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

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

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

Complex exponential smoothing

Exponential smoothing has been one of the most popular forecasting methods for business and industry. Its simplicity and transparency have made it very attractive. Nonetheless, modelling and identifying trends has been met with mixed success, resulting in the development of different modifications of trend models. We present a new approach to time series modelling, using the notion of "information potential" and the theory of functions of complex variables. A new exponential smoothing method that uses this approach is proposed, the "Complex exponential smoothing" (CES). It has an underlying statistical model described in the paper and has several advantages in comparison with the customary exponential smoothing models, that allow CES to model and forecast effectively both trended and level time series, effectively overcoming the model selection problem

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

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

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