Farah Yasmeen, Rob J Hyndman and Bircan Erbas

Cancer Epidemiology, to appear

Abstract:
The disparity in breast cancer mortality rates among white and black US women is widening, with higher mortality rates among black women. We apply functional time series models on age-​​specific breast cancer mortality rates for each group of women, and forecast their mortality curves using exponential smoothing state-​​space models with damping.

The data were obtained from the Surveillance, Epidemiology and End Results (SEER) program of the US. Mortality data were obtained from the National Centre for Health Statistics (NCHS) available on the SEER*Stat database. We use annual unadjusted breast cancer mortality rates from 1969 to 2004 in 5-​​year age groups (45−49, 50–54, 55–59, 60–64, 65–69, 70–74, 75–79, 80–84). Age-​​specific mortality curves were obtained using nonparametric smoothing methods. The curves are then decomposed using functional principal components and we fit functional time series models with four basis functions for each population separately. The curves from each population are forecast and prediction intervals are calculated.

Twenty-​​year forecasts indicate an over-​​all decline in future breast cancer mortality rates for both groups of women. This decline is steeper among white women aged 55–73 and black women aged 60–84. For black women under 55 years of age, the forecast rates are relatively stable indicating no significant change in future breast cancer mortality rates among young black women in the next 20 years.

Keywords: Breast cancer mortality, racial and ethnic disparities, screening, trends, forecasting, functional data analysis

Working paper

Published paper

Han Lin Shang and Rob J Hyndman

Mathematics and Computers in Simulation (2010), to appear.

Abstract
We present a nonparametric method to forecast a seasonal univariate time series, and propose four dynamic updating methods to improve point forecast accuracy. Our methods consider a seasonal univariate time series as a functional time series. We propose first to reduce the dimensionality by applying functional principal component analysis to the historical observations, and then to use univariate time series forecasting and functional principal component regression techniques. When data in the most recent year are partially observed, we improve point forecast accuracy using dynamic updating methods. We also introduce a nonparametric approach to construct prediction intervals of updated forecasts, and compare the empirical coverage probability with an existing parametric method. Our approaches are data-​​driven and computationally fast, and hence they are feasible to be applied in real time high frequency dynamic updating. The methods are demonstrated using monthly sea surface temperatures from 1950 to 2008.

Keywords: Functional time series, Functional principal component analysis, Ordinary least squares, Penalized least squares, Ridge regression, Sea surface temperatures, Seasonal time series.

Working paper

Published paper

George Athanasopoulos, Rob J Hyndman, Haiyan Song and Doris Wu

International Journal of Forecasting (2011) 27(2), to appear

Abstract We evaluate the performance of various methods for forecasting tourism demand. The data used include 366 monthly series, 427 quarterly series and 518 yearly series, all supplied to us by tourism bodies or by academics from previous tourism forecasting studies. The forecasting methods implemented in the competition are univariate and multivariate time series approaches, and econometric models. This forecasting competition differs from previous competitions in several ways: (i) we concentrate only on tourism demand data; (ii) we include approaches with explanatory variables; (iii) we evaluate the forecast interval coverage as well as point forecast accuracy; (iv) we observe the effect of temporal aggregation on forecasting accuracy; and (v) we consider the mean absolute scaled error as an alternative forecasting accuracy measure. We find that pure time series approaches provide more accurate forecasts for tourism data than models with explanatory variables. For seasonal data we implement three fully automated pure time series algorithms that generate accurate point forecasts and two of these also produce forecast coverage probabilities which are satisfactorily close to the nominal rates. For annual data we find that Naïve forecasts are hard to beat.

Keywords: ARIMA, exponential smoothing, state space model, time varying parameter model, dynamic regression, autoregressive distributed lag model, vector autoregression.

Working paper

Online paper

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