Hybrid demand forecasting models: pre-pandemic and pandemic use studies

Equilibrium. Quarterly Journal of Economics and Economic Policy Volume 17 Issue 3 September 2022 p-ISSN 1689-765X, e-ISSN 2353-3293 www.economic-policy.pl Copyright © Instytut Badań Gospodarczych / Institute of Economic Research (Poland) This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ORIGINAL ARTICLE Citation: Kolková, A., & Rozehnal, P. (2022). Hybrid demand forecasting models: pre-pandemic and pandemic use studies. Equilibrium. Quarterly Journal of Economics and Economic Policy, 17(3), 699–725. doi: 10.24136/eq.2022.024 Contact to corresponding author: Andrea Kolková, [email protected] Article history: Received: 3.04.2022; Accepted: 15.07.2022; Published online: 30.09.2022 Andrea Kolková VSB - Technical University Ostrava, Czechia orcid.org/0000-0002-4764-3164 Petr Rozehnal VSB - Technical University Ostrava, Czechia orcid.org/0000-0002-1339-9992 Hybrid demand forecasting models: pre-pandemic and pandemic use studies JEL Classification: M21; M15; C53 Keywords: forecastHybrid; demand forecasting; statistic model; neural networks Abstract Research background: In business practice and academic sphere, the question of which of the prognostic models is the most accurate is constantly present. The accuracy of models based on artificial intelligence and statistical models has long been discussed. By combining the advantages of both groups, hybrid models have emerged. These models show high accuracy. Moreover, the question remains whether data in a dynamically changing economy (for example, in a pandemic period) have changed the possibilities of using these models. The changing economy will continue to be an important element in demand forecasting in the years to come. In business, where the concept of just in time already proves to be insufficient, it is necessary to open new research questions in the field of demand forecasting. Purpose of the article: The aim of the article is to apply hybrid models to bicycle sales e-shop data with a comparison of accuracy models in the pre-pandemic period and in the pandemic period. The paper examines the hypothesis that the pandemic period has changed the accuracy of hybrid models in comparison with statistical models and models based on artificial neural networks. Models: In this study, hybrid models will be used, namely the Theta model and the new forecastHybrid, compared to the statistical models ETS, ARIMA, and models based on artificial neural networks. They will be applied to the data of the e-shop with the cycle assortment in the period from 1.1. 2019 to 5.10 2021. Whereas the period will be divided into two parts, pre- Equilibrium. Quarterly Journal of Economics and Economic Policy, 17(3), 699–725 700 pandemic, i.e. until 1 March 2020 and pandemic after that date. The accuracy evaluation will be based on the RMSE, MAE, and ACF1 indicators. Findings & value added: In this study, we have concluded that the prediction of the Hybrid model was the most accurate in both periods. The study can thus provide a scientific basis for any other dynamic changes that may occur in demand forecasting in the future. In other periods when there will be volatile demand, it is essential to choose models in which accuracy will decrease the least. Therefore, this study provides guidance for the use of methods in future periods as well. The stated results are likely to be valid even in an international comparison. Introduction In the academic sphere as well as in business practice, there are still discussions about models of demand forecasting in business economics. These still used statistical models are consequently such a standard solution of many forecasting systems even nowadays. In recent years, models based on artificial intelligence have come to fore, primarily artificial neural networks, in spite of the fact that these models may not always be the best. Practice shows that the training data indicates great accuracy on the test data; this may not be the case (Kolková, 2018, pp. 102–119). The most modern models used in forecasting were hybrid models, which take advantage of both approaches. As early as 1969, Bates and Granger (2017) introduced combined models and herewith provided the conceptual foundations for the further use of existing models. Hybrid models combine existing methods with artificial intelligence. Not only their mutual combination, but also the possibility of calculating model parameters on a static basis using artificial intelligence. Initially in M4-Competition (Petropoulos & Makridakis, 2020, pp. 3–6), these models were rated as the most successful. However, it is clear that each model has its justification, and its use depends mainly on the selected data. This article uses the models that were evaluated as more successful in this competition. And they were hybrid methods that successfully participated in this competition. As noted earlier, the aim of this article is to apply hybrid models to bicycle sales e-shop data with a comparison of accuracy models in the prepandemic period by contrast in the pandemic period. The paper examines the hypothesis that the pandemic period has changed the accuracy of hybrid models in comparison with statistical models and models based on artificial neural networks. Subsequently, hypotheses were specified to meet the goal. The first hypothesis: that the pandemic period has changed the accuracy of hybrid models compared to statistical models and models based on artificial neural Equilibrium. Quarterly