Forecasting day-ahead electricity load using a multiple equation time series approach

The quality of short-term electricity load forecasting is crucial to the operation and trading activities of market participants in an electricity market. In this paper, it is shown that a multiple equation time-series model, which is estimated by repeated application of ordinary least squares, has the potential to match or even outperform more complex nonlinear and nonparametric forecasting models. The key ingredient of the success of this simple model is the effective use of lagged information by allowing for interaction between seasonal patterns and intra-day dependencies. Although the model is built using data for the Queensland region of Australia, the method is completely generic and applicable to any load forecasting problem. The model’s forecasting ability is assessed by means of the mean absolute percentage error (MAPE). For day-ahead forecast, the MAPE returned by the model over a period of 11 years is an impressive 1.36%. The forecast accuracy of the model is compared with a number of benchmarks including three popular alternatives and one industrial standard reported by the Australia Energy Market Operator (AEMO). The performance of the model developed in this paper is superior to all benchmarks and outperforms the AEMO forecasts by about a third in terms of the MAPE criterion.

Groundwater visualisation system (GVS) : a software framework for integrated display and interrogation of conceptual hydrogeological models, data and time-series animation

Management of groundwater systems requires realistic conceptual hydrogeological models as a framework for numerical simulation modelling, but also for system understanding and communicating this to stakeholders and the broader community. To help overcome these challenges we developed GVS (Groundwater Visualisation System), a stand-alone desktop software package that uses interactive 3D visualisation and animation techniques. The goal was a user-friendly groundwater management tool that could support a range of existing real-world and pre-processed data, both surface and subsurface, including geology and various types of temporal hydrological information. GVS allows these data to be integrated into a single conceptual hydrogeological model. In addition, 3D geological models produced externally using other software packages, can readily be imported into GVS models, as can outputs of simulations (e.g. piezometric surfaces) produced by software such as MODFLOW or FEFLOW. Boreholes can be integrated, showing any down-hole data and properties, including screen information, intersected geology, water level data and water chemistry. Animation is used to display spatial and temporal changes, with time-series data such as rainfall, standing water levels and electrical conductivity, displaying dynamic processes. Time and space variations can be presented using a range of contouring and colour mapping techniques, in addition to interactive plots of time-series parameters. Other types of data, for example, demographics and cultural information, can also be readily incorporated. The GVS software can execute on a standard Windows or Linux-based PC with a minimum of 2 GB RAM, and the model output is easy and inexpensive to distribute, by download or via USB/DVD/CD. Example models are described here for three groundwater systems in Queensland, northeastern Australia: two unconfined alluvial groundwater systems with intensive irrigation, the Lockyer Valley and the upper Condamine Valley, and the Surat Basin, a large sedimentary basin of confined artesian aquifers. This latter example required more detail in the hydrostratigraphy, correlation of formations with drillholes and visualisation of simulation piezometric surfaces. Both alluvial system GVS models were developed during drought conditions to support government strategies to implement groundwater management. The Surat Basin model was industry sponsored research, for coal seam gas groundwater management and community information and consultation. The “virtual” groundwater systems in these 3D GVS models can be interactively interrogated by standard functions, plus production of 2D cross-sections, data selection from the 3D scene, rear end database and plot displays. A unique feature is that GVS allows investigation of time-series data across different display modes, both 2D and 3D. GVS has been used successfully as a tool to enhance community/stakeholder understanding and knowledge of groundwater systems and is of value for training and educational purposes. Projects completed confirm that GVS provides a powerful support to management and decision making, and as a tool for interpretation of groundwater system hydrological processes. A highly effective visualisation output is the production of short videos (e.g. 2–5 min) based on sequences of camera ‘fly-throughs’ and screen images. Further work involves developing support for multi-screen displays and touch-screen technologies, distributed rendering, gestural interaction systems. To highlight the visualisation and animation capability of the GVS software, links to related multimedia hosted online sites are included in the references.

