arXiv subjects

James W. Taylor

Publications and source records attributed to James W. Taylor.

9 recordsLinked to original sources

arXiv2026

A Forecast Combination Framework for Hierarchical and Grouped Time Series Reconciliation

Forecast combining and forecast reconciliation for hierarchical and grouped time series have largely developed as separate research areas. This paper connects the two by developing a forecast combination framework for forecast reconciliation. For each bottom-level series, we construct a maximal linearly independent set of structured candidate forecasts from aggregation constraints, and show that combining these candidates and aggregating the resulting bottom-level forecasts is equivalent to standard unbiased linear reconciliation. Within this representation, we prove that mean-squared-error optimal combination weights exactly recover the widely used Minimum Trace (MinT) reconciliation. We further show that the optimal weight problem is separable across different bottom-level series, each yielding a Bates--Granger optimal forecast combination. This reveals MinT as a collection of optimal combinations over hierarchy-induced candidate forecasts. For finite-sample estimation, we propose a modular penalized framework that nests existing MinT variants and supports rich extensions including covariance shrinkage, weight penalization, and scalable series-wise separate estimation. Empirical results show that the framework is practically implementable, competitive with existing methods, and can improve accuracy while preserving coherence. Overall, the forecast combination perspective offers new interpretations of existing reconciliation approaches and provides a flexible basis for designing new methods.

stat.ME↗

arXiv2026

Combining a Large Pool of Forecasts of Value-at-Risk and Expected Shortfall

We consider the combination of value-at-risk (VaR) and expected shortfall (ES) forecasts when a large pool of candidate forecasts is available. Given the limited literature in this area, we implement a variety of new combining methods. In terms of simplistic methods, in addition to the mean, we consider the median and mode. As a complement to the previously proposed performance-based weighted combinations, we use regularisation to reduce overfitting in the presence of many weights. Treating VaR and ES forecasts jointly as interval forecasts allows the application of adapted interval forecast combination methods, including trimmed means and a mixtures approach based on inferred probability distributions. In an empirical study involving 90 forecasting methods, trimmed mean combinations, the mixtures method, and performance-based weighting delivered particularly strong results. However, greater forecasting accuracy resulted for a pool of just six methods, chosen to ensure diversity, with performance-based weighting producing the best overall performance.

q-fin.RM↗

arXiv2025

Angular Combining of Forecasts of Probability Distributions

When multiple forecasts are available for a probability distribution, forecast combining enables a pragmatic synthesis of the information to extract the wisdom of the crowd. The linear opinion pool has been widely used, whereby the combining is applied to the probabilities of the distributional forecasts. However, it has been argued that this will tend to deliver overdispersed distributions, prompting the combination to be applied, instead, to the quantiles of the distributional forecasts. Results from different applications are mixed, leaving it as an empirical question whether to combine probabilities or quantiles. In this paper, we present an alternative approach. Looking at the distributional forecasts, combining the probabilities can be viewed as vertical combining, with quantile combining seen as horizontal combining. Our proposal is to allow combining to take place on an angle between the extreme cases of vertical and horizontal combining. We term this angular combining. The angle is a parameter that can be optimized using a proper scoring rule. For implementation, we provide a pragmatic numerical approach and a simulation algorithm. Among our theoretical results, we show that, as with vertical and horizontal averaging, angular averaging results in a distribution with mean equal to the average of the means of the distributions that are being combined. We also show that angular averaging produces a distribution with lower variance than vertical averaging, and, under certain assumptions, greater variance than horizontal averaging. We provide empirical results for distributional forecasts of Covid mortality, macroeconomic survey data, and electricity prices.

stat.ME↗

arXiv2023

Scores for Multivariate Distributions and Level Sets

Forecasts of multivariate probability distributions are required for a variety of applications. Scoring rules enable the evaluation of forecast accuracy, and comparison between forecasting methods. We propose a theoretical framework for scoring rules for multivariate distributions, which encompasses the existing quadratic score and multivariate continuous ranked probability score. We demonstrate how this framework can be used to generate new scoring rules. In some multivariate contexts, it is a forecast of a level set that is needed, such as a density level set for anomaly detection or the level set of the cumulative distribution as a measure of risk. This motivates consideration of scoring functions for such level sets. For univariate distributions, it is well-established that the continuous ranked probability score can be expressed as the integral over a quantile score. We show that, in a similar way, scoring rules for multivariate distributions can be decomposed to obtain scoring functions for level sets. Using this, we present scoring functions for different types of level set, including density level sets and level sets for cumulative distributions. To compute the scores, we propose a simple numerical algorithm. We perform a simulation study to support our proposals, and we use real data to illustrate usefulness for forecast combining and CoVaR estimation.

math.ST↗

arXiv2020

A Comparison of Aggregation Methods for Probabilistic Forecasts of COVID-19 Mortality in the United States

