1,721,173 research outputs found
Supplemental Material - Hierarchical Time Series Forecasting in Emergency Medical Services
No full textSupplemental Material for Hierarchical Time Series Forecasting in Emergency Medical Services by Bahman Rostami-Tabar and Rob J. Hyndman in Journal of Service Research</p
sj-pdf-2-jtr-10.1177_00472875211059240 – Supplemental material for Probabilistic Forecasts Using Expert Judgment: The Road to Recovery From COVID-19
No full textSupplemental material, sj-pdf-2-jtr-10.1177_00472875211059240 for Probabilistic Forecasts Using Expert Judgment: The Road to Recovery From COVID-19 by George Athanasopoulos, Rob J. Hyndman, Nikolaos Kourentzes and Mitchell O’Hara-Wild in Journal of Travel Research</p
sj-pdf-1-jtr-10.1177_00472875211059240 – Supplemental material for Probabilistic Forecasts Using Expert Judgment: The Road to Recovery From COVID-19
No full textSupplemental material, sj-pdf-1-jtr-10.1177_00472875211059240 for Probabilistic Forecasts Using Expert Judgment: The Road to Recovery From COVID-19 by George Athanasopoulos, Rob J. Hyndman, Nikolaos Kourentzes and Mitchell O’Hara-Wild in Journal of Travel Research</p
Lee-Carter mortality forecasting: a multi-country comparison of variants and extensions
No full textHeather Booth, Rob J. Hyndman, Leonie Tickle and Piet de Jong compare the short- to medium- term accuracy of five variants or extensions of the Lee-Carter method for mortality forecasting
Measuring forecast accuracy
No full textEveryone wants to know how accurate their forecasts are. Does your forecasting method give good forecasts? Are they better than the competitor methods? There are many ways of measuring the accuracy of forecasts, and the answers to these questions depends on what is being forecast, what accuracy measure is used, and what data set is used for computing the accuracy measure. In this chapter, I will summarize the most important and useful approaches. 1 Training and test sets It is important to evaluate forecast accuracy using genuine forecasts. That is, it is invalid to look at how well a model fits the historical data; the accuracy of forecasts can only be determined by considering how well a model performs on new data that were not used when estimating the model. When choosing models, it is common to use a portion of the available data for testing, and use the rest of the data for estimating (or “training”) the model. Then the testing data can be used to measure how well the model is likely to forecast on new data. Training data Test data ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● time Figure 1: A time series is often divided into training data (used to estimate the model) and test data (used to evaluate the forecasts). The size of the test data set is typically about 20 % of the total sample, although this value depends on how long the sample is and how far ahead you want to forecast. The size of the test set should ideally be at least as large as the maximum forecast horizon required. 1 This chapter is based on Section 2.5 of Forecasting: principles and practice by Rob J Hyndman and George Athanasopoulos, available online at www.otexts.org/fpp/2/5, and used with permission. 1 Measuring forecast accuracy The following points should be noted. • A model which fits the data well does not necessarily forecast well. • A perfect fit can always be obtained by using a model with enough parameters. • Over-fitting a model to data is as bad as failing to identify the systematic pattern in the data. Some references describe the test data as the “hold-out set ” because these data are “held out ” of the data used for fitting. Other references call the training data the “in-sample data ” and the test data the “out-of-sample data”. 2 Forecas
Automatic Time Series Forecasting: The forecast Package for R
Full text linkAutomatic forecasts of large numbers of univariate time series are often needed in business and other contexts. We describe two automatic forecasting algorithms that have been implemented in the forecast package for R. The first is based on innovations state space models that underly exponential smoothing methods. The second is a step-wise algorithm for forecasting with ARIMA models. The algorithms are applicable to both seasonal and non-seasonal data, and are compared and illustrated using four real time series. We also briefly describe some of the other functionality available in the forecast package.
A gradient boosting approach to the Kaggle load forecasting competition
Full text linkWe describe and analyse the approach used by Team TinTin (Souhaib Ben Taieb and Rob J Hyndman) in the Load Forecasting track of the Kaggle Global Energy Forecasting Competition 2012. The competition involved a hierarchical load forecasting problem for a US utility with 20 geographical zones. The data available consisted of the hourly loads for the 20 zones and hourly temperatures from 11 weather stations, for four and a half years. For each zone, the hourly electricity loads for nine different weeks needed to be predicted without having the locations of either the zones or stations. We used separate models for each hourly period, with component-wise gradient boosting for estimating each model using univariate penalised regression splines as base learners. The models allow for the electricity demand changing with the time-of-year, day-of-week, time-of-day, and on public holidays, with the main predictors being current and past temperatures, and past demand. Team TinTin ranked fifth out of 105 participating teams. © 2013 International Institute of Forecasters.SCOPUS: ar.jinfo:eu-repo/semantics/publishe
Modeling time series with complex seasonal patterns using exponential smoothing
No full textNew innovations state space modeling tools, incorporating Box-Cox transformations, Fourier series with time varying coefficients and ARMA error correction, are introduced for modeling complex seasonal time series. Such complex seasonal time series include those with multiple seasonal periods, high frequency seasonality, non-integer seasonality and dual-calendar effects. It is demonstrated that the new modeling practices provide alternatives to existing exponential smoothing approaches, but are shown to have several key advantages. The new approaches are complete with well-defined methods for initialization and estimation, including likelihood evaluation and the derivation of analytical expressions for point forecasts and interval predictions under the assumption of Gaussian errors, leading to simple, comprehensible approaches to modeling complex seasonal time series. The new approaches are capable of forecasting and decomposing non-seasonal, single seasonal and complex seasonal time series, and are useful in a broad range of applications. Their versatility is illustrated in various empirical studies, and it is also shown that the new approaches lead to the identification and extraction of seasonal components, which are otherwise not apparent in the time series plot itself. In addition, the new procedures are demonstrated as automated algorithms, and are shown to provide competitive forecast accuracy compared to the existing methods with several options. Relevant R software programs have been developed, and the implementation is presented using real life time series
Functional linear models for mortality forecasting