Journal of Economics and Economic Policy, 17(3), 699–725 701 networks. The second hypothesis then assumes that hybrid models were the most accurate in the pre-pandemic period. The third hypothesis then implies that the most accurate statistical models remained in the pandemic period. To make certain these hypotheses, static models, models based on artificial neural networks, and hybrid models on daily e-shop data in the years 2019–2021 were applied. Additionally, the literature review will define previous research on hybrid models and the application of models to practical data. Hybrid models will be described in detail in the methodology chapter, and a statistical description of the data will be performed. In the results section, the results of the calculations will be presented in the figures and tables. These were subsequently commented on in the discussions and the achievement of the goal and the acceptance or refutation of hypotheses were evaluated. Finally, the results will be summarized in conclusion. Literature review Hybrid models represent a combination of models based on artificial intelligence and statistical models (Smyl, 2020, pp. 75–85). In 2018, a large competition of forecasting models was organized. These competitions are very important in the forecasting community. It is currently attended by leading researchers from all over the world. These are not only researchers from the academic sphere, but also researchers from business practice. This makes these competitions even more serious. The results of the M4 Competition (Makridakis et al., 2018, pp. 802– 808) demonstrate that the combination of several prognostic models gives the best results. Of the 17 models evaluated as the most accurate in this competition, 12 were mainly combinations of statistical models. The biggest surprise of the M4 Competition was the hybrid approach. The hybrid model was also the absolute winner of this competition. The hybrid model in the M4 Competition was presented by Smyl (2020, pp. 75– 85), a data scientist from Uber Technologies. Smyl applied a hybrid model based on artificial neural networks and a statistical model inspired by exponential smoothing. He used exponential smoothing formulas to deseasonize and normalize time series and used advanced neural networks to extrapolate. Hereafter the second most accurate model in this competition was one that combined seven statistical and one machine learning model. The weights here were calculated using a machine learning algorithm. This model was presented by the Spanish University of A Coruña and the Aus- Equilibrium. Quarterly Journal of Economics and Economic Policy, 17(3), 699–725 702 tralian Monash University (Montero-Manso et al. 2020, pp. 86–92). Another new hybrid model was developed by Nontapa et al. (2021), the model uses the SARIMAX prediction model and an artificial neural network. The results of the M5Competition (Makridakis et al., 2022) are currently being published. This competition focused on forecasting retail sales, so it was very close to demand forecasting, which is also applied in this article. However, not all results are currently available yet. Another important forecasting competition is provided by Kaggle forecasting competitions (Bojer & Meldgaard, 2021). Here it follows that models using cross-learning tend, decision trees and neural networks are strong prognostic models. As a result, in this study we will supplement neural networks with other models and by creating hybrid models we want to examine their usability. In this context, it is worthwhile to consider an interesting study on hybrid models in a study of Zougagh et al. (2021). In this study, contributions to hybrid prediction models since 2005 published in Scopus databases have been analysed; IEEE; ERIC; Google scholar. A total of 70 articles dealing with hybrid forecasting models were analysed. The results show that interest in hybrid models has grown significantly since 2016. Artificial neural networks are most often included in hybrid models, which were in 41% of models. They were also applied in 20% autoregressive models (AR, ARIMA or ARMA). In 15%, the authors of hybrid models used the Genetic algorithm and the support vector machine was used in 13% and fuzzy systems 11%. Furthermore, they dealt with hybrid models directly in demand forecasting (Siddiqui et al., 2021, pp. 1–11). A parallel series hybridization of seasonal intelligent-based statistical model for demand forecasting (Bahrami & Khashei & Amindoust, 2021) and a selected hybrid model used for demand forecasting have been used (e.g. Zhang et al., 2021; Kolková & Ključnikov, 2021, pp. 1063–1094). At the same time, there are still discussions about whether models based on artificial intelligence or statistical models are more accurate (Kolková, 2020, pp. 90–105). Spiliotis et al. (2022) state that some machine learning models provide better predictions, both in terms of accuracy. He came to similar conclusions to Cuhadar (2020, pp. 55–70), who forecasted tourism in Croatia and concluded that models based on artificial neural networks always work more accurately than statistical models. Similarly to Pereira and Cerqueira (2021, pp. 1–18) in forecasting the demand for hotel services, he established that the use of machine learning models can reduce the mean square error by up to 54% for the 1-day forecast horizon and by up to 45% compared to traditional models of exponential smoothing for a 14-day Equilibrium. Quarterly Journal of Economics and Economic Policy, 17(3), 