Exact and approximate Bayesian inference for low count time series models with intractable likelihoods

In this paper we present a new simulation methodology in order to obtain exact or approximate Bayesian inference for models for low-valued count time series data that have computationally demanding likelihood functions. The algorithm fits within the framework of particle Markov chain Monte Carlo (PMCMC) methods. The particle filter requires only model simulations and, in this regard, our approach has connections with approximate Bayesian computation (ABC). However, an advantage of using the PMCMC approach in this setting is that simulated data can be matched with data observed one-at-a-time, rather than attempting to match on the full dataset simultaneously or on a low-dimensional non-sufficient summary statistic, which is common practice in ABC. For low-valued count time series data we find that it is often computationally feasible to match simulated data with observed data exactly. Our particle filter maintains $N$ particles by repeating the simulation until $N+1$ exact matches are obtained. Our algorithm creates an unbiased estimate of the likelihood, resulting in exact posterior inferences when included in an MCMC algorithm. In cases where exact matching is computationally prohibitive, a tolerance is introduced as per ABC. A novel aspect of our approach is that we introduce auxiliary variables into our particle filter so that partially observed and/or non-Markovian models can be accommodated. We demonstrate that Bayesian model choice problems can be easily handled in this framework.

Parameterizing Unconditional Skewness in Models for Financial Time Series

In this paper we consider the third-moment structure of a class of time series models. It is often argued that the marginal distribution of financial time series such as returns is skewed. Therefore it is of importance to know what properties a model should possess if it is to accommodate unconditional skewness. We consider modeling the unconditional mean and variance using models that respond nonlinearly or asymmetrically to shocks. We investigate the implications of these models on the third-moment structure of the marginal distribution as well as conditions under which the unconditional distribution exhibits skewness and nonzero third-order autocovariance structure. In this respect, an asymmetric or nonlinear specification of the conditional mean is found to be of greater importance than the properties of the conditional variance. Several examples are discussed and, whenever possible, explicit analytical expressions provided for all third-order moments and cross-moments. Finally, we introduce a new tool, the shock impact curve, for investigating the impact of shocks on the conditional mean squared error of return series.

Stochastic modelling of financial time series with memory and multifractal scaling

Financial processes may possess long memory and their probability densities may display heavy tails. Many models have been developed to deal with this tail behaviour, which reflects the jumps in the sample paths. On the other hand, the presence of long memory, which contradicts the efficient market hypothesis, is still an issue for further debates. These difficulties present challenges with the problems of memory detection and modelling the co-presence of long memory and heavy tails. This PhD project aims to respond to these challenges. The first part aims to detect memory in a large number of financial time series on stock prices and exchange rates using their scaling properties. Since financial time series often exhibit stochastic trends, a common form of nonstationarity, strong trends in the data can lead to false detection of memory. We will take advantage of a technique known as multifractal detrended fluctuation analysis (MF-DFA) that can systematically eliminate trends of different orders. This method is based on the identification of scaling of the q-th-order moments and is a generalisation of the standard detrended fluctuation analysis (DFA) which uses only the second moment; that is, q = 2. We also consider the rescaled range R/S analysis and the periodogram method to detect memory in financial time series and compare their results with the MF-DFA. An interesting finding is that short memory is detected for stock prices of the American Stock Exchange (AMEX) and long memory is found present in the time series of two exchange rates, namely the French franc and the Deutsche mark. Electricity price series of the five states of Australia are also found to possess long memory. For these electricity price series, heavy tails are also pronounced in their probability densities. The second part of the thesis develops models to represent short-memory and longmemory financial processes as detected in Part I. These models take the form of continuous-time AR(∞) -type equations whose kernel is the Laplace transform of a finite Borel measure. By imposing appropriate conditions on this measure, short memory or long memory in the dynamics of the solution will result. A specific form of the models, which has a good MA(∞) -type representation, is presented for the short memory case. Parameter estimation of this type of models is performed via least squares, and the models are applied to the stock prices in the AMEX, which have been established in Part I to possess short memory. By selecting the kernel in the continuous-time AR(∞) -type equations to have the form of Riemann-Liouville fractional derivative, we obtain a fractional stochastic differential equation driven by Brownian motion. This type of equations is used to represent financial processes with long memory, whose dynamics is described by the fractional derivative in the equation. These models are estimated via quasi-likelihood, namely via a continuoustime version of the Gauss-Whittle method. The models are applied to the exchange rates and the electricity prices of Part I with the aim of confirming their possible long-range dependence established by MF-DFA. The third part of the thesis provides an application of the results established in Parts I and II to characterise and classify financial markets. We will pay attention to the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX), the NASDAQ Stock Exchange (NASDAQ) and the Toronto Stock Exchange (TSX). The parameters from MF-DFA and those of the short-memory AR(∞) -type models will be employed in this classification. We propose the Fisher discriminant algorithm to find a classifier in the two and three-dimensional spaces of data sets and then provide cross-validation to verify discriminant accuracies. This classification is useful for understanding and predicting the behaviour of different processes within the same market. The fourth part of the thesis investigates the heavy-tailed behaviour of financial processes which may also possess long memory. We consider fractional stochastic differential equations driven by stable noise to model financial processes such as electricity prices. The long memory of electricity prices is represented by a fractional derivative, while the stable noise input models their non-Gaussianity via the tails of their probability density. A method using the empirical densities and MF-DFA will be provided to estimate all the parameters of the model and simulate sample paths of the equation. The method is then applied to analyse daily spot prices for five states of Australia. Comparison with the results obtained from the R/S analysis, periodogram method and MF-DFA are provided. The results from fractional SDEs agree with those from MF-DFA, which are based on multifractal scaling, while those from the periodograms, which are based on the second order, seem to underestimate the long memory dynamics of the process. This highlights the need and usefulness of fractal methods in modelling non-Gaussian financial processes with long memory.