No full textOver the last two decades, a number of approaches have been developed for modeling and forecasting mortality rates. However, using these models for two or more groups leads to inconsistent results, and various approaches have been proposed to resolve this problem. In this thesis, I present two new classes of functional linear models for analyzing, modeling and forecasting multiple time series corresponding to age-specific mortality rates of two or more groups within similar populations, which have related dynamics. Such groups might be males and females in the same population, different parts of a country (e.g. different provinces and states), races within a country (such as African American, White and Hispanic women in the United States), or different countries within a particular geographical region (for example, countries in the G7 group). The definition of “group” here depends on the forecaster’s judgement. It is desirable for the disaggregated forecasts to be coherent with the overall forecast. In particular, a common restriction is that the sub-group forecasts should not diverge in the long run, and that the relative mortality rates of the sub-groups should be approximately the same in the forecast period as in the historical period. This thesis is concerned with both theoretical and methodological developments of coherent mortality forecasting and the practical application of these new methods to various problems of real and current interest. I develop methods that are suitable for forecasting not only all-cause mortality data, but also cause-specific mortality, such as mortality rates of chronic diseases, in contrast to the traditional age-period-cohort models. The first contribution of this thesis is to obtain age-related predictions of black and white breast cancer mortality rates in the United States. To the best of my knowledge, this is the first such study. I have successfully applied functional time series models to the breast cancer mortality data, as an alternative to the widely used APC models. I have shown that these models not only provide a basis for modeling age-specific mortality rates, but can also be used to provide mortality forecasts and prediction intervals. A new method for the coherent forecasting of two or more functional time series of mortality rates is proposed in chapter 4. This method is based on modelling the products and ratios of mortality rates from each individual group, rather than modelling the mortality rates themselves. The proposed method simplifies the modelling procedure greatly, and provides a convenient and interpretable way of imposing coherence on the resulting forecasts. Relative to other recent proposals for coherent forecasting, the new approach is simpler to apply, is more flexible in allowing different types of dynamics, and produces more accurate forecasts. In this thesis, I relate some of the model extensions proposed by Hyndman & Ullah (2007), to the common principal components (CPC) and partial common principal components (PCPC) models introduced by Flury (1988). I combine the ideas of functional principal components and CPC analysis with time series, and call the resulting models common functional principal component (CFPC) models. I then use these models for the coherent forecasting of mortality rates. Although Hyndman & Ullah (2007) proposed these models, they did not discuss how they might be estimated or implemented. I therefore provide the methods for parameter estimation and forecasting using these models. I propose a sequential procedure to estimate the common and non-common/specific components, and use vector error correction models (VECM) to forecast the specific time series coefficients. I have applied the new methods to several types of disaggregated mortality rate data (disaggregated by sex, by region and by race). The newly developed functional linear models allow for non-divergence constraints to be imposed simply and naturally. Through the application of these new forecasting methods to the breast cancer mortalitydata of black and white women in the United States, I have found that the breast cancer mortality rates for both races are expected to decline, with the mortality rates of blacks remaining higher than those of whites for all age-groups. My analysis suggests that black women do not benefit equally from mammography and screening programs, and that a Forecasting disparity between the breast cancer mortality rates of the two races is expected to continue into the future
Estimating and forecasting a time series of densities using a functional data approach
No full textFunctional data analysis is a branch of statistics that uses a collection of statistical methods to analyse data in the form of functions or curves. Density functions are a specific case of functional data. In recent years, forecasting functional data has received much attention; however, forecasting functional data when functions are density functions has not been extensively addressed in the literature. This thesis has demonstrated that a time series of densities can be effectively forecast using a functional data approach. The first contribution of this thesis is to propose an estimation method to nonparametrically estimate a time series of densities, taking account of the time ordering of densities. A data set comprising many observations is recorded at each time period, and the associated probability density function is to be estimated for each time period. A logspline approach is applied to each data set separately where each estimated density has common knots but different coefficients. These estimated densities form a 'functional time series'. The second contribution of this thesis is to propose three conditional density estimation methods with time as the discrete conditioning variable: (1) a conditional logspline approach accounting for the time variation by flexibly adjusting the smoothness of the conditional density functions; (2) a conditional logspline approach applied to all data simultaneously with common knots and kernel weights to account for the time variation; (3) a conditional kernel approach with two new bandwidth selection methods where the kernel weights account for the time variation. The proposed conditional density estimation methods are compared with conditional kernel estimation using two existing bandwidth selection methods: the uniform reference rule and the bootstrap method. The third contribution of this thesis is to propose a decomposition and forecasting algorithm to forecast future densities by decomposing the functional time series into orthonormal basis functions and their uncorrelated coefficients. Different sets of future densities are forecast using univariate time series models applied to the coefficients obtained from various decomposition methods: the functional principal component analysis with log-transformation, three multidimensional scaling methods and eight projection pursuit methods. The prediction intervals of the forecast density functions are constructed. The fourth contribution of this thesis is to propose a new method to evaluate the reliability of density forecasts assessing calibration using probability integral transforms, considering thousands of observations for each future time period. We apply our methods to two simulated data sets (unimodal and bimodal) and four real data sets. The four real data sets comprise United Kingdom and Australian income and age data over many years with thousands of observations per year. Proper scoring rules are then used to evaluate the relative accuracy of the density forecasts by assessing both calibration and sharpness simultaneously
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