699–725 703 forecast horizon. Balaji Prabhu and Dakshayini (2020, pp. 35–47) argue that the multiple linear regression model and the artificial neural network model are both useful, reliable, and relatively effective tools for optimizing the effects of demand prediction in food harvest supply management to satisfactorily match social needs. The study by Abbasimehr et al. (2020, pp. 345–366) compared artificial intelligence models with statistical ones. The LSTM multilayer network model was the most accurate, the second most accurate model was artificial neural networks, however, in the third place it was marked as the most accurate ETS model. Furthermore, scientists and especially practitioners evaluate whether the most accurate models are always the best for practical use (Kolková & Navrátil, 2021, pp. 123–141). Especially due to the computational demand of the prediction or the financial cost of maintaining such a model in real business operations. In Kolková and Navrátil (2021, pp. 123–141) parameters other than accuracy were also examined. The results of this study illustrated that models based on deep learning have proven to be the worst on runtime and computing demand. On the other hand, the authors address the issue whether or not the differences between the accuracy of models based on artificial intelligence and statistical models are related to the time series studied. Foldvik Eikeland et al. (2021) conclude in their study that statistical models achieve higher accuracy over longer prediction horizons compared to neural networks, while machine learning approaches work better in predicting loads at shorter time intervals. On the contrary, Marček (2019, pp. 317–322) showed that all the models he applied (ARIMA, NN, SVM) are suitable as prediction models for use in prognostic systems that commonly predict the values of variables in competitive energy markets. Bui et al. (2020, pp. 382–406) recommend new models of data filtering to increase the accuracy of models based on artificial neural networks. Sudden changes in demand can occur, especially in data from developing countries. The results confirm that the accuracy of these models can be significantly improved by virtue of the proposed model of statistical data filtering. Time-series research, which is affected by external shocks, is still an important element of demand forecasting. Principally in the pandemic period, demand may have developed abnormally. In this study, data are distributed and the most accurate prognostic model is selected in a period of stable development and in a period of economic shocks caused by a pandemic. Research is not yet focused on this area. Data on bicycle sales in the Czech Republic during the pandemic were selected for this study. Only a few scientific works deal with this issue. The results of Habib and Anik (2022) showed that bicycle sales increased sig- Equilibrium. Quarterly Journal of Economics and Economic Policy, 17(3), 699–725 704 nificantly in the pandemic, while car sales decreased. The same logic underlies an article by Ramírez et al. (2021) where the authors found, via a machine learning model, that there was a 29.76% decrease in sales in the automotive industry in the Mexican market. Studies comparing online sales also provide interesting results. According to Fairlie and Fossen (2022), it is possible to distinguish the fields affected by the pandemic, such as accommodation facilities, which lost up to 91% of taxable sales in the place of study, on the contrary, online sales of goods increased up to 180%. Wang et al. (2020) declare how the pandemic affected the change in sales style in the dairy industry. For the time being, the authors have not dealt with the analysis of methods suitable for quantifying the demand for bicycles yet. Research methods We illustrate this procedure for this study by using data from the online store with bicycle sales. The data declares purchases via the e-shop. The data set contains 878 values of daily revenues and daily number of e-shop orders for the years 2019, 2020 and part of the year 2021. Exactly, there is from 1.1. 2019 to 8.9.2021. The descriptive characteristics are defined in Tab. 1. These data are chosen mainly because there has been a spike in demand for this product due to the pandemic. Such a change in consumer preferences is very likely to affect the degree of accuracy of demand forecasting models as well. Also, the online distribution channel is currently becoming one of the important distribution channels. During the pandemic period, this distribution channel also spread among small and medium-sized enterprises, and its further use can be expected in the future. The estimated Hurst exponent of the affected variables, shown in Tab. 1, is significantly greater than 0.5. This suggests that the series is not random and is controlled by persistent patterns (the Hurst exponent is an indicator of randomness). If this is not accidental, the use of prediction models is justified. The minimum daily turnover and the number of orders were 0. The maximum daily turnover was CZK 2,371,324 and the maximum number of orders placed per day was 330. The data on mean and median are also shown in Tab. 1. The data were decomposed using additive decomposition. Fig. 1 shows the breakdown of daily turnover. This chart clearly shows an increase in the time of the pandemic. However, the seasonality of the demand for these Equilibrium. Quarterly Journal of Economics and Economic Policy, 17(3), 699–725 705 goods remains the same. Fig. 2 defines