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  • 1.
    Athanasopoulos, George
    et al.
    Department of Econometrics and Business Statistics, Monash University, Australia.
    Hyndman, Rob. J.
    Department of Econometrics and Business Statistics, Monash University, Australia.
    Kourentzes, Nikolaos
    epartment of Management Science, Lancaster University Management School, United Kingdom.
    Petropoulos, Fotios
    Information, Decision and Operations Division, School of Management, University of Bath, United Kingdom.
    Forecasting with temporal hierarchies2017In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 262, no 1, p. 60-74Article in journal (Refereed)
    Abstract [en]

    This paper introduces the concept of Temporal Hierarchies for time series forecasting. A temporal hierarchy can be constructed for any time series by means of non-overlapping temporal aggregation. Predictions constructed at all aggregation levels are combined with the proposed framework to result in temporally reconciled, accurate and robust forecasts. The implied combination mitigates modelling uncertainty, while the reconciled nature of the forecasts results in a unified prediction that supports aligned decisions at different planning horizons: from short-term operational up to long-term strategic planning. The proposed methodology is independent of forecasting models. It can embed high level managerial forecasts that incorporate complex and unstructured information with lower level statistical forecasts. Our results show that forecasting with temporal hierarchies increases accuracy over conventional forecasting, particularly under increased modelling uncertainty. We discuss organisational implications of the temporally reconciled forecasts using a case study of Accident & Emergency departments. 

  • 2.
    Barrow, Devon K.
    et al.
    School of Strategy and Leadership, Faculty of Business and Law, Coventry University, Coventry, West Midlands, United Kingdom.
    Kourentzes, Nikolaos
    Lancaster University Management School, Department of Management Science, Lancaster, United Kingdom.
    Distributions of forecasting errors of forecast combinations: Implications for inventory management2016In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 177, p. 24-33Article in journal (Refereed)
    Abstract [en]

    Inventory control systems rely on accurate and robust forecasts of future demand to support decisions such as setting of safety stocks. The combination of multiple forecasts is shown to be effective not only in reducing forecast errors, but also in being less sensitive to limitations of a single model. Research on forecast combination has primarily focused on improving accuracy, largely ignoring the overall shape and distribution of forecast errors. Nonetheless, these are essential for managing the level of aversion to risk and uncertainty for companies. This study examines the forecast error distributions of base and combination forecasts and their implications for inventory performance. It explores whether forecast combinations transform the forecast error distribution towards desired properties for safety stock calculations, typically based on the assumption of normally distributed errors and unbiased forecasts. In addition, it considers the similarity between in- and out-of-sample characteristics of such errors and the impact of different lead times. The effects of established combination methods are explored empirically using a representative set of forecasting methods and a dataset of 229 weekly demand series from a leading household and personal care UK manufacturer. Findings suggest that forecast combinations make the in- and out-of-sample behaviour more consistent, requiring less safety stock on average than base forecasts. Furthermore we find that using in-sample empirical error distributions of combined forecasts approximates well the out-of-sample ones, in contrast to base forecasts. 

  • 3.
    Barrow, Devon
    et al.
    Faculty of Business, Environment and Society, Coventry University, Coventry, West Midlands, United Kingdom.
    Kourentzes, Nikolaos
    Lancaster University Management School, Department of Management Science, Lancaster, United Kingdom.
    The impact of special days in call arrivals forecasting: A neural network approach to modelling special days2018In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 264, no 3, p. 967-977Article in journal (Refereed)
    Abstract [en]

    A key challenge for call centres remains the forecasting of high frequency call arrivals collected in hourly or shorter time buckets. In addition to the complex intraday, intraweek and intrayear seasonal cycles, call arrival data typically contain a large number of anomalous days, driven by the occurrence of holidays, special events, promotional activities and system failures. This study evaluates the use of a variety of univariate time series forecasting methods for forecasting intraday call arrivals in the presence of such outliers. Apart from established, statistical methods, we consider artificial neural networks (ANNs). Based on the modelling flexibility of the latter, we introduce and evaluate different methods to encode the outlying periods. Using intraday arrival series from a call centre operated by one of Europe's leading entertainment companies, we provide new insights on the impact of outliers on the performance of established forecasting methods. Results show that ANNs forecast call centre data accurately, and are capable of modelling complex outliers using relatively simple outlier modelling approaches. We argue that the relative complexity of ANNs over standard statistical models is offset by the simplicity of coding multiple and unknown effects during outlying periods. 

  • 4.
    Crone, Sven F.
    et al.
    Lancaster University Management School, Department of Management Science, Centre for Forecasting, Bailrigg campus, Lancaster, United Kingdom.
    Kourentzes, Nikolaos
    Lancaster University Management School, Department of Management Science, Centre for Forecasting, Bailrigg campus, Lancaster, United Kingdom.
    Feature selection for time series prediction: A combined filter and wrapper approach for neural networks2010In: Neurocomputing, ISSN 0925-2312, E-ISSN 1872-8286, Vol. 73, no 10-12, p. 1923-1936Article in journal (Refereed)
    Abstract [en]

    Modelling artificial neural networks for accurate time series prediction poses multiple challenges, in particular specifying the network architecture in accordance with the underlying structure of the time series. The data generating processes may exhibit a variety of stochastic or deterministic time series patterns of single or multiple seasonality, trends and cycles, overlaid with pulses, level shifts and structural breaks, all depending on the discrete time frequency in which it is observed. For heterogeneous datasets of time series, such as the 2008 ESTSP competition, a universal methodology is required for automatic network specification across varying data patterns and time frequencies. We propose a fully data driven forecasting methodology that combines filter and wrapper approaches for feature selection, including automatic feature evaluation, construction and transformation. The methodology identifies time series patterns, creates and transforms explanatory variables and specifies multilayer perceptrons for heterogeneous sets of time series without expert intervention. Examples of the valid and reliable performance in comparison to established benchmark methods are shown for a set of synthetic time series and for the ESTSP'08 competition dataset, where the proposed methodology obtained second place. 

