Forecasting COVID-19 daily cases using phone call data

The need to forecast COVID-19 related variables continues to be pressing as the epidemic unfolds. Different efforts have been made, with compartmental models in epidemiology and statistical models such as AutoRegressive Integrated Moving Average (ARIMA), Exponential Smoothing (ETS) or computing intelligence models. These efforts have proved useful in some instances by allowing decision makers to distinguish different scenarios during the emergency, but their accuracy has been disappointing, forecasts ignore uncertainties and less attention is given to local areas. In this study, we propose a simple Multiple Linear Regression model, optimised to use call data to forecast the number of daily confirmed cases. Moreover, we produce a probabilistic forecast that allows decision makers to better deal with risk. Our proposed approach outperforms ARIMA, ETS and a regression model without call data, evaluated by three point forecast error metrics, one prediction interval and two probabilistic forecast accuracy measures. The simplicity, interpretability and reliability of the model, obtained in a careful forecasting exercise, is a meaningful contribution to decision makers at local level who acutely need to organise resources in already strained health services. We hope that this model would serve as a building block of other forecasting efforts that on the one hand would help front-line personal and decision makers at local level, and on the other would facilitate the communication with other modelling efforts being made at the national level to improve the way we tackle this pandemic and other similar future challenges.Comment: 13 pages, 7 figure

Exploring the association between time series features and forecasting by temporal aggregation using machine learning

When a forecast of the total value over several time periods ahead is required, forecasters are presented with two temporal aggregation (TA) approaches to produce required forecasts: i) aggregated forecast (AF) or ii) aggregate data using non-overlapping temporal aggregation (AD). Often, the recommendation is to aggregate data to a frequency relevant to the decision the eventual forecast will support and then produce the forecast. However, this might not be always the best choice and we argue that both AF and AD approaches may outperform each other in different situations. Moreover, there is a lack of evidence on what indicators may determine the superiority of each approach. We design and execute an empirical experiment framework to first explore the performance of these approaches using monthly time series of M4 competition dataset. We further turn the problem into a classification supervised learning by constructing a database consisting of features of each time series as predictor and model class labelled as AF/AD as response/outcome. We then build machine learning algorithms to investigate the association between time series features and the performance of AF and AD. Our findings suggest that both AF and AD approaches may not consistently generate accurate results for every individual series. AF is shown to be significantly better than AD for the monthly M4 time series, especially for longer horizons. We build several machine learning approaches using a set of extracted time series features as input to predict accurately whether AD or AF should be used. We find out that Random Forest (RF) is the most accurate approach in correctly classifying the outcome assessed both by statistical measures such as misclassification error, F-statistics, area under the curve, and a utility measure. The RF approach reveals that curvature, nonlinearity, seas_pacf, unitroot_pp, mean, ARCHM.LM, Coefficient of Variation, stability, linearity, and max_level_shif are among the most important features in driving the predictions of the model. Our findings indicate that the strength of trend, ARCH.LM, hurst, autocorrelation lag 1, unitroot_pp, and seas_pacf may favour AF approach, while lumpiness, entropy, nonlinearity, curvature, and strength of seasonality may increase the chance of AD performing bet

Demand forecasting by temporal aggregation:Using optimal or multiple aggregation levels?

Recent advances have demonstrated the benefits of temporal aggregation for demand forecasting, including increased accuracy, improved stock control and reduced modelling uncertainty. With temporal aggregation a series is transformed, strengthening or attenuating different elements and thereby enabling better identification of the time series structure. Two different schools of thought have emerged. The first focuses on identifying a single optimal temporal aggregation level at which a forecasting model maximises its accuracy. In contrast, the second approach fits multiple models at multiple levels, each capable of capturing different features of the data. Both approaches have their merits, but so far they have been investigated in isolation. We compare and contrast them from a theoretical and an empirical perspective, discussing the merits of each, comparing the realised accuracy gains under different experimental setups, as well as the implications for business practice. We provide suggestions when to use each for maximising demand forecasting gains

Anticipating special events in emergency department forecasting

Accurate daily forecast of Emergency Department (ED) attendance helps roster planners in allocating available resources more effectively and potentially influences staffing. Since special events affect human behaviours, they may increase or decrease the demand for ED services. Therefore, it is crucial to model their impact and use them to forecast future attendance to improve roster planning and avoid reactive strategies. In this paper, we propose, for the first time, a forecasting model to generate both point and probabilistic daily forecast of ED attendance. We model the impact of special events on ED attendance by considering real-life ED data. We benchmark the accuracy of our model against three time-series techniques and a regression model that does not consider special events. We show that the proposed model outperforms its benchmarks across all horizons for both point and probabilistic forecasts. Results also show that our model is more robust with an increasing forecasting horizon. Moreover, we provide evidence on how different types of special events may increase or decrease ED attendance. Our model can easily be adapted for use not only by EDs but also by other health services. It could also be generalised to include more types of special events

Non-stationary demand forecasting by cross-sectional aggregation

In this paper the relative effectiveness of top-down (TD) versus bottom-up (BU) approaches is compared for cross-sectionally forecasting aggregate and sub-aggregate demand. We assume that the sub-aggregate demand follows a non-stationary Integrated Moving Average (IMA) process of order one and a Single Exponential Smoothing (SES) procedure is used to extrapolate future requirements. Such demand processes are often encountered in practice and SES is one of the standard estimators used in industry (in addition to being the optimal estimator for an IMA process). Theoretical variances of forecast error are derived for the BU and TD approach in order to contrast the relevant forecasting performances. The theoretical analysis is supported by an extensive numerical investigation at both the aggregate and sub-aggregate level, in addition to empirically validating our findings on a real dataset from a European superstore. The results demonstrate the increased benefit resulting from cross-sectional forecasting in a non-stationary environment than in a stationary one. Valuable insights are offered to demand planners and the paper closes with an agenda for further research in this area. © 2015 Elsevier B.V. All rights reserved

Hierarchical time series forecasting in emergency medical services

Accurate forecasts of ambulance demand are crucial inputs when planning and deploying staff and fleet. Such demand forecasts are required at national, regional, and sub-regional levels, and must take account of the nature of incidents and their priorities. These forecasts are often generated independently by different teams within the organization. As a result, forecasts at different levels may be inconsistent, resulting in conflicting decisions and a lack of coherent coordination in the service. To address this issue, we exploit the hierarchical and grouped structure of the demand time series and apply forecast reconciliation methods to generate both point and probabilistic forecasts that are coherent and use all the available data at all levels of disaggregation. The methods are applied to daily incident data from an ambulance service in Great Britain, from October 2015 to July 2019, disaggregated by nature of incident, priority, managing health board, and control area. We use an ensemble of forecasting models and show that the resulting forecasts are better than any individual forecasting model. We validate the forecasting approach using time series cross validation

The bullwhip effect under count time series: The case of first order integer auto-regressive demand processes

The impact of fast moving items, modeled by auto-regressive moving average (ARMA) type processes, on the bullwhip effect is well known. However, slow moving items that can be modeled using integer ARMA processes have received little attention. Herein, we measure the impact of bullwhip effect under a first order integer auto-regressive, INAR(1), demand process. We consider a simple two-stage supply chain consisting of a retailer and a manufacturer. We assume that the retailer employs a base stock inventory policy when the demand is forecasted using a minimum mean squared error method. We investigate the impact of the INAR(1) demand process parameter, , and the replenishment lead time, L, on the bullwhip effect generated by the order-up-to replenishment policy. We show that the bullwhip effect is increasing with the lead-time L