows replicated independent stationary vector time series to be modelled as one stationary series without ‘end of series’ discontinuities, as would be the case if say the series were merely concatenated together. Bowden & Clarke () contains a discussion of these discontinuity effects for a univariate series.…”

“…Detrending involved identifying and fitting a univariate interleaved AR(2) model (Bowden & Clarke ) separately to both daily maximum and minimum temperatures with associated intervention terms for the change in location and for the long‐term trend in temperature. The resulting intervention terms (without the autoregressive filters) were then used to adjust the two univariate time series for the change in location and for the long‐term increase in temperatures.…”

“…The time series modelling of daily temperatures used in this paper employs the interleaving method (see Bowden & Clarke ) extended herein to the multivariate case to model replicated realisations of a multiple time series process (specifically the Perth daily maximum and minimum temperature records since 1943). This extension allows fully efficient estimation of locational and climate change effects as well as of the time series coefficients.…”

Modelling Joint Autoregressive Moving Average Processes

“…The interleaving method for both univariate and multivariate time series was applied to over sixty years of daily maximum and minimum temperatures for Perth, Western Australia [1,2]. This shows that there have been changes in mean temperatures due to location and climate change.…”