  • 5.
    Fildes, Robert
    et al.
    Lancaster Centre for Forecasting, Lancaster University, Department of Management Science, United Kingdom.
    Kourentzes, Nikolaos
    Lancaster Centre for Forecasting, Lancaster University, Department of Management Science, United Kingdom.
    Validation and forecasting accuracy in models of climate change2011In: International Journal of Forecasting, ISSN 0169-2070, E-ISSN 1872-8200, Vol. 27, no 4, p. 968-995Article in journal (Refereed)
    Abstract [en]

    Forecasting researchers, with few exceptions, have ignored the current major forecasting controversy: global warming and the role of climate modelling in resolving this challenging topic. In this paper, we take a forecaster's perspective in reviewing established principles for validating the atmospheric-ocean general circulation models (AOGCMs) used in most climate forecasting, and in particular by the Intergovernmental Panel on Climate Change (IPCC). Such models should reproduce the behaviours characterising key model outputs, such as global and regional temperature changes. We develop various time series models and compare them with forecasts based on one well-established AOGCM from the UK Hadley Centre. Time series models perform strongly, and structural deficiencies in the AOGCM forecasts are identified using encompassing tests. Regional forecasts from various GCMs had even more deficiencies. We conclude that combining standard time series methods with the structure of AOGCMs may result in a higher forecasting accuracy. The methodology described here has implications for improving AOGCMs and for the effectiveness of environmental control policies which are focussed on carbon dioxide emissions alone. Critically, the forecast accuracy in decadal prediction has important consequences for environmental planning, so its improvement through this multiple modelling approach should be a priority.

  • 6.
    Kourentzes, Nikolaos
    Department of Management Science, Lancaster University Management School, Lancaster, United Kingdom.
    Demand Forecasting for Managers2018In: International Journal of Forecasting, ISSN 0169-2070, E-ISSN 1872-8200, Vol. 34, no 1, p. 117-118Article, book review (Other academic)
  • 7.
    Kourentzes, Nikolaos
    University of Skövde, School of Informatics. University of Skövde, Informatics Research Environment.
    Elucidate structure in intermittent demand series2020In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860Article in journal (Refereed)
    Abstract [en]

    Intermittent demand forecasting has been widely researched in the context of spare parts management. However, it is becoming increasingly relevant to many other areas, such as retailing, where at the very disaggregate level time series may be highly intermittent, but at more aggregate levels are likely to exhibit trends and seasonal patterns. The vast majority of intermittent demand forecasting methods are inappropriate for producing forecasts with such features. We propose using temporal hierarchies to produce forecasts that demonstrate these traits at the various aggregation levels, effectively informing the resulting intermittent forecasts of these patterns that are identifiable only at higher levels. We conduct an empirical evaluation on real data and demonstrate statistically significant gains for both point and quantile forecasts.

  • 8.
    Kourentzes, Nikolaos
    Department of Management Science, Lancaster University Management School, Lancaster, Lancashire, United Kingdom.
    Intermittent demand forecasts with neural networks2013In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 143, no 1, p. 198-206Article in journal (Refereed)
    Abstract [en]

    Intermittent demand appears when demand events occur only sporadically. Typically such time series have few observations making intermittent demand forecasting challenging. Forecast errors can be costly in terms of unmet demand or obsolescent stock. Intermittent demand forecasting has been addressed using established forecasting methods, including simple moving averages, exponential smoothing and Croston's method with its variants. This study proposes a neural network (NN) methodology to forecast intermittent time series. These NNs are used to provide dynamic demand rate forecasts, which do not assume constant demand rate in the future and can capture interactions between the non-zero demand and the inter-arrival rate of demand events. This overcomes the limitations of Croston's method. In order to mitigate the issue of limited fitting sample, which is common in intermittent demand, the proposed models use regularised training and median ensembles over multiple training initialisations to produce robust forecasts. The NNs are evaluated against established benchmarks using both forecasting accuracy and inventory metrics. The findings of forecasting and inventory metrics are conflicting. While NNs achieved poor forecasting accuracy and bias, all NN variants achieved higher service levels than the best performing Croston's method variant, without requiring analogous increases in stock holding volume. Therefore, NNs are found to be effective for intermittent demand applications. This study provides further arguments and evidence against the use of conventional forecasting accuracy metrics to evaluate forecasting methods for intermittent demand, concluding that attention to inventory metrics is desirable. 

  • 9.
    Kourentzes, Nikolaos
    Department of Management Science, Lancaster University Management School, Lancaster, Lancashire, United Kingdom.
    On intermittent demand model optimisation and selection2014In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 156, p. 180-190Article in journal (Refereed)
    Abstract [en]

    Intermittent demand time series involve items that are requested infrequently, resulting in sporadic demand. Crostons method and its variants have been proposed in the literature to address this forecasting problem. Recently other novel methods have appeared. Although the literature provides guidance on the suggested range for model parameters, a consistent and valid optimisation methodology is lacking. Growing evidence in the literature points against the use of conventional accuracy error metrics for model evaluation for intermittent demand time series. Consequently these may be inappropriate for parameter or model selection. This paper contributes to the discussion by evaluating a series of conventional time series error metrics, along with two novel ones for parameter optimisation for intermittent demand methods. The proposed metrics are found to not only perform best, but also provide consistent parameters with the literature, in contrast to conventional metrics. Furthermore, this work validates that employing different parameters for smoothing the non-zero demand and the inter-demand intervals of Crostons method and its variants is beneficial. The evaluated error metrics are considered for automatic model selection for each time series. Although they are found to perform similar to theory driven model selection schemes, they fail to outperform single models substantially. These findings are validated using both out-of-sample forecast evaluation and inventory simulations. 

