Shu Fan and Rob J Hyndman

Abstract
Short-​​term load forecasting is an essential instrument in power system planning, operation and control. Many operating decisions are based on load forecasts, such as dispatch scheduling of generating capacity, reliability analysis, and maintenance planning for the generators. Overestimation of electricity demand will cause a conservative operation, which leads to the start-​​up of too many units or excessive energy purchase, thereby supplying an unnecessary level of reserve. On the contrary, underestimation may result in a risky operation, with insufficient preparation of spinning reserve, causing the system to operate in a vulnerable region to the disturbance.

In this paper, semi-​​parametric additive models are proposed to estimate the relationships between demand and the driver variables. Specifically, the inputs for these models are calendar variables, lagged actual demand observations and historical and forecast temperature traces for one or more sites in the target power system. In addition to point forecasts, prediction intervals are also estimated using a modified bootstrap method suitable for the complex seasonality seen in electricity demand data. The proposed methodology has been used to forecast the half-​​hourly electricity demand for up to seven days ahead for power systems in the Australian National Electricity Market. The performance of the methodology is validated via out-​​of-​​sample experiments with real data from the power system, as well as through on-​​site implementation by the system operator.

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Shu Fan and Rob J Hyndman

Business and Economic Forecasting Unit, Monash University, Clayton, Victoria 3800, Australia

Abstract
In this paper, the price elasticity of electricity demand, representing the sensitivity of customer demand to the price of electricity, has been estimated for South Australia. We first undertake a review of the scholarly literature regarding electricity price elasticity for different regions and systems. Then we perform an empirical evaluation of the historic South Australian price elasticity, focussing on the relationship between price and demand quantiles at each half-​​hour of the day.

This work attempts to determine whether there is any variation in price sensitivity with the time of day or quantile, and to estimate the form of any relationships that might exist in South Australia.

Keywords: Electricity demand; Price elasticity.

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John L Pearce^a, Jason Beringer^a, Neville Nicholls^a, Rob J Hyndman^b, Petteri Uotila^a, and Nigel J Tapper^a

^a School of Geography and Environmental Science, Monash University, Melbourne, Australia
^b Department of Econometrics and Business Statistics, Monash University, Melbourne, Australia

Abstract
The influence of synoptic-​​scale circulations on air quality is an area of increasing interest to air quality management in regards to future climate change. This study presents an analysis where the dominant synoptic ‘types’ over the region of Melbourne, Australia are determined and linked to regional air quality. First, a self-​​organising map (SOM) is used to generate a time series of synoptic charts that classify the annual daily circulation affecting Melbourne into 20 different synoptic types. SOM results are then employed within the framework of a generalized additive model (GAM) to identify links between synoptic-​​scale circulations and observed changes air pollutant concentrations. The GAMs estimate shifts in pollutant concentrations under each synoptic type after controlling for long-​​term trends, seasonality, weekly emissions, spatial variation, and temporal persistence. Results showed the aggregate impact of synoptic circulations in the models to be quite modest as only 5.1% of the daily variance in O3, 4.7% in PM10, and 7.1% in NO2 were explained by shifts in synoptic circulations. Further analysis of the partial residual plots identified that despite a modest response at the aggregate level, individual synoptic categories had differential effects on air pollutants. In particular, increases of up to 40% in NO2 and PM10 and 30% in O3 occur when a synoptic conditions result in a north-​​easterly gradient wind over the Melbourne area. Additionally, NO2 and PM10 levels also showed increases of up to 40% when a strong high pressure system was centered directly over the Melbourne area. In sum, the unified approach of SOM and GAM proved to be a complementary suite of tools capable of identifying the entire range synoptic circulation patterns over a particular region and quantifying how they influence local air quality.

Keywords: air pollution, generalized additive models, self-​​organizing maps, and synoptic meteorology.

Working paper

John L Pearce^a, Jason Beringer^a, Neville Nicholls^a, Rob J Hyndman^b and Nigel J Tapper^a

^a School of Geography and Environmental Science, Monash University, Melbourne, Australia
^b Department of Econometrics and Business Statistics, Monash University, Melbourne, Australia

Abstract
Quantifying the observed relationships between local meteorology and air pollution provides air quality managers with a knowledge base that may prove useful in understanding how climate change may potentially impact air quality. This paper presents the estimated response of ozone (O3), particulate matter ≤ 10 μm (PM10), and nitrogen dioxide (NO2) to individual local meteorological variables in Melbourne, Australia over the period of 1999 to 2006. The relationships have been quantified after controlling for long-​​term trends, seasonality, weekly emissions, spatial variation, and temporal persistence using the framework of a generalized additive modelling (GAM). The nature of the response of each pollutant to individual meteorological variables is presented using partial residual plots described on a percentage scale as marginal effects. The aggregate impact of local meteorology in the models was found to explain 26.3% of the variance in O3, 21.1% in PM10, and 26.7% in NO2. High temperatures resulted in strongest positive response for all pollutants with a 150% increase above the mean for O3 and PM10 and a 120% for NO2. Other variables, such as boundary layer height, winds, water vapour pressure, radiation, precipitation and mean sea-​​level pressure, display some importance for one or more of the pollutants, but their impact in the models was less pronounced. Overall, this analysis presents a solid foundation for understanding the importance of local meteorology as a driver of regional air pollution in Melbourne in a framework that can be applied in other regions. Additionally, these results can be used to corroborate findings from studies using numerical air quality models.

