Ross Bowden

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 employed. The data is from Perth, Western Australia, the main electricity demand centre for the South-West (of Western Australia) Interconnected System. 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 VARMA 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.

This paper shows that the interleaving of replicated multiple time series allows the estimation methods available in standard multiple time series packages to be applied simultaneously to each of the replicated series without loss of information. The methodology employs a non-trivial multivariate extension of an earlier univariate result involving interleaving. The interleaving approach is used to model more than sixty years of daily maximum and minimum temperatures for Perth, Western Australia.

The purpose of this report is to present the detailed statistical analysis of a randomised, placebo-controlled trial comparing two different treatment modalities to an intervention of no known benefit for people with acute or subacute thoracic spine pain. The therapy arms consist of Spinal Manipulative Therapy (SMT) and Graston Technique (GT) and the placebo is a non-functional ultrasound. A placebo group was utilised because at present there are no proven treatments for non-specific thoracic pain. This trial is registered with the Australia and New Zealand Clinical Trials Registry. Ethics approval has been granted by Murdoch University Human Research and Ethics Committee, number 2007/274. The aim of this three arm trial was to test the efficacy of SMT and GT as independent modalities compared to detuned ultrasound for the outcomes of pain and disability. The latter were measured using the Visual Analogue Scale (VAS) and a modified Oswestry Back Pain Disability Index. The study was conducted at the Murdoch University Chiropractic student clinic in Perth, Australia, and the protocol published in Crothers et al (2008). In this report, Section 2 provides an initial exploratory analysis of the data, Section 3 outlines the statistical models used in the final analysis, Section 4 defines these models in mathematical terms, Section 5 discusses the management of missing values via multiple imputation and Section 6 presents the results of the statistical modelling and hypothesis tests. The clinical study will be published in full elsewhere.