  • 10.
    Kourentzes, Nikolaos
    et al.
    Lancaster University Management School, Department of Management Science, Lancaster, United Kingdom.
    Athanasopoulos, George
    Department of Econometrics and Business Statistics, Monash University, Australia.
    Cross-temporal coherent forecasts for Australian tourism2019In: Annals of Tourism Research, ISSN 0160-7383, E-ISSN 1873-7722, Vol. 75, p. 393-409Article in journal (Refereed)
    Abstract [en]

    Key to ensuring a successful tourism sector is timely policy making and detailed planning. National policy formulation and strategic planning requires long-term forecasts at an aggregate level, while regional operational decisions require short-term forecasts, relevant to local tourism operators. For aligned decisions at all levels, supporting forecasts must be ‘coherent’ that is they should add up appropriately, across relevant demarcations (e.g., geographical divisions or market segments) and also across time. We propose an approach for generating coherent forecasts across both cross-sections and planning horizons for Australia. This results in significant improvements in forecast accuracy with substantial decision making benefits. Coherent forecasts help break intra- and inter-organisational information and planning silos, in a data driven fashion, blending information from different sources. This article also launches the Annals of Tourism Research Curated Collection on Tourism Demand Forecast, a special selection of research in this field.

  • 11.
    Kourentzes, Nikolaos
    et al.
    Lancaster University Management School, Department of Management Science, Lancaster, United Kingdom.
    Barrow, Devon K.
    Lancaster University Management School, Department of Management Science, Lancaster, United Kingdom.
    Crone, Sven F.
    Lancaster University Management School, Department of Management Science, Lancaster, United Kingdom.
    Neural network ensemble operators for time series forecasting2014In: Expert systems with applications, ISSN 0957-4174, E-ISSN 1873-6793, Vol. 41, no 9, p. 4235-4244Article in journal (Refereed)
    Abstract [en]

    The combination of forecasts resulting from an ensemble of neural networks has been shown to outperform the use of a single "best" network model. This is supported by an extensive body of literature, which shows that combining generally leads to improvements in forecasting accuracy and robustness, and that using the mean operator often outperforms more complex methods of combining forecasts. This paper proposes a mode ensemble operator based on kernel density estimation, which unlike the mean operator is insensitive to outliers and deviations from normality, and unlike the median operator does not require symmetric distributions. The three operators are compared empirically and the proposed mode ensemble operator is found to produce the most accurate forecasts, followed by the median, while the mean has relatively poor performance. The findings suggest that the mode operator should be considered as an alternative to the mean and median operators in forecasting applications. Experiments indicate that mode ensembles are useful in automating neural network models across a large number of time series, overcoming issues of uncertainty associated with data sampling, the stochasticity of neural network training, and the distribution of the forecasts. 

  • 12.
    Kourentzes, Nikolaos
    et al.
    Department of Management Science, Lancaster University Management School, Lancaster University, United Kingdom.
    Barrow, Devon
    Faculty of Business, Environment and Society, Coventry University, United Kingdom.
    Petropoulos, Fotios
    School of Management, University of Bath, United Kingdom.
    Another look at forecast selection and combination: Evidence from forecast pooling2019In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 209, p. 226-235Article in journal (Refereed)
    Abstract [en]

    Forecast selection and combination are regarded as two competing alternatives. In the literature there is substantial evidence that forecast combination is beneficial, in terms of reducing the forecast errors, as well as mitigating modelling uncertainty as we are not forced to choose a single model. However, whether all forecasts to be combined are appropriate, or not, is typically overlooked and various weighting schemes have been proposed to lessen the impact of inappropriate forecasts. We argue that selecting a reasonable pool of forecasts is fundamental in the modelling process and in this context both forecast selection and combination can be seen as two extreme pools of forecasts. We evaluate forecast pooling approaches and find them beneficial in terms of forecast accuracy. We propose a heuristic to automatically identify forecast pools, irrespective of their source or the performance criteria, and demonstrate that in various conditions it performs at least as good as alternative pools that require additional modelling decisions and better than selection or combination. 

  • 13.
    Kourentzes, Nikolaos
    et al.
    Lancaster University Management School, University of Lancaster, Lancaster, United Kingdom.
    Li, Dong
    The York Management School, University of York, York, United Kingdom.
    Strauss, Arne K.
    Warwick Business School, University of Warwick, Coventry, United Kingdom.
    Unconstraining methods for revenue management systems under small demand2019In: Journal of Revenue and Pricing Management, ISSN 1476-6930, E-ISSN 1477-657X, Vol. 18, no 1, p. 27-41Article in journal (Refereed)
    Abstract [en]

    Sales data often only represent a part of the demand for a service product owing to constraints such as capacity or booking limits. Unconstraining methods are concerned with estimating the true demand from such constrained sales data. This paper addresses the frequently encountered situation of observing only a few sales events at the individual product level and proposes variants of small demand forecasting methods to be used for unconstraining. The usual procedure is to aggregate data; however, in that case we lose information on when restrictions were imposed or lifted within a given booking profile. Our proposed methods exploit this information and are able to approximate convex, concave or homogeneous booking curves. Furthermore, they are numerically robust due to our proposed group-based parameter optimization. Empirical results on accuracy and revenue performance based on data from a major car rental company indicate revenue improvements over a best practice benchmark by statistically significant 0.5–1.4% in typical scenarios.

  • 14.
    Kourentzes, Nikolaos
    et al.
    Lancaster University Management School, Department of Management Science, Lancaster, Lancashire, United Kingdom.
    Petropoulos, Fotios
    Logistics and Operations Management Section, Cardiff Business School, Cardiff University, United Kingdom.
    Forecasting with multivariate temporal aggregation: The case of promotional modelling2016In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 181, p. 145-153Article in journal (Refereed)
    Abstract [en]

    Demand forecasting is central to decision making and operations in organisations. As the volume of forecasts increases, for example due to an increased product customisation that leads to more SKUs being traded, or a reduction in the length of the forecasting cycle, there is a pressing need for reliable automated forecasting. Conventionally, companies rely on a statistical baseline forecast that captures only past demand patterns, which is subsequently adjusted by human experts to incorporate additional information such as promotions. Although there is evidence that such process adds value to forecasting, it is questionable how much it can scale up, due to the human element. Instead, in the literature it has been proposed to enhance the baseline forecasts with external well-structured information, such as the promotional plan of the company, and let experts focus on the less structured information, thus reducing their workload and allowing them to focus where they can add most value. This change in forecasting support systems requires reliable multivariate forecasting models that can be automated, accurate and robust. This paper proposes an extension of the recently proposed Multiple Aggregation Prediction Algorithm (MAPA), which uses temporal aggregation to improve upon the established exponential smoothing family of methods. MAPA is attractive as it has been found to increase both the accuracy and robustness of exponential smoothing. The extended multivariate MAPA is evaluated against established benchmarks in modelling a number of heavily promoted products and is found to perform well in terms of forecast bias and accuracy. Furthermore, we demonstrate that modelling time series using multiple temporal aggregation levels makes the final forecast robust to model mis-specification. 

