Art’s many contributions to the quantitative modeling of spatial processes provide a solid foundation for generations of researchers to come. In this review, we take a roughly chronological path through Art’s published research, starting with his work on spatial point processes, which demonstrated the frequent pattern of inhibition at a very local scale and clustering at a larger scale. In turn, this led to his development of local statistics for detecting hotspots and related inferential procedures. When data are spatially aggregated, the form of dependence is often specified using a weighting matrix and Art developed a flexible framework for specifying the matrix structure. His later research on the spread of infectious diseases was also important in understanding the nature of disease spread. Art’s keen insights and his ability to formulate novel issues are apparent throughout his published works.

‘Epidemics in Small Communities’ develops an understanding of the ways in which an infection can achieve community circulation in small geographical areas. It begins by examining the local disease records of two doctors in general practice in the United Kingdom (William Pickles of Wensleydale and Edgar Hope-Simpson of Cirencester) to shed light on the processes whereby individual cases of diseases, such as measles and influenza, can develop into full-blown epidemics. The second half of the chapter focuses on Iceland as an island laboratory for the study of epidemic diffusion processes in the period 1902–1988. For this 87-year period, records of 131 discrete epidemic waves (with a recorded total of >0.5 million cases) of measles, influenza, and five other infectious diseases are examined in terms of wave spacing, wave velocity, and wave geography. These findings are related both to epidemiological theory and to aspects of the changing historical geography of the island.

‘Infectious Disease Control’ examines the historical development of approaches to the geographical control, elimination, and eradication of infectious diseases. It begins at a local spatial scale, seven centuries ago, among the plague-ridden lazarettos of Venice. It ends at the global scale with twenty-first-century developments in the Internet-based monitoring and surveillance of infectious diseases. Basic spatial strategies for the control of infectious diseases (defensive isolation and offensive containment) are outlined, their historical development and application in the form of such measures as cordons sanitaires, isolation, and quarantine are reviewed, and their present-day forms highlighted. Vaccines and vaccination are reviewed as a second approach to disease control, alongside initiatives for the global eradication of infectious diseases such as smallpox and poliomyelitis. Disease surveillance continues to form a cornerstone of spatially focused control activities and, so, the chapter ends with a review of the evolution of disease intelligence systems down the centuries.

Exponential smoothing has been one of the most popular forecasting methods used to support various decisions in organizations, in activities such as inventory management, scheduling, revenue management, and other areas. Although its relative simplicity and transparency have made it very attractive for research and practice, identifying the underlying trend remains challenging with significant impact on the resulting accuracy. This has resulted in the development of various modifications of trend models, introducing a model selection problem. With the aim of addressing this problem, we propose the complex exponential smoothing (CES), based on the theory of functions of complex variables. The basic CES approach involves only two parameters and does not require a model selection procedure. Despite these simplifications, CES proves to be competitive with, or even superior to existing methods. We show that CES has several advantages over conventional exponential smoothing models: it can model and forecast both stationary and non‐stationary processes, and CES can capture both level and trend cases, as defined in the conventional exponential smoothing classification. CES is evaluated on several forecasting competition datasets, demonstrating better performance than established benchmarks. We conclude that CES has desirable features for time series modeling and opens new promising avenues for research.

This note provides an evaluation of the contributions of the M5 Competition to the construction of prediction intervals. We consider the choice of criteria used in the evaluations, the relative performance of designed and benchmark methods and the take-home lessons both for statistical forecasters and for those interested in forecasting retail sales.

‘Global Origins and Dispersals’ addresses two key questions. First, how do epidemic diseases emerge and can their geographical origins be traced to any particular part of the world? Second, why do more infectious diseases appear to be emerging in recent decades and how far does this crudescence relate to the unprecedented changes in the global environment? The examination covers factors that, inter alia, have tended to increase the geographical scale of disease cycles, including the growth and relocation of the human population, globalization and the collapse of geographical space, and environmental changes associated with land use and climate change and variability. The origin and the spread of newly emerging infectious diseases are illustrated with reference to recent international epidemics of ‘bird flu’ associated with the avian influenza A (H5N1) virus, severe acute respiratory syndrome, and Ebola virus disease in West Africa (2013–16).

‘Pandemics, II: COVID-19’ explores the spatial and temporal patterns of infection, illness, and death due to the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the causative agent of coronavirus disease 2019 (COVID-19). It covers the period from the putative beginning of the COVID-19 pandemic in late 2019 to the turn of 2021. Consecutive sections review the basic epidemiological properties of the virus and the disease, the pattern of global dispersal, and the resulting patterns of reported disease activity in the United Kingdom and the United States. The swash–backwash model is used to analyse the spatial spread of the first wave of COVID-19 in England and to estimate the spatial velocity of wave expansion and retreat, January–June 2020. Approaches to the short- and longer-term forecasting of COVID-19 are illustrated with reference to sample states of the United States.

