Nikolaos Kourentzes

Forecast Combinations for Intermittent Demand

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.

An evaluation of neural network ensembles and model selection for time series prediction

Ensemble methods represent an approach to combine a set of models, each capable of solving a given task, but which together produce a composite global model whose accuracy and robustness exceeds that of the individual models. Ensembles of neural networks have traditionally been applied to machine learning and pattern recognition but more recently have been applied to forecasting of time series data. Several methods have been developed to produce neural network ensembles ranging from taking a simple average of individual model outputs to more complex methods such as bagging and boosting. Which ensemble method is best; what factors affect ensemble performance, under what data conditions are ensembles most useful and when is it beneficial to use ensembles over model selection are a few questions which remain unanswered. In this paper we present some initial findings using neural network ensembles based on the mean and median applied to forecast synthetic time series data. We vary factors such as the number of models included in the ensemble and how the models are selected, whether randomly or based on performance. We compare the performance of different ensembles to model selection and present the results.

On the identification of sales forecasting models in the presence of promotions

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.

Forecasting with Temporal Hierarchies

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.

Input-variable specification for Neural Networks - An analysis of forecasting low and high time series frequency

Prior research in forecasting time series with Neural Networks (NN) has provided inconsistent evidence on their predictive accuracy. In management, NN have shown only inferior performance on well established benchmark time series of monthly, quarterly or annual frequency. In contrast, NN have shown preeminent accuracy in electrical load forecasting on daily or hourly time series, leading to successful real life applications. While this inconsistency has been traditionally attributed to the lack of a reliable methodology to model NNs, recent research indicates that the particular data properties of high frequency time series may be equally important. High frequency time series of daily, hourly or even shorter time intervals pose additional modelling challenges in the length and structure of the time series, which may abet the use of novel methods. This analysis aims to identify and contrast the challenges in modelling NN for low and high frequency data in order to develop a unifying forecasting methodology tailored to the properties of the dataset. We conduct a set of experiments in three different frequency domains of daily, weekly and monthly data of one empirical time series of cash machine withdrawals, using a consistent modelling procedure. While our analysis provides evidence that NN are suitable to predict high frequency data, it also identifies a set of challenges in modelling NN that arise from high frequency data, in particular in specifying the input vector, and that require specific modelling approaches applicable to both low and high frequency data.

Frequency independent automatic input variable selection for Neural Networks for forecasting

Key issue in time series forecasting with Neural Networks (NN) is the selection of the relevant input variables, which is often the result of data exploration by human experts, leading to dataset specific solutions and limiting forecasting automation. This becomes even more important in heterogeneous datasets, where each time series requires special modeling and can exhibit a different variety of stochastic and deterministic components of different unknown frequencies. Fully automated forecasting with NNs requires a methodology that can address these issues in an entirely data driven approach. This paper proposes a fully automated input selection methodology based on a novel iterative NN filter that automatically identifies for each time series the seasonal frequencies, if such are present, the dynamic structure of the time series, distinguishing between stochastic and deterministic components, ultimately producing a parsimonious set of input variables. The robustness and performance of the algorithm are evaluated against established time series forecasting methods.

Naive Support Vector Regression and Multilayer Perceptron benchmarks for the 2010 neural network grand competition (NNGC) on time series prediction

In recent forecasting competitions, algorithms of Support Vector Regression (SVR) and Neural Networks (NN) have provided some of the most accurate time series predictions, but also some of the least accurate contenders failing to outperform even simple statistical benchmark methods. As both SVR and NN offer substantial degrees of freedom in model building (e.g. selecting input variables, kernel or activation functions, etc.), a myriad of heuristics and ad-hoc rules have emerged which may lead to different models with substantial differences in performance. The heterogeneity of results impairs our ability to compare the adequacy of a class of algorithms for a given dataset, and fails to develop an understanding of their presumed nonlinear and non-parametric capabilities. In order to determine a generalized estimate of performance for both SVR and NN in the absence of an accepted ‘best practice’ methodology, this paper seeks to compute benchmark results employing a naïve methodology which attempts to mimic many of the common mistakes in model building. The naive methodologies serve primarily as a lower error bound, representative of a within class benchmark for both algorithms in predicting the 66 time series of the NNGC Competition. In addition, their discussion aims to draw attention to the most common mistakes in modelling that regularly lead to model misspecification of MLPs and SVRs in time series forecasting.

Tactical sales forecasting using a very large set of macroeconomic indicators

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.

Impact of Demand Nature on the Bullwhip Effect. Bridging the Gap between Theoretical and Empirical Research

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 de- mand 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 quan- tify 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.

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.