  • 15.
    Kourentzes, Nikolaos
    et al.
    Lancaster University Management School, Department of Management Science, Lancaster, Lancashire, United Kingdom.
    Petropoulos, Fotios
    Lancaster University Management School, Department of Management Science, Lancaster, Lancashire, United Kingdom.
    Trapero, Juan R.
    Universidad de Castilla-La Mancha, Departamento de Administracion de Empresas, Ciudad Real, Spain.
    Improving forecasting by estimating time series structural components across multiple frequencies2014In: International Journal of Forecasting, ISSN 0169-2070, E-ISSN 1872-8200, Vol. 30, no 2, p. 291-302Article in journal (Refereed)
    Abstract [en]

    Identifying the most appropriate time series model to achieve a good forecasting accuracy is a challenging task. We propose a novel algorithm that aims to mitigate the importance of model selection, while increasing the accuracy. Multiple time series are constructed from the original time series, using temporal aggregation. These derivative series highlight different aspects of the original data, as temporal aggregation helps in strengthening or attenuating the signals of different time series components. In each series, the appropriate exponential smoothing method is fitted and its respective time series components are forecast. Subsequently, the time series components from each aggregation level are combined, then used to construct the final forecast. This approach achieves a better estimation of the different time series components, through temporal aggregation, and reduces the importance of model selection through forecast combination. An empirical evaluation of the proposed framework demonstrates significant improvements in forecasting accuracy, especially for long-term forecasts. 

  • 16.
    Kourentzes, Nikolaos
    et al.
    Lancaster University Management School Department of Management Science, Lancaster, United Kingdom.
    Rostami-Tabar, Bahman
    Cardiff Business School, Cardiff University, Cardiff, United Kingdom.
    Barrow, Devon K.
    School of Strategy and Leadership, Faculty of Business and Law Coventry University, Coventry, West Midlands, United Kingdom.
    Demand forecasting by temporal aggregation: Using optimal or multiple aggregation levels?2017In: Journal of Business Research, ISSN 0148-2963, E-ISSN 1873-7978, Vol. 78, p. 1-9Article in journal (Refereed)
    Abstract [en]

    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. 

  • 17.
    Kourentzes, Nikolaos
    et al.
    Lancaster University Management School, United Kingdom.
    Sagaert, Yves
    Faculty of Engineering and Architecture of Ghent University, Belgium.
    Incorporating Leading Indicators into Sales Forecasts2018In: Foresight: The International Journal of Applied Forecasting, ISSN 1555-9068, no 48, p. 24-30Article in journal (Refereed)
    Abstract [en]

    Using leading indicators for business forecasting-in contrast to macroeconomic forecasting-has been relatively rare, partly because our traditional time-series methods do not readily allow incorporation of external variables. Nowadays, however, we have an abundance of potentially useful indicators, and there is evidence that utilizing relevant ones in a forecasting model can significantly improve forecast accuracy and transparency. In this article, Nikolaos and Yves show how to find appropriate leading indicators and make good use of them for sales forecasting. 

  • 18.
    Kourentzes, Nikolaos
    et al.
    University of Skövde, School of Informatics. University of Skövde, Informatics Research Environment. Department of Management Science, Lancaster University Management School, UK.
    Trapero, Juan R.
    Department of Business Administration, Universidad de Castilla-La Mancha, Ciudad Real, Spain.
    Barrow, Devon K.
    Birmingham Business School, University of Birmingham, UK.
    Optimising forecasting models for inventory planning2020In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 225, article id 107597Article in journal (Refereed)
    Abstract [en]

    Inaccurate forecasts can be costly for company operations, in terms of stock-outs and lost sales, or over-stocking, while not meeting service level targets. The forecasting literature, often disjoint from the needs of the forecast users, has focused on providing optimal models in terms of likelihood and various accuracy metrics. However, there is evidence that this does not always lead to better inventory performance, as often the translation between forecast errors and inventory results is not linear. In this study, we consider an approach to parametrising forecasting models by directly considering appropriate inventory metrics and the current inventory policy. We propose a way to combine the competing multiple inventory objectives, i.e. meeting demand, while eliminating excessive stock, and use the resulting cost function to identify inventory optimal parameters for forecasting models. We evaluate the proposed parametrisation against established alternatives and demonstrate its performance on real data. Furthermore, we explore the connection between forecast accuracy and inventory performance and discuss the extent to which the former is an appropriate proxy of the latter. 

  • 19.
    Petropoulos, Fotios
    et al.
    Cardiff Business School of Cardiff University, United Kingdom.
    Kourentzes, Nikolaos
    Lancaster University, United Kingdom.
    Commentary: Two Sides of the Same Coin2016In: Foresight: The International Journal of Applied Forecasting, ISSN 1555-9068, no 42, p. 37-39Article in journal (Refereed)
  • 20.
    Petropoulos, Fotios
    et al.
    Lancaster Centre for Forecasting, Lancaster University Management School, Lancaster University, Lancaster, United Kingdom.
    Kourentzes, Nikolaos
    Lancaster Centre for Forecasting, Lancaster University Management School, Lancaster University, Lancaster, United Kingdom.
    Forecast combinations for intermittent demand2015In: Journal of the Operational Research Society, ISSN 0160-5682, E-ISSN 1476-9360, Vol. 66, no 6, p. 914-924Article in journal (Refereed)
    Abstract [en]

    Intermittent demand is characterised by infrequent demand arrivals, where many periods have zero demand, coupled with varied demand sizes. The dual source of variation renders forecasting for intermittent demand a very challenging task. Many researchers have focused on the development of specialised methods for intermittent demand. However, apart from a case study on hierarchical forecasting, the effects of combining, which is a standard practice for regular demand, have not been investigated. This paper empirically explores the efficiency of forecast combinations in the intermittent demand context. We examine both method and temporal combinations of forecasts. The first are based on combinations of different methods on the same time series, while the latter use combinations of forecasts produced on different views of the time series, based on temporal aggregation. Temporal combinations of single or multiple methods are investigated, leading to a new time-series classification, which leads to model selection and combination. Results suggest that appropriate combinations lead to improved forecasting performance over single methods, as well as simplifying the forecasting process by limiting the need for manual selection of methods or hyper-parameters of good performing benchmarks. This has direct implications for intermittent demand forecasting in practice. 

