Rob J Hyndman and Han Lin Shang

Journal of Computational and Graphical Statistics (2010), 19(1), 29-45.

Abstract: We propose new tools for visualizing large numbers of functional data in the form of smooth curves or surfaces. The proposed tools include functional versions of the bagplot and boxplot, and make use of the first two robust principal component scores, Tukey’s data depth and highest density regions.

By-products of our graphical displays are outlier detection methods for functional data. We compare these new outlier detection methods with existing methods for detecting outliers in functional data and show that our methods are better able to identify the outliers.

Keywords: Highest density regions, Robust principal component analysis, Kernel density estimation, Outlier detection, Tukey’s halfspace depth.

Online paper

Working paper

R package

Bircan Erbas¹, Muhammad Akram², Dorota M Gertig³, Dallas English^4,5, John L. Hopper⁵, Anne M Kavanagh⁶ and Rob J Hyndman²

Journal of Epidemiology (2010), 20(2), 159-165.

1. School of Public Health, La Trobe University, Bundoora, 3086 Australia
2. Business and Economic Forecasting Unit, Monash University, Clayton, 3800, Australia.
3. Victoria Cytology Service Inc, Carlton, 3053 Australia.
4. Cancer Epidemiology Centre, The Cancer Council Victoria, Carlton 3053 Australia.
5. Centre for MEGA Epidemiology, The University of Melbourne, Parkville 3053 Australia.
6. Key Centre for Women’s Health in Society, School of Population Health, The University of Melbourne, Parkville, 3053 Australia.

ABSTRACT

Background: Mortality/incidence predictions are used for planning public health resources and need to accurately reflect age-related changes through time. We present a new forecasting model to estimate future trends in age-related breast cancer mortality for the United States and England-Wales.

Material and methods: We use functional data analysis techniques to model breast cancer mortality-age relationships in the United States from 1950 to 2001 and England-Wales from 1950 to 2003, and estimate 20-year predictions using a new forecasting method.

Results: In the United States, trends for women aged 45–54 years continued to decline since 1980. In contrast, trends in women aged 60 – 84 years increased in the 1980s and declined in the 1990s. For England-Wales, trends for women aged 45 to 74 years slightly increased prior to 1980, but declined thereafter. The greatest age-related changes for both countries were during the 1990s. For both the United States and England-Wales, trends are expected to decline and then stabilize with the greatest decline in women aged 60 – 70 years. Forecasts suggest relatively stable trends for women over 75 years.

Conclusions: Predicting age related changes in mortality/incidence can be used for planning and targeting programs for specific age groups. Currently, these models are being extended to incorporate other variables that may influence age-related changes in mortality/incidence trends. In their current form, these models will be most useful for modelling and projecting future trends of diseases where there has been very little advancement in treatment and minimal cohort effects such as lethal cancers.

Key words: breast cancer, forecasting, functional-data-analysis models, mortality trends

Online paper

Jan Verbesselt¹, Rob J Hyndman², Glenn Newnham¹, Darius Culvenor¹

Remote Sensing of Environment (2010), 114(1), 106-115.

1. Remote sensing team, CSIRO Sustainable Ecosystems, Private Bag 10, Melbourne VIC 3169, Australia
2. Department of Econometrics and Business Statistics, Monash University, Melbourne VIC 3800, Australia

Abstract

A wealth of remotely sensed time series covering large areas is now available to the earth science community. Change detection methods are often not capable of detecting land cover changes within time series that are heavily influenced by seasonal climatic variations. Detecting change within the trend and seasonal components of time series enables the detection of different types of changes. Changes occurring in the trend component indicate disturbances (e.g., insect attack), while changes occurring in the seasonal component indicate phenological changes (e.g., change in land cover type). An approach is proposed for automated change detection in time series by detecting and characterizing Breaks For Additive Seasonal and Trend (BFAST). BFAST integrates the decomposition of time series into trend, seasonal, and remainder components with methods for detecting significant change within time series. BFAST iteratively estimates the time and number of changes, and characterizes change by its magnitude and direction. We tested BFAST by simulating 16-day composites of Normalized Difference Vegetation Index (NDVI) time series with varying amounts of seasonality and noise, and by adding abrupt changes at different times and magnitudes. This revealed that BFAST can robustly detect change with different magnitudes (>0.1 NDVI) within time series with different noise levels (0.01–0.07 σ) and seasonal amplitudes (0.1–0.5 NDVI) Additionally, BFAST was applied to 16-day NDVI MODIS (Moderate Resolution Imaging Spectroradiometer) composites for a forested study area in south eastern Australia. This showed that BFAST is able to detect and characterize spatial and temporal changes in a forested landscape. BFAST is developed as a generic change detection approach, and can be applied to time series without the need to normalize for specific land cover types, select a reference period, or define a threshold or change trajectory. The method can be used to detect and characterize changes within time series or can be integrated within monitoring frameworks and used as an alarm system to flag when and where significant changes occur.

Online paper

Rob J Hyndman and Shu Fan

IEEE Transactions on Power Systems, 2010, to appear.

Abstract: Long-term electricity demand forecasting plays an important role in planning for future generation facilities and transmission augmentation. In a long term context, planners must adopt a probabilistic view of potential peak demand levels, therefore density forecasts (providing estimates of the full probability distributions of the possible future values of the demand) are more helpful than point forecasts, and are necessary for utilities to evaluate and hedge the financial risk accrued by demand variability and forecasting uncertainty. This paper proposes a new methodology to forecast the density of long-term peak electricity demand.

Peak electricity demand in a given season is subject to a range of uncertainties, including underlying population growth, changing technology, economic conditions, prevailing weather conditions (and the timing of those conditions), as well as the general randomness inherent in individual usage. It is also subject to some known calendar effects due to the time of day, day of week, time of year, and public holidays.

We describe a comprehensive forecasting solution in this paper. First, we use semi-parametric additive models to estimate the relationships between demand and the driver variables, including temperatures, calendar effects and some demographic and economic variables. Then we forecast the demand distributions using a mixture of temperature simulation, assumed future economic scenarios, and residual bootstrapping. The temperature simulation is implemented through a new seasonal bootstrapping method with variable blocks.

The proposed methodology has been used to forecast the probability distribution of annual and weekly peak electricity demand for South Australia since 2007. We evaluate the performance of the methodology by comparing the forecast results with the actual demand of the summer 2007/08.

Keywords: Long-term demand forecasting, density forecast, time series, simulation.

Online article

Ashton de Silva¹, Rob J Hyndman² and Ralph D Snyder²

Statistical modelling (2010), to appear.

1. School of Economics, Finance and Marketing, RMIT, VIC 3000, Australia.
2. Department of Econometrics and Business Statistics, Monash University, VIC 3800, Australia.

Abstract The vector innovations structural time series framework is proposed as a way of modelling a set of related time series. Like all multivariate approaches, the aim is to exploit potential inter-series dependencies to improve the fit and forecasts. The model is based around an unobserved vector of components representing features such as the level and slope of each time series. Equations that describe the evolution of these components through time are used to represent the inter-temporal dependencies. The approach is illustrated on a bivariate data set comprising Australian exchange rates of the UK pound and US dollar. The forecasting accuracy of the new modelling framework is compared to other common uni- and multivariate approaches in an experiment using time series from a large macroeconomic database.

Keywords: vector innovations structural time series, state space model, multivariate time series, exponential smoothing, forecast comparison, vector autoregression.

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