Evaluating Specification Tests for Markov-Switching Time-Series Models

We evaluate the performance of several specification tests for Markov regime-switching time-series models. We consider the Lagrange multiplier (LM) and dynamic specification tests of Hamilton (1996) and Ljung–Box tests based on both the generalized residual and a standard-normal residual constructed using the Rosenblatt transformation. The size and power of the tests are studied using Monte Carlo experiments. We find that the LM tests have the best size and power properties. The Ljung–Box tests exhibit slight size distortions, though tests based on the Rosenblatt transformation perform better than the generalized residual-based tests. The tests exhibit impressive power to detect both autocorrelation and autoregressive conditional heteroscedasticity (ARCH). The tests are illustrated with a Markov-switching generalized ARCH (GARCH) model fitted to the US dollar–British pound exchange rate, with the finding that both autocorrelation and GARCH effects are needed to adequately fit the data.

Spatiotemporal model or time series model for assessing city-wide temperature effects on mortality?

Most studies examining the temperature–mortality association in a city used temperatures from one site or the average from a network of sites. This may cause measurement error as temperature varies across a city due to effects such as urban heat islands. We examined whether spatiotemporal models using spatially resolved temperatures produced different associations between temperature and mortality compared with time series models that used non-spatial temperatures. We obtained daily mortality data in 163 areas across Brisbane city, Australia from 2000 to 2004. We used ordinary kriging to interpolate spatial temperature variation across the city based on 19 monitoring sites. We used a spatiotemporal model to examine the impact of spatially resolved temperatures on mortality. Also, we used a time series model to examine non-spatial temperatures using a single site and the average temperature from three sites. We used squared Pearson scaled residuals to compare model fit. We found that kriged temperatures were consistent with observed temperatures. Spatiotemporal models using kriged temperature data yielded slightly better model fit than time series models using a single site or the average of three sites' data. Despite this better fit, spatiotemporal and time series models produced similar associations between temperature and mortality. In conclusion, time series models using non-spatial temperatures were equally good at estimating the city-wide association between temperature and mortality as spatiotemporal models.

Alive SMC^2: Bayesian model selection for low-count time series models with intractable likelihoods

In this paper we present a new method for performing Bayesian parameter inference and model choice for low count time series models with intractable likelihoods. The method involves incorporating an alive particle filter within a sequential Monte Carlo (SMC) algorithm to create a novel pseudo-marginal algorithm, which we refer to as alive SMC^2. The advantages of this approach over competing approaches is that it is naturally adaptive, it does not involve between-model proposals required in reversible jump Markov chain Monte Carlo and does not rely on potentially rough approximations. The algorithm is demonstrated on Markov process and integer autoregressive moving average models applied to real biological datasets of hospital-acquired pathogen incidence, animal health time series and the cumulative number of poison disease cases in mule deer.