  • 21.
    Petropoulos, Fotios
    et al.
    Lancaster University, United Kingdom.
    Kourentzes, Nikolaos
    Lancaster University, United Kingdom.
    Improving Forecasting via Multiple Temporal Aggregation2014In: Foresight: The International Journal of Applied Forecasting, ISSN 1555-9068, no 34, p. 12-17Article in journal (Refereed)
    Abstract [en]

    In most business forecasting applications, the decision-making need we have directs the frequency of the data we collect (monthly, weekly, etc.) and use for forecasting. In this article, Fotios and Nikolaos introduce an approach that combines forecasts generated by modeling the different frequencies (levels of temporal aggregation). Their technique augments our information about the data used for forecasting and, as such, can result in more accurate forecasts. It also automatically reconciles the forecasts at different levels.

  • 22.
    Petropoulos, Fotios
    et al.
    Logistics and Operations Management Section, Cardiff Business School, Cardiff University, United Kingdom.
    Kourentzes, Nikolaos
    Department of Management Science, Lancaster University Management School, Lancaster University, United Kingdom.
    Nikolopoulos, Konstantinos
    Bangor Business School, Bangor University, United Kingdom.
    Another look at estimators for intermittent demand2016In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 181, p. 154-161Article in journal (Refereed)
    Abstract [en]

    In this paper we focus on forecasting for intermittent demand data. We propose a new aggregation framework for intermittent demand forecasting that performs aggregation over the demand volumes, in contrast to the standard framework that employs temporal (over time) aggregation. To achieve this we construct a transformed time series, the inverse intermittent demand series. The new algorithm is expected to work best on erratic and lumpy demand, as a result of the variance reduction of the non-zero demands. The improvement in forecasting performance is empirically demonstrated through an extensive evaluation in more than 8000 time series of two well-researched spare parts data sets from the automotive and defence sectors. Furthermore, a simulation is performed so as to provide a stock-control evaluation. The proposed framework could find popularity among practitioners given its suitability when dealing with clump sizes. As such it could be used in conjunction with existing popular forecasting methods for intermittent demand as an exception handling mechanism when certain types of demand are observed.

  • 23.
    Petropoulos, Fotios
    et al.
    School of Management, University of Bath, United Kingdom.
    Kourentzes, Nikolaos
    Lancaster University Management School, Lancaster University, United Kingdom.
    Nikolopoulos, Konstantinos
    Bangor Business School, Bangor University, United Kingdom.
    Siemsen, Enno
    Wisconsin School of Business, University of Wisconsin, USA.
    Judgmental selection of forecasting models2018In: Journal of Operations Management, ISSN 0272-6963, E-ISSN 1873-1317, Vol. 60, p. 34-46Article in journal (Refereed)
    Abstract [en]

    In this paper, we explored how judgment can be used to improve the selection of a forecasting model. We compared the performance of judgmental model selection against a standard algorithm based on information criteria. We also examined the efficacy of a judgmental model-build approach, in which experts were asked to decide on the existence of the structural components (trend and seasonality) of the time series instead of directly selecting a model from a choice set. Our behavioral study used data from almost 700 participants, including forecasting practitioners. The results from our experiment suggest that selecting models judgmentally results in performance that is on par, if not better, to that of algorithmic selection. Further, judgmental model selection helps to avoid the worst models more frequently compared to algorithmic selection. Finally, a simple combination of the statistical and judgmental selections and judgmental aggregation significantly outperform both statistical and judgmental selections.

  • 24.
    Sagaert, Yves R.
    et al.
    Department of Industrial Systems Engineering and Product Design, Ghent University, Zwijnaarde, Belgium / Solventure NV, Gent, Belgium.
    Aghezzaf, El-Houssaine
    Department of Industrial Systems Engineering and Product Design, Ghent University, Zwijnaarde, Belgium / Flanders Make.
    Kourentzes, Nikolaos
    Department of Management Science, Lancaster University Management School, Lancaster, United Kingdom.
    Desmet, Bram
    Solventure NV, Gent, Belgium.
    Tactical sales forecasting using a very large set of macroeconomic indicators2018In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 264, no 2, p. 558-569Article in journal (Refereed)
    Abstract [en]

    Tactical forecasting in supply chain management supports planning for inventory, scheduling production, and raw material purchase, amongst other functions. It typically refers to forecasts up to 12 months ahead. Traditional forecasting models take into account univariate information extrapolating from the past, but cannot anticipate macroeconomic events, such as steep increases or declines in national economic activity. In practice this is countered by using managerial expert judgement, which is well known to suffer from various biases, is expensive and not scalable. This paper evaluates multiple approaches to improve tactical sales forecasting using macro-economic leading indicators. The proposed statistical forecast selects automatically both the type of leading indicators, as well as the order of the lead for each of the selected indicators. However as the future values of the leading indicators are unknown an additional uncertainty is introduced. This uncertainty is controlled in our methodology by restricting inputs to an unconditional forecasting setup. We compare this with the conditional setup, where future indicator values are assumed to be known and assess the theoretical loss of forecast accuracy. We also evaluate purely statistical model building against judgement aided models, where potential leading indicators are pre-filtered by experts, quantifying the accuracy-cost trade-off. The proposed framework improves on forecasting accuracy over established time series benchmarks, while providing useful insights about the key leading indicators. We evaluate the proposed approach on a real case study and find 18.8% accuracy gains over the current forecasting process. 