A Geography of Infection explores the distinctive spatial patterns and processes by which infectious diseases spread from place to place and can grow from local and regional epidemics into global pandemics. The book focuses initially on the local scale of doctors’ practices and small islands where epidemic outbreaks are slight in the numbers infected and in geographical extent. Such local area studies raise two questions. First, how and where do epidemic diseases emerge and second, why do more diseases appear to be emerging now? To approach such questions implies a shift in spatial gear from painting epidemics with a fine-tipped local brush to an expanded palette on which doctors’ practices and small islands are replaced by regional and global populations. Simultaneously, time bands are extended backwards to the origins of civilization and forwards into the twenty-first century. It eventually leads to a consideration of global pandemics—both historical (e.g. plague, cholera, and influenza) and contemporary (HIV/AIDS and COVID-19)—and examines the ways the spread of infection can be prevented.

‘Pandemics, I: Pandemics in History’ surveys the historical geography of pandemic events. Special attention is paid to those diseases that have manifested as worldwide epidemics and to which the term global pandemic is commonly applied, namely plague, cholera, influenza, and the human immunodeficiency virus/acquired immunodeficiency syndrome (HIV/AIDS). A synoptic overview of approximately 35 such pandemics since the sixth century AD is presented. Consecutive sections survey the three great plague pandemics of history (Plague of Justinian, Black Death, and the Third Pandemic of the 1850s–1950s); the seven cholera pandemics of the nineteenth to twenty-first centuries (including the ongoing pandemic of El Tor cholera); the 24 influenza pandemics of the modern era (including the H1N1/Spanish, H2N2/Asian, H3N2/Hong Kong, and H1N1/09 ‘swine flu’ pandemics of the twentieth and twenty-first centuries); and the ongoing pandemic of HIV/AIDS that first emerged in the 1980s.

It is generally accepted in the operations literature that a firm should strive to maximize its expected profit. However, in practice it is not uncommon for a firm to offer a bonus to managers for achieving some pre-established target profit, possibly yielding managerial actions that differ from the profit-maximizing approach (given a profit target, we assume managers will maximize the probability of reaching that target). We use the Newsvendor framework to illustrate how the firm's shareholders (e.g., through its board of directors) can align these two seemingly different decision approaches: maximizing expected profit versus maximizing the probability of reaching a target profit. Alignment is achieved by setting what we call an “aligned profit target” (APT) – a target profit that yields the same managerial action namely, the same stocking quantity, across both decision approaches. We find that the APT should typically be an aggressive profit target, one that is significantly higher than the maximum expected profit, with a corresponding low probability of achievement – this result is consistent across demand distributions with light tails (uniform), moderate tails (normal) and heavy tails (lognormal). Notably, the aggressive APT target should be distinguished from any target that the firm might set to signal future profit expectations to financial analysts.

Reliable demand forecasts are critical for effective supply chain management. Several endogenous and exogenous variables can influence the dynamics of demand, and hence a single statistical model that only consists of historical sales data is often insufficient to produce accurate forecasts. In practice, the forecasts generated by baseline statistical models are often judgmentally adjusted by forecasters to incorporate factors and information that are not incorporated in the baseline models. There are however systematic events whose effect can be quantified and modeled to help minimize human intervention in adjusting the baseline forecasts. In this paper, we develop and test a novel regime-switching approach to quantify systematic information/events and objectively incorporate them into the baseline statistical model. Our simple yet practical and effective model can help limit forecast adjustments to only focus on the impact of less systematic events such as sudden climate change or dynamic market activities. The model is validated empirically using sales and promotional data from two Australian companies. The model is also benchmarked against commonly employed statistical and machine learning forecasting models. Discussions focus on thorough analysis of promotions impact and benchmarking results. We show that the proposed model can successfully improve forecast accuracy and avoid poor forecasts when compared to the current industry practice which heavily relies on human judgment to factor in all types of information/events. The proposed model also outperforms sophisticated machine learning methods by mitigating the generation of extremely poor forecasts that drastically differ from actual sales due to changes in demand states.

The goal is to predict the final extent of the Ebola epidemic in West Africa, 2014–2015, well before its end. Our models are based on the nature of the reported data, and the social, medical, and technological conditions that existed in real time during the course of the epidemic. The spatial and temporal nature of Ebola transmission is considered. A modified, classical compartmental model is used to develop variations of Gompertz and logistic‐type predictive models. A map analysis strongly hints at the existence of an initial rural component of the transmission of the disease followed by an urban component. Cumulative and weekly data for the three countries illustrate how the disease intensified and spread over the 90 weeks of the epidemic. A spatial autocorrelation study shows the clustering locational changes of the disease over time. A cross‐correlation study gives credence to both a rural and an urban transmission pattern. Our early estimates of the toll of the disease, crude as they are, stand in marked contrast to some of the official estimates at the time, which greatly inflated the number of new cases.