The COVID-19 pandemic has placed forecasting models at the forefront of health policy making. Predictions of mortality and hospitalization help governments meet planning and resource allocation challenges. In this paper, we consider the weekly forecasting of the cumulative mortality due to COVID-19 at the national and state level in the U.S. Optimal decision-making requires a forecast of a probability distribution, rather than just a single point forecast. Interval forecasts are also important, as they can support decision making and provide situational awareness. We consider the case where probabilistic forecasts have been provided by multiple forecasting teams, and we aggregate the forecasts to extract the wisdom of the crowd. With only limited information available regarding the historical accuracy of the forecasting teams, we consider aggregation (i.e. combining) methods that do not rely on a record of past accuracy. In this empirical paper, we evaluate the accuracy of aggregation methods that have been previously proposed for interval forecasts and predictions of probability distributions. These include the use of the simple average, the median, and trimming methods, which enable robust estimation and allow the aggregate forecast to reduce the impact of a tendency for the forecasting teams to be under- or overconfident. We use data that has been made publicly available from the COVID-19 Forecast Hub. While the simple average performed well for the high mortality series, we obtained greater accuracy using the median and certain trimming methods for the low and medium mortality series. It will be interesting to see if this remains the case as the pandemic evolves.

stat.AP↗

arXiv2020

Probabilistic Forecasting of Patient Waiting Times in an Emergency Department

We study the estimation of the probability distribution of individual patient waiting times in an emergency department (ED). Our feature-rich modelling allows for dynamic updating and refinement of waiting time estimates as patient- and ED-specific information (e.g., patient condition, ED congestion levels) is revealed during the waiting process. Aspects relating to communicating forecast uncertainty to patients, and implementing this methodology in practice, are also discussed.

stat.AP↗

arXiv2018

Rule-based Autoregressive Moving Average Models for Forecasting Load on Special Days: A Case Study for France

This paper presents a case study on short-term load forecasting for France, with emphasis on special days, such as public holidays. We investigate the generalisability to French data of a recently proposed approach, which generates forecasts for normal and special days in a coherent and unified framework, by incorporating subjective judgment in univariate statistical models using a rule-based methodology. The intraday, intraweek, and intrayear seasonality in load are accommodated using a rule-based triple seasonal adaptation of a seasonal autoregressive moving average (SARMA) model. We find that, for application to French load, the method requires an important adaption. We also adapt a recently proposed SARMA model that accommodates special day effects on an hourly basis using indicator variables. Using a rule formulated specifically for the French load, we compare the SARMA models with a range of different benchmark methods based on an evaluation of their point and density forecast accuracy. As sophisticated benchmarks, we employ the rule-based triple seasonal adaptations of Holt-Winters-Taylor (HWT) exponential smoothing and artificial neural networks (ANNs). We use nine years of half-hourly French load data, and consider lead times ranging from one half-hour up to a day ahead. The rule-based SARMA approach generated the most accurate forecasts.

stat.AP↗

arXiv2014

Forecasting Electricity Smart Meter Data Using Conditional Kernel Density Estimation

The recent advent of smart meters has led to large micro-level datasets. For the first time, the electricity consumption at individual sites is available on a near real-time basis. Efficient management of energy resources, electric utilities, and transmission grids, can be greatly facilitated by harnessing the potential of this data. The aim of this study is to generate probability density estimates for consumption recorded by individual smart meters. Such estimates can assist decision making by helping consumers identify and minimize their excess electricity usage, especially during peak times. For suppliers, these estimates can be used to devise innovative time-of-use pricing strategies aimed at their target consumers. We consider methods based on conditional kernel density (CKD) estimation with the incorporation of a decay parameter. The methods capture the seasonality in consumption, and enable a nonparametric estimation of its conditional density. Using eight months of half-hourly data for one thousand meters, we evaluate point and density forecasts, for lead times ranging from one half-hour up to a week ahead. We find that the kernel-based methods outperform a simple benchmark method that does not account for seasonality, and compare well with an exponential smoothing method that we use as a sophisticated benchmark. To gauge the financial impact, we use density estimates of consumption to derive prediction intervals of electricity cost for different time-of-use tariffs. We show that a simple strategy of switching between different tariffs, based on a comparison of cost densities, delivers significant cost savings for the great majority of consumers.

stat.AP↗

arXiv2014

Short-term Forecasting of Anomalous Load Using Rule-based Triple Seasonal Methods

Numerous methods have been proposed for forecasting load for normal days. Modeling of anomalous load, however, has often been ignored in the research literature. Occurring on special days, such as public holidays, anomalous load conditions pose considerable modeling challenges due to their infrequent occurrence and significant deviation from normal load. To overcome these limitations, we adopt a rule-based approach, which allows incorporation of prior expert knowledge of load profiles into the statistical model. We use triple seasonal Holt-Winters-Taylor (HWT) exponential smoothing, triple seasonal autoregressive moving average (ARMA), artificial neural networks (ANNs), and triple seasonal intraweek singular value decomposition (SVD) based exponential smoothing. These methods have been shown to be competitive for modeling load for normal days. The methodological contribution of this paper is to demonstrate how these methods can be adapted to model load for special days, when used in conjunction with a rule-based approach. The proposed rule-based method is able to model normal and anomalous load in a unified framework. Using nine years of half-hourly load for Great Britain, we evaluate point forecasts, for lead times from one half-hour up to a day ahead. A combination of two rule-based methods generated the most accurate forecasts.

stat.AP↗