  • 25.
    Sagaert, Yves R.
    et al.
    Univ Ghent, Dept Ind Syst Engn & Prod Design, Ghent, Belgium / Solventure NV, Ghent, Belgium.
    Aghezzaf, El-Houssaine
    Univ Ghent, Dept Ind Syst Engn & Prod Design, Ghent, Belgium / Flanders Make, Lommel, Belgium.
    Kourentzes, Nikolaos
    Univ Lancaster, Sch Management, Dept Management Sci, Lancaster, United Kingdom.
    Desmet, Bram
    Solventure NV, Ghent, Belgium.
    Temporal big data for tactical sales forecasting in the tire industry2018In: Interfaces, ISSN 0092-2102, E-ISSN 1526-551X, Vol. 48, no 2, p. 121-129Article in journal (Refereed)
    Abstract [en]

    We propose a forecasting method to improve the accuracy of tactical sales predictions for a major supplier to the tire industry. This level of forecasting, which serves as direct input to the demand-planning process and steers the global supply chain, is typically done up to a year in advance. The product portfolio of the company for which we did our research is sensitive to external events. Univariate statistical methods, which are commonly used in practice, cannot be used to anticipate and forecast changes in the market; and forecasts by human experts are known to be biased and inconsistent. The method we propose allows us to automate the identification of key leading indicators, which drive sales, from a massive set of macroeconomic indicators, across di erent regions and markets; thus, we can generate accurate forecasts. Our method also allows us to handle the additional complexity that results from short-term and long-term dynamics of product sales and external indicators. For the company we study, accuracy improved by 16.1 percent over its current practice. Furthermore, our method makes the market dynamics transparent to company managers, thus allowing them to better understand the events and economic variables that a ect the sales of their products. 

  • 26.
    Sagaert, Yves R.
    et al.
    Department of Industrial Management, Ghent University, Belgium / Department of Management Science, Lancaster University Management School, Lancaster, United Kingdom.
    Kourentzes, Nikolaos
    Department of Management Science, Lancaster University Management School, Lancaster, United Kingdom.
    De Vuyst, Stijn
    Department of Industrial Management, Ghent University, Belgium.
    Aghezzaf, El-Houssaine
    Department of Industrial Management, Ghent University, Belgium.
    Desmet, Bram
    Solventure NV, Gent, Belgium.
    Incorporating macroeconomic leading indicators in tactical capacity planning2019In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 209, p. 12-19Article in journal (Refereed)
    Abstract [en]

    Tactical capacity planning relies on future estimates of demand for the mid- to long-term. On these forecast horizons there is increased uncertainty that the analysts face. To this purpose, we incorporate macroeconomic variables into microeconomic demand forecasting. Forecast accuracy metrics, which are typically used to assess improvements in predictions, are proxies of the real decision associated costs. However, measuring the direct impact on decisions is preferable. In this paper, we examine the capacity planning decision at plant level of a manufacturer. Through an inventory simulation setup, we evaluate the gains of incorporating external macroeconomic information in the forecasts, directly, in terms of achieving target service levels and inventory performance. Furthermore, we provide an approach to indicate capacity alerts, which can serve as input for global capacity pooling decisions. Our work has two main contributions. First, we demonstrate the added value of leading indicator information in forecasting models, when evaluated directly on capacity planning. Second, we provide additional evidence that traditional metrics of forecast accuracy exhibit weak connection with the real decision costs, in particular for capacity planning. We propose a more realistic assessment of the forecast quality by evaluating both the first and second moment of the forecast distribution. We discuss implications for practice, in particular given the typical over-reliance on forecast accuracy metrics for choosing the appropriate forecasting model. 

  • 27.
    Schaer, Oliver
    et al.
    Centre for Marketing Analytics and Forecasting, Department of Management Science, Lancaster University Management School, United Kingdom.
    Kourentzes, Nikolaos
    Centre for Marketing Analytics and Forecasting, Department of Management Science, Lancaster University Management School, United Kingdom.
    Fildes, Robert
    Centre for Marketing Analytics and Forecasting, Department of Management Science, Lancaster University Management School, United Kingdom.
    Demand forecasting with user-generated online information2019In: International Journal of Forecasting, ISSN 0169-2070, E-ISSN 1872-8200, Vol. 35, no 1, p. 197-212Article in journal (Refereed)
    Abstract [en]

    Recently, there has been substantial research on the augmentation of aggregate forecasts with individual consumer data from internet platforms, such as search traffic or social network shares. Although the majority of studies have reported increases in accuracy, many exhibit design weaknesses, including a lack of adequate benchmarks or rigorous evaluation. Furthermore, their usefulness over the product life-cycle has not been investigated, even though this may change, as consumers may search initially for pre-purchase information, but later for after-sales support. This study begins by reviewing the relevant literature, then attempts to support the key findings using two forecasting case studies. Our findings are in stark contrast to those in the previous literature, as we find that established univariate forecasting benchmarks, such as exponential smoothing, consistently perform better those that include online information. Our research underlines the need for a thorough forecast evaluation and argues that the usefulness of online platform data for supporting operational decisions may be limited.

  • 28.
    Spiliotis, Evangelos
    et al.
    Forecasting and Strategy Unit, School of Electrical and Computer Engineering, National Technical University of Athens, Athens, Greece.
    Petropoulos, Fotios
    School of Management, University of Bath, Bath, United Kingdom.
    Kourentzes, Nikolaos
    Lancaster University Management School, Department of Management Science, Lancaster, United Kingdom.
    Assimakopoulos, Vassilios
    Forecasting and Strategy Unit, School of Electrical and Computer Engineering, National Technical University of Athens, Athens, Greece.
    Cross-temporal aggregation: Improving the forecast accuracy of hierarchical electricity consumption2020In: Applied Energy, ISSN 0306-2619, E-ISSN 1872-9118, Vol. 261, article id 114339Article in journal (Refereed)
    Abstract [en]