A framework for the forecasting of composite time series, such as market shares, is proposed. Based on Gaussian multi-series innovations state space models, it relies on the log-ratio function to transform the observed shares (proportions) onto the real line. The models possess an unrestricted covariance matrix, but also have certain structural elements that are common to all series, which is proved to be both necessary and sufficient to ensure that the predictions of shares are invariant to the choice of base series. The framework includes a computationally efficient maximum likelihood approach to estimation, relying on exponential smoothing methods, which can be adapted to handle series that start late or finish early (new or withdrawn products). Simulated joint prediction distributions provide approximations to the required prediction distributions of individual shares and the associated quantities of interest. The approach is illustrated on US automobile market share data for the period 1961–2013.

The main objective of this paper is to provide analytical expressions for forecast variances that can be used in prediction intervals for the exponential smoothing methods. These expressions are based on state space models with a single source of error that underlie the exponential smoothing methods. Three general classes of the state space models are presented. The first class is the standard linear state space model with homoscedastic errors, the second retains the linear structure but incorporates a dynamic form of heteroscedasticity, and the third allows for non-linear structure in the observation equation as well as heteroscedasticity. Exact matrix formulas for the forecast variances are found for each of these three classes of models. These formulas are specialized to non-matrix formulas for fifteen state space models that underlie nine exponential smoothing methods, including all the widely used methods. In cases where an ARIMA model also underlies an exponential smoothing method, there is an equivalent state space model with the same variance expression. We also discuss relationships between these new ideas and previous suggestions for finding forecast variances and prediction intervals for the exponential smoothing methods.

Privatization and fiscal deficits have been linked theoretically as emerging market countries completed transitions from command to market-based economies. This study examines the joint relationships among relative fiscal deficits, privatization, and exogenous factors for twenty-five Central and Eastern European emerging market countries. Pooled regression models suggest that increased privatization does not reduce fiscal deficits, but fiscal deficits increase as privatization increases over time. These effects are dependent upon the set of countries considered and the privatization measure employed. There is limited support for the hypothesis that privatization is increased when fiscal deficits decline for the nine early privatizers.

The commentary recommends a plot of the probability of a positive outcome as a tool for improving the interpretation of regression models in a forecasting context.

Outliers in time series have the potential to affect parameter estimates and forecasts when using exponential smoothing. The aim of this study is to show the way in which important types of outliers can be incorporated into linear innovations state space models for exponential smoothing methods. The types of outliers include an additive outlier, a level shift, and a transitory change. The general innovations state space model and a special case which encompasses the common linear exponential smoothing methods are examined. A method for identifying outliers using innovations state space models is proposed. This method is investigated using both simulations and applications to real time series. The impact of an outlier’s location on the forecasts and the estimation of parameters is examined. The forecasts from outlier and basic non-outlier models are compared. An automatic method is found to result in improved forecasts for both the simulated and real data.

This paper is concerned with identifying an effective method for forecasting the lead time demand of slow-moving inventories. Particular emphasis is placed on prediction distributions instead of point predictions alone. It is also placed on methods which work with small samples as well as large samples in recognition of the fact that the typical range of items has a mix of vintages due to different commissioning and decommissioning dates over time. Various forecasting methods are compared using monthly demand data for more than one thousand car parts. It is found that a multi-series version of exponential smoothing coupled with a Polya (negative binomial) distribution works better than the other twenty-four methods considered, including the Croston method.

Organizations with large-scale inventory systems typically have a large proportion of items for which demand is intermittent and low volume. We examine various different approaches to demand forecasting for such products, paying particular attention to the need for inventory planning over a multi-period lead-time when the underlying process may be non-stationary. This emphasis leads to the consideration of prediction distributions for processes with time-dependent parameters. A wide range of possible distributions could be considered, but we focus upon the Poisson (as a widely used benchmark), the negative binomial (as a popular extension of the Poisson), and a hurdle shifted Poisson (which retains Croston’s notion of a Bernoulli process for the occurrence of active demand periods). We also develop performance measures which are related to the entire prediction distribution, rather than focusing exclusively upon point predictions. The three models are compared using data on the monthly demand for 1046 automobile parts, provided by a US automobile manufacturer. We conclude that inventory planning should be based upon dynamic models using distributions that are more flexible than the traditional Poisson scheme.