On intermittent demand model optimisation and selection

Intermittent demand time series involve items that are requested infrequently, resulting in sporadic demand. Croston's 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 Croston's 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 similarly 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

Forecasting with multivariate temporal aggregation:the case of promotional modelling

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 Muliple 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 misspecification

Modelling Deterministic Seasonality with Artificial Neural Networks for Time Series Forecasting

This study explores both from a theoretical and empirical perspective how to model deterministic seasonality with artificial neural networks (ANN) to achieve the best forecasting accuracy. The aim of this study is to maximise the available seasonal information to the ANN while identifying the most economic form to code it; hence reducing the modelling degrees of freedom and simplifying the network’s training. An empirical evaluation on simulated and real data is performed and in agreement with the theoretical analysis no deseasonalising is required. A parsimonious coding based on seasonal indices is proposed that showed the best forecasting accuracy

Analysis of judgmental adjustments in the presence of promotions

Sales forecasting is increasingly complex due to many factors, such as product life cycles that have become shorter, more 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 add information to the forecast, like future promotions, potentially improving accuracy. Despite the importance of judgment and promotions, the literature devoted to study their relationship on forecasting performance is scarce. We analyze managerial adjustments accuracy under 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

Improving forecasting via multiple temporal aggregation

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 we 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

Distributions of forecasting errors of forecast combinations: implications for inventory management

Inventory control systems rely on accurate and robust forecasts of future demand to support decisions such as setting of safety stocks. Combining 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 household and personal care leading 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

The Impact of Special Days in Call Arrivals Forecasting:A Neural Network Approach to Modelling Special Days

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.NOTICE: this is the author’s version of a work that was accepted for publication in European Journal of Operational Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in European Journal of Operational Research, [264, 3, (2016)] DOI: 10.1016/j.ejor.2016.07.015© 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0

Advances in forecasting with artificial neural networks

There is decades long research interest in artificial neural networks (ANNs) that has led to several successful applications. In forecasting, both in theoretical and empirical works, ANNs have shown evidence of good performance, in many cases outperforming established benchmark models. However, our understanding of their inner workings is still limited, which makes it difficult for academicians and practitioners alike to use them. Furthermore, while there is a growing literature supporting their good performance in forecasting, there is also a lot of scepticism whether ANNs are able to provide reliable and robust forecasts. This analysis presents the advances of ANNs in the time series forecasting field, highlighting the current state of the art, which modelling issues have been solved and which are still critical for forecasting with ANNs, indicating future research directions

Short-term solar irradiation forecasting based on dynamic harmonic regression

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 to 24 hours) 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 24 hours ahead