    Achieving high accuracy in energy consumption forecasting is critical for improving energy management and planning. However, this requires the selection of appropriate forecasting models, able to capture the individual characteristics of the series to be predicted, which is a task that involves a lot of system and region level, not only the model selection problem is expanded to multiple time series, but we also require aggregation consistency of the forecasts across levels. Although hierarchical forecasting, such as the bottom-up, the top-down, and the optimal reconciliation methods, can address the aggregation consistency concerns, it does not resolve the model selection uncertainty. To address this issue, we rely on Multiple Temporal Aggregation (MTA), which has been shown to mitigate the model selection problem for low-frequency time series. We propose a modification of the Multiple Aggregation Prediction Algorithm, a special implementation of MTA, for high-frequency time series to better handle the undesirable effect of seasonality shrinkage that MTA implies and combine it with conventional cross-sectional hierarchical forecasting. The impact of incorporating temporal aggregation in hierarchical forecasting is empirically assessed using a real data set from five bank branches. We show that the proposed MTA approach, combined with the optimal reconciliation method, demonstrates superior accuracy, aggregation consistency, and reliable automatic forecasting. 

  • 29.
    Trapero, Juan R.
    et al.
    Universidad de Castilla-La Mancha, Department of Business Administration, Ciudad Real, Spain.
    Cardós, Manuel
    Universidad Politécnica de Valencia, Department of Business Administration, Valencia, Spain.
    Kourentzes, Nikolaos
    Lancaster University Management School, Department of Management Science, Lancaster, United Kingdom.
    Empirical safety stock estimation based on kernel and GARCH models2019In: Omega: The International Journal of Management Science, ISSN 0305-0483, E-ISSN 1873-5274, Vol. 84, p. 199-211Article in journal (Refereed)
    Abstract [en]

    Supply chain risk management has drawn the attention of practitioners and academics alike. One source of risk is demand uncertainty. Demand forecasting and safety stock levels are employed to address this risk. Most previous work has focused on point demand forecasting, given that the forecast errors satisfy the typical normal i.i.d. assumption. However, the real demand for products is difficult to forecast accurately, which means that—at minimum—the i.i.d. assumption should be questioned. This work analyzes the effects of possible deviations from the i.i.d. assumption and proposes empirical methods based on kernel density estimation (non-parametric) and GARCH(1,1) models (parametric), among others, for computing the safety stock levels. The results suggest that for shorter lead times, the normality deviation is more important, and kernel density estimation is most suitable. By contrast, for longer lead times, GARCH models are more appropriate because the autocorrelation of the variance of the forecast errors is the most important deviation. In fact, even when no autocorrelation is present in the original demand, such autocorrelation can be present as a consequence of the overlapping process used to compute the lead time forecasts and the uncertainties arising in the estimation of the parameters of the forecasting model. Improvements are shown in terms of cycle service level, inventory investment and backorder volume. Simulations and real demand data from a manufacturer are used to illustrate our methodology.

  • 30.
    Trapero, Juan R.
    et al.
    University of Castilla-La Mancha, Department of Business Administration, Spain.
    Cardós, Manuel
    Universitat Politècnica de València, Department of Business Organization, Valencia, Spain.
    Kourentzes, Nikolaos
    Lancaster University Management School, Department of Management Science, Lancaster, United Kingdom.
    Quantile forecast optimal combination to enhance safety stock estimation2019In: International Journal of Forecasting, ISSN 0169-2070, E-ISSN 1872-8200, Vol. 35, no 1, p. 239-250Article in journal (Refereed)
    Abstract [en]

    The safety stock calculation requires a measure of the forecast error uncertainty. Such errors are usually assumed to be Gaussian iid (independently and identically distributed). However, deviations from iid lead to a deterioration in the performance of the supply chain. Recent research has shown that, contrary to theoretical approaches, empirical techniques that do not rely on the aforementioned assumptions can enhance the calculation of safety stocks. In particular, GARCH models cope with time-varying heterocedastic forecast error, and kernel density estimation does not need to rely on a determined distribution. However, if the forecast errors are time-varying heterocedastic and do not follow a determined distribution, the previous approaches are inadequate. We overcome this by proposing an optimal combination of the empirical methods that minimizes the asymmetric piecewise linear loss function, also known as the tick loss. The results show that combining quantile forecasts yields safety stocks with a lower cost. The methodology is illustrated with simulations and real data experiments for different lead times.

  • 31.
    Trapero, Juan R.
    et al.
    Department of Business Administration, Universidad de Castilla-La Mancha, Ciudad Real, Spain.
    García, Fausto. P.
    Department of Business Administration, Universidad de Castilla-La Mancha, Ciudad Real, Spain.
    Kourentzes, Nikolaos
    Department of Management Science, Lancaster University, Lancaster, United KingdomUK.
    Impact of demand nature on the bullwhip effect: Bridging the gap between theoretical and empirical research2014In: Proceedings of the Seventh International Conference on Management Science and Engineering Management / [ed] Jiuping Xu, John A. Fry, Benjamin Lev, Asaf Hajiyev, Springer, 2014, Vol. 242, no VOL. 2, p. 1127-1137Conference paper (Refereed)
    Abstract [en]

    The bullwhip effect (BE) consists of the demand variability amplification that exists in a supply chain when moving upwards. This undesirable effect produces excess inventory and poor customer service. Recently, several research papers from either a theoretical or empirical point of view have indicated the nature of the demand process as a key aspect to defining the BE. Nonetheless, they reached different conclusions. On the one hand, theoretical research quantified the BE depending on the lead time and ARIMA parameters, where ARIMA functions were employed to model the demand generator process. In turn, empirical research related nonlinearly the demand variability extent with the BE size. Although, it seems that both results are contradictory, this paper explores how those conclusions complement each other. Essentially, it is shown that the theoretical developments are precise to determine the presence of the BE based on its ARIMA parameter estimates. Nonetheless, to quantify the size of the BE, the demand coefficient of variation should be incorporated. The analysis explores a two-staged serially linked supply chain, where weekly data at SKU level from a manufacturer specialized in household products and a major UK grocery retailer have been collected. 