Keywords: air pollution, climate change, generalized additive models, and meteorology.

Working paper

Han Lin Shang, Rob J Hyndman and Heather Booth

Abstract:

Keywords: mortality forecasting, life expectancy forecasting, principal component methods, Lee-​​Carter method, interval forecasts, forecasting time series.

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Alysha M De Livera and Rob J Hyndman

Abstract
A new innovations state space modeling framework, incorporating Box-​​Cox transformations, Fourier series with time varying coefficients and ARMA error correction, is introduced for forecasting complex seasonal time series that cannot be handled using existing forecasting models. Such complex time series include time series with multiple seasonal periods, high frequency seasonality, non-​​integer seasonality and dual-​​calendar effects. Our new modelling framework provides an alternative to existing exponential smoothing models, and is shown to have many advantages. The methods for initialization and estimation, including likelihood evaluation, are presented, and analytical expressions for point forecasts and interval predictions under the assumption of Gaussian errors are derived, leading to a simple, comprehensible approach to forecasting complex seasonal time series. Our trigonometric formulation is also presented as a means of decomposing complex seasonal time series, which cannot be decomposed using any of the existing decomposition methods. The approach is useful in a broad range of applications, and we illustrate its versatility in three empirical studies where it demonstrates excellent forecasting performance over a range of prediction horizons. In addition, we show that our trigonometric decomposition leads to the identification and extraction of seasonal components, which are otherwise not apparent in the time series plot itself.

Keywords: exponential smoothing, Fourier series, prediction intervals, seasonality, state space models, time series decomposition.

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Andrey V Kostenko and Rob J Hyndman

Abstract: Statistical significance testing has little useful purpose in business forecasting, and other tools are to be preferred. For selecting or ranking forecasting methods (especially those based on models) there exist simple but powerful and practical alternative approaches that are not tests in any sense. It is suggested that forecasters place less emphasis on $p$ values and more emphasis on the predictive ability of models.

Online article

Rob J. Hyndman¹ , Roman A. Ahmed¹ and George Athanasopoulos¹

1. Department of Econometrics and Business Statistics, Monash University, VIC 3800, Australia.

Abstract In many applications, there are multiple time series that are hierarchically organized and can be aggregated at several different levels in groups based on products, geography or some other features. We call these “hierarchical time series”. They are commonly forecast using either a “bottom-​​up” or a “top-​​down” method. In this paper we propose a new approach to hierarchical forecasting which provides optimal forecasts that are better than forecasts produced by either a top-​​down or a bottom-​​up approach. Our method is based on independently forecasting all series at all levels of the hierarchy and then using a regression model to optimally combine and reconcile these forecasts. The resulting revised forecasts add up appropriately across the hierarchy, are unbiased and have minimum variance amongst all combination forecasts under some simple assumptions. We show in a simulation study that our method performs well compared to two variants of the top-​​down approach and the bottom-​​up method. It also allows us to construct prediction intervals for the resultant forecasts. Finally, we apply the method to forecasting Australian tourism demand where the data are disaggregated by purpose of visit and geographical region.

Keywords: bottom-​​up forecasting, combining forecasts, GLS regression, hierarchical forecasting, Moore-​​Penrose inverse, reconciling forecasts, top-​​down forecasting.

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Pim Ouwehand¹ , Rob J Hyndman² , Ton G. de Kok¹ and Karel H. van Donselaar¹

1. Department of Technology Management, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.
2. Department of Econometrics and Business Statistics, Monash University, VIC 3800, Australia.

Abstract We present an approach to improve forecast accuracy by simultaneously forecasting a group of products that exhibit similar seasonal demand patterns. Better seasonality estimates can be made by using information on all products in a group, and using these improved estimates when forecasting at the individual product level. This approach is called the group seasonal indices (GSI) approach, and is a generalization of the classical Holt-​​Winters procedure. This article describes an underlying state space model for this method and presents simulation results that show when it yields more accurate forecasts than Holt-​​Winters.

Keywords: common seasonality, demand forecasting, exponential smoothing, Holt-​​Winters, state space model.

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Jae H. Kim¹ , Iain Fraser² and Rob J. Hyndman¹

1. Department of Econometrics and Business Statistics, Monash University, VIC 3800, Australia.
2. University of Kent, UK.

Abstract This paper proposes a new method of interval estimation for the long run response (or elasticity) parameter from a general linear dynamic model. We employ the bias-​​corrected bootstrap, in which small sample biases associated with the parameter estimators are adjusted in two stages of the bootstrap. As a means of bias-​​correction, we use alternative analytic and bootstrap methods. To take atypical properties of the long run elasticity estimator into account, the highest density region (HDR) method is adopted for the construction of confidence intervals. From an extensive Monte Carlo experiment, we found that the HDR confidence interval based on indirect analytic bias-​​correction performs better than other alternatives, providing tighter intervals with excellent coverage properties. Two case studies (demand for oil and demand for beef) illustrate the results of the Monte Carlo experiment with respect to the superior performance of the confidence interval based on indirect analytic bias-​​correction.

Keywords: ARDL model, bias-​​correction, bootstrapping, Highest density region, long run elasticity.

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