Application of data mining techniques in the prediction of coronary artery disease : use of anaesthesia time-series and patient risk factor data

The high morbidity and mortality associated with atherosclerotic coronary vascular disease (CVD) and its complications are being lessened by the increased knowledge of risk factors, effective preventative measures and proven therapeutic interventions. However, significant CVD morbidity remains and sudden cardiac death continues to be a presenting feature for some subsequently diagnosed with CVD. Coronary vascular disease is also the leading cause of anaesthesia related complications. Stress electrocardiography/exercise testing is predictive of 10 year risk of CVD events and the cardiovascular variables used to score this test are monitored peri-operatively. Similar physiological time-series datasets are being subjected to data mining methods for the prediction of medical diagnoses and outcomes. This study aims to find predictors of CVD using anaesthesia time-series data and patient risk factor data. Several pre-processing and predictive data mining methods are applied to this data. Physiological time-series data related to anaesthetic procedures are subjected to pre-processing methods for removal of outliers, calculation of moving averages as well as data summarisation and data abstraction methods. Feature selection methods of both wrapper and filter types are applied to derived physiological time-series variable sets alone and to the same variables combined with risk factor variables. The ability of these methods to identify subsets of highly correlated but non-redundant variables is assessed. The major dataset is derived from the entire anaesthesia population and subsets of this population are considered to be at increased anaesthesia risk based on their need for more intensive monitoring (invasive haemodynamic monitoring and additional ECG leads). Because of the unbalanced class distribution in the data, majority class under-sampling and Kappa statistic together with misclassification rate and area under the ROC curve (AUC) are used for evaluation of models generated using different prediction algorithms. The performance based on models derived from feature reduced datasets reveal the filter method, Cfs subset evaluation, to be most consistently effective although Consistency derived subsets tended to slightly increased accuracy but markedly increased complexity. The use of misclassification rate (MR) for model performance evaluation is influenced by class distribution. This could be eliminated by consideration of the AUC or Kappa statistic as well by evaluation of subsets with under-sampled majority class. The noise and outlier removal pre-processing methods produced models with MR ranging from 10.69 to 12.62 with the lowest value being for data from which both outliers and noise were removed (MR 10.69). For the raw time-series dataset, MR is 12.34. Feature selection results in reduction in MR to 9.8 to 10.16 with time segmented summary data (dataset F) MR being 9.8 and raw time-series summary data (dataset A) being 9.92. However, for all time-series only based datasets, the complexity is high. For most pre-processing methods, Cfs could identify a subset of correlated and non-redundant variables from the time-series alone datasets but models derived from these subsets are of one leaf only. MR values are consistent with class distribution in the subset folds evaluated in the n-cross validation method. For models based on Cfs selected time-series derived and risk factor (RF) variables, the MR ranges from 8.83 to 10.36 with dataset RF_A (raw time-series data and RF) being 8.85 and dataset RF_F (time segmented time-series variables and RF) being 9.09. The models based on counts of outliers and counts of data points outside normal range (Dataset RF_E) and derived variables based on time series transformed using Symbolic Aggregate Approximation (SAX) with associated time-series pattern cluster membership (Dataset RF_ G) perform the least well with MR of 10.25 and 10.36 respectively. For coronary vascular disease prediction, nearest neighbour (NNge) and the support vector machine based method, SMO, have the highest MR of 10.1 and 10.28 while logistic regression (LR) and the decision tree (DT) method, J48, have MR of 8.85 and 9.0 respectively. DT rules are most comprehensible and clinically relevant. The predictive accuracy increase achieved by addition of risk factor variables to time-series variable based models is significant. The addition of time-series derived variables to models based on risk factor variables alone is associated with a trend to improved performance. Data mining of feature reduced, anaesthesia time-series variables together with risk factor variables can produce compact and moderately accurate models able to predict coronary vascular disease. Decision tree analysis of time-series data combined with risk factor variables yields rules which are more accurate than models based on time-series data alone. The limited additional value provided by electrocardiographic variables when compared to use of risk factors alone is similar to recent suggestions that exercise electrocardiography (exECG) under standardised conditions has limited additional diagnostic value over risk factor analysis and symptom pattern. The effect of the pre-processing used in this study had limited effect when time-series variables and risk factor variables are used as model input. In the absence of risk factor input, the use of time-series variables after outlier removal and time series variables based on physiological variable values’ being outside the accepted normal range is associated with some improvement in model performance.