  • 32.
    Trapero, Juan R.
    et al.
    Lancaster University, Department of Management Science, United Kingdom.
    Kourentzes, Nikolaos
    Lancaster University, Department of Management Science, United Kingdom.
    Fildes, R.
    Lancaster University, Department of Management Science, United Kingdom.
    Impact of information exchange on supplier forecasting performance2012In: Omega: The International Journal of Management Science, ISSN 0305-0483, E-ISSN 1873-5274, Vol. 40, no 6, p. 738-747Article in journal (Refereed)
    Abstract [en]

    Forecasts of demand are crucial to drive supply chains and enterprise resource planning systems. Usually, well-known univariate methods that work automatically such as exponential smoothing are employed to accomplish such forecasts. The traditional Supply Chain relies on a decentralized system where each member feeds its own Forecasting Support System (FSS) with incoming orders from direct customers. Nevertheless, other collaboration schemes are also possible, for instance, the Information Exchange framework allows demand information to be shared between the supplier and the retailer. Current theoretical models have shown the limited circumstances where retailer information is valuable to the supplier. However, there has been very little empirical work carried out. Considering a serially linked two-level supply chain, this work assesses the role of sharing market sales information obtained by the retailer on the supplier forecasting accuracy. Weekly data from a manufacturer and a major UK grocery retailer have been analyzed to show the circumstances where information sharing leads to improved forecasting accuracy. Without resorting to unrealistic assumptions, we find significant evidence of benefits through information sharing with substantial improvements in forecast accuracy. 

  • 33.
    Trapero, Juan R.
    et al.
    Universidad de Castilla-La Mancha, Ciudad Real, Spain.
    Kourentzes, Nikolaos
    Lancaster University, Lancaster, United Kingdom.
    Fildes, Robert
    Lancaster University, Lancaster, United Kingdom.
    On the identification of sales forecasting models in the presence of promotions2015In: Journal of the Operational Research Society, ISSN 0160-5682, E-ISSN 1476-9360, Vol. 66, no 2, p. 299-307Article in journal (Refereed)
    Abstract [en]

    Shorter product life cycles and aggressive marketing, among other factors, have increased the complexity of sales forecasting. Forecasts are often produced using a Forecasting Support System that integrates univariate statistical forecasting with managerial judgment. Forecasting sales under promotional activity is one of the main reasons to use expert judgment. Alternatively, one can replace expert adjustments by regression models whose exogenous inputs are promotion features (price, display, etc). However, these regression models may have large dimensionality as well as multicollinearity issues. We propose a novel promotional model that overcomes these limitations. It combines Principal Component Analysis to reduce the dimensionality of the problem and automatically identifies the demand dynamics. For items with limited history, the proposed model is capable of providing promotional forecasts by selectively pooling information across established products. The performance of the model is compared against forecasts provided by experts and statistical benchmarks, on weekly data; outperforming both substantially.

  • 34.
    Trapero, Juan R.
    et al.
    Universidad de Castilla-La Mancha, Departamento de Administracion de Empresas, Ciudad Real, Spain.
    Kourentzes, Nikolaos
    Lancaster University, Department of Management Science, United Kingdom.
    Martin, A.
    Universidad de Castilla-La Mancha, Departamento de Administracion de Empresas, Ciudad Real, Spain.
    Short-term solar irradiation forecasting based on Dynamic Harmonic Regression2015In: Energy, ISSN 0360-5442, E-ISSN 1873-6785, Vol. 84, p. 289-295Article in journal (Refereed)
    Abstract [en]

    Solar power generation is a crucial research area for countries that have high dependency on fossil energy sources and is gaining prominence with the current shift to renewable sources of energy. In order to integrate the electricity generated by solar energy into the grid, solar irradiation must be reasonably well forecasted, where deviations of the forecasted value from the actual measured value involve significant costs. The present paper proposes a univariate Dynamic Harmonic Regression model set up in a State Space framework for short-term (1-24h) solar irradiation forecasting. Time series hourly aggregated as the Global Horizontal Irradiation and the Direct Normal Irradiation will be used to illustrate the proposed approach. This method provides a fast automatic identification and estimation procedure based on the frequency domain. Furthermore, the recursive algorithms applied offer adaptive predictions. The good forecasting performance is illustrated with solar irradiance measurements collected from ground-based weather stations located in Spain. The results show that the Dynamic Harmonic Regression achieves the lowest relative Root Mean Squared Error; about 30% and 47% for the Global and Direct irradiation components, respectively, for a forecast horizon of 24h ahead. 

  • 35.
    Trapero, Juan R.
    et al.
    Universidad de Castilla-La Mancha, Departamento de Administracion de Empresas, Ciudad Real, Spain.
    Pedregal, Diego. J.
    Universidad de Castilla-La Mancha, Departamento de Administracion de Empresas, Ciudad Real, Spain.
    Fildes, R.
    Lancaster University Management School, Department of Management Science, Lancaster, United Kingdom.
    Kourentzes, Nikolaos
    Lancaster University Management School, Department of Management Science, Lancaster, United Kingdom.
    Analysis of judgmental adjustments in the presence of promotions2013In: International Journal of Forecasting, ISSN 0169-2070, E-ISSN 1872-8200, Vol. 29, no 2, p. 234-243Article in journal (Refereed)
    Abstract [en]

    Sales forecasting is becoming increasingly complex, due to a range of factors, such as the shortening of product life cycles, increasingly competitive markets, and aggressive marketing. Often, forecasts are produced using a Forecasting Support System that integrates univariate statistical forecasts with judgment from experts in the organization. Managers then add information to the forecast, such as future promotions, potentially improving the accuracy. Despite the importance of judgment and promotions, papers devoted to studying their relationship with forecasting performance are scarce. We analyze the accuracy of managerial adjustments in periods of promotions, based on weekly data from a manufacturing company. Intervention analysis is used to establish whether judgmental adjustments can be replaced by multivariate statistical models when responding to promotional information. We show that judgmental adjustments can enhance baseline forecasts during promotions, but not systematically. Transfer function models based on past promotions information achieved lower overall forecasting errors. Finally, a hybrid model illustrates the fact that human experts still added value to the transfer function models. 

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