The short-term effect of air pollution on cardiovascular mortality in Tianjin, China : comparison of time series and case–crossover analyses

Background: Many studies have illustrated that ambient air pollution negatively impacts on health. However, little evidence is available for the effects of air pollution on cardiovascular mortality (CVM) in Tianjin, China. Also, no study has examined which strata length for the time-stratified case–crossover analysis gives estimates that most closely match the estimates from time series analysis. Objectives: The purpose of this study was to estimate the effects of air pollutants on CVM in Tianjin, China, and compare time-stratified case–crossover and time series analyses. Method: A time-stratified case–crossover and generalized additive model (time series) were applied to examine the impact of air pollution on CVM from 2005 to 2007. Four time-stratified case–crossover analyses were used by varying the stratum length (Calendar month, 28, 21 or 14 days). Jackknifing was used to compare the methods. Residual analysis was used to check whether the models fitted well. Results: Both case–crossover and time series analyses show that air pollutants (PM10, SO2 and NO2) were positively associated with CVM. The estimates from the time-stratified case–crossover varied greatly with changing strata length. The estimates from the time series analyses varied slightly with changing degrees of freedom per year for time. The residuals from the time series analyses had less autocorrelation than those from the case–crossover analyses indicating a better fit. Conclusion: Air pollution was associated with an increased risk of CVM in Tianjin, China. Time series analyses performed better than the time-stratified case–crossover analyses in terms of residual checking.

Assessing the short-term effects of heatwaves on mortality and morbidity in Brisbane, Australia : comparison of case-crossover and time series analyses

Background Heat-related impacts may have greater public health implications as climate change continues. It is important to appropriately characterize the relationship between heatwave and health outcomes. However, it is unclear whether a case-crossover design can be effectively used to assess the event- or episode-related health effects. This study examined the association between exposure to heatwaves and mortality and emergency hospital admissions (EHAs) from non-external causes in Brisbane, Australia, using both case-crossover and time series analyses approaches. Methods Poisson generalised additive model (GAM) and time-stratified case-crossover analyses were used to assess the short-term impact of heatwaves on mortality and EHAs. Heatwaves exhibited a significant impact on mortality and EHAs after adjusting for air pollution, day of the week, and season. Results For time-stratified case-crossover analysis, odds ratios of mortality and EHAs during heatwaves were 1.62 (95% confidence interval (CI): 1.36–1.94) and 1.22 (95% CI: 1.14–1.30) at lag 1, respectively. Time series GAM models gave similar results. Relative risks of mortality and EHAs ranged from 1.72 (95% CI: 1.40–2.11) to 1.81 (95% CI: 1.56–2.10) and from 1.14 (95% CI: 1.06–1.23) to 1.28 (95% CI: 1.21–1.36) at lag 1, respectively. The risk estimates gradually attenuated after the lag of one day for both case-crossover and time series analyses. Conclusions The risk estimates from both case-crossover and time series models were consistent and comparable. This finding may have implications for future research on the assessment of event- or episode-related (e.g., heatwave) health effects.

Polarization of forecast densities : a new approach to time series classification

Time series classification has been extensively explored in many fields of study. Most methods are based on the historical or current information extracted from data. However, if interest is in a specific future time period, methods that directly relate to forecasts of time series are much more appropriate. An approach to time series classification is proposed based on a polarization measure of forecast densities of time series. By fitting autoregressive models, forecast replicates of each time series are obtained via the bias-corrected bootstrap, and a stationarity correction is considered when necessary. Kernel estimators are then employed to approximate forecast densities, and discrepancies of forecast densities of pairs of time series are estimated by a polarization measure, which evaluates the extent to which two densities overlap. Following the distributional properties of the polarization measure, a discriminant rule and a clustering method are proposed to conduct the supervised and unsupervised classification, respectively. The proposed methodology is applied to both simulated and real data sets, and the results show desirable properties.