the breakdown of the daily number of orders, where a similar progress is evident. The study verifies three hypotheses. With these hypotheses, we want to verify whether the pandemic affected the forecasting possibilities in terms of the accuracy of hybrid models in contrast to statistical models and models based on artificial neural networks. H1: The pandemic period has changed the accuracy of hybrid models compared to models based on standard statistical indicators (hereafter statistical models) and the neural network model. H2: In the pre-pandemic period, hybrid models were the most accurate. H3: In the pandemic period, the most accurate models are statistical. Prior research has suggested each model is evaluated using accuracy. The RMSE (root mean square error) coefficient was used to calculate accuracy. This is defined by Hyndman and Athanasopoulos (2018), and can be described by formulas (1) and (2),  = √, (1) where RMSE has the same unit as the original time series. The MAE indicator is also declared in the same units, which expresses the average deviation of the actual values from the forecasted ones. The median can also be used instead of the mean deviation. We then describe both calculations as follows,  =   ∑  −      or  = |  | (2) The last accuracy used is ACF1. This indicator is defined as the autocorrelation of delay errors 1. In essence, it expresses the degree to which the current value is affected by previous values in a time series. The autocorrelation function for a delay of length k can be defined as   =     =    ! (3) Mentioned above, ETS, ARIMA, models based on artificial neural networks, are used in this work. These will be compared with two hybrid Equilibrium. Quarterly Journal of Economics and Economic Policy, 17(3), 699–725 706 models. The first is the Theta model, the second is the forecastHybrid model. The deterministic model ETS (Error, Trend, Seasonal) according to Brown (1959); Holt (2004); Winters (1960) can be defined using formulas (4), (5), (6) and (7),   = " # + % # + & #' + (  , (4) where "  = " # + % # + )(  (5) %  = % # + *(  (7) &  = & #' + +(  , (6) where "  is estimate level, bt are estimated trend, t and s t express the seasonality, ), * and + are weight coefficients. ARIMA (AutoRegressive Integrated Moving Average) is defined in (Box & Jenkins, 1976). ARIMA models use the Box-Jenkins model. The ARIMA model with the seasonal component can be expressed in the form ARIMA (p, d, q) (P, D, Q), where p represents the degree of the autoregressive part, d the degree of differentiation, and q the degree of the moving average part. Formulas can be used to calculate ARIMA (7) and (8), ,-./0  = 1-./(  , (7) where 0  = ∆ 3   (8) This model can also be described in a special form, ARFIMA (AutoRegresive Integrated Moving Average). According to this model (Box & Jenkins, 1976), it is possible to estimate and determine the correlation in stationary processes even for very distant random variables. ARFIMA in this article is defined by the relationship (9), ,-./-1 − ./ 3   = 1-./(  (9) Equilibrium. Quarterly Journal of Economics and Economic Policy, 17(3), 699–725 707 Artificial neural networks are inspired by processes in the human brain. The output of a neuron is calculated when the sum of the inputs to the neuron xi multiplied by their specific weights w i exceeds a certain value, which we call the distortion. The neuron can be described in this way . 5 = 67∑8 9 ∙ 0 5,9 − % 5 ' 9 <, (10) where x i is the specific value on the i-th input, w j,i are the weights of this input, b j is bias, m is the total number of inputs, f is a transformation function, and the output values of y. Process artificial neural networks is shown in Figure 3. In this article, the Nnar(p,k) model is used, where k is the number of hidden nodes. The inputs are for lags 1 to p. This model tends to be very accurate on training data, but is usually less accurate on test data. However, it usually achieves good accuracy. The first selected hybrid model forecastHybrid is defined in Shaub and Ellis (2020). This model combines ARIMA, ETS, and Theta, Tbats (the name this model is an acronym denoting its salient features T for trigonometric regressors to model multiple-seasonalities, B for Box-Cox transformations, A for ARMA errors, T for trend and S for seasonality, and artificial neural networks). The whole forecasfHybrid model is then defined by formula (11), -=/=∑0 ' ∙ 6 ' -=/  ' , (11) where 0 ' is weight to each m of the n model, 6 ' -=/ individual model for time horizont i. This model is called forecastHybrid and is published in a package in the statistical program R (Shaub & Ellis, 2020). The Theta model was created by Assimakopoulos and Nikopoulos (2000, pp. 521–530). The model is based on the concept of modification of local fluctuations of the time series using the coefficient Theta (denoted by the Greek letter θ). 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Mean Median Standard deviation Hurst exponent Revenues 0 Kč 2 371 324 Kč 260 993 Kč 168 619 Kč 296 840.9421 0.9378 Number of orders 0 Kč 330 64 46 56.3552 0.9591 2019 Revenues 0 Kč 918 742 Kč 138 705 Kč 102 916 Kč 131 155.9072 0.8812 Number of orders 0 Kč 118 35 31 23.1490 1.0096 2020–2021 Revenues 0 Kč 2 371 324 Kč 330 113 Kč 232 863 Kč 339 065.7547 0.8597 Number of orders 0 Kč 330 81 63 62.4749 0.8812 Table 2. Accuracy results according to the ETS model data RMSE MAE ACF1 Revenues forecast: pre - pandemic data 123660.7 91029.67 0.0251 Revenues forecast: post - pandemic data 220112.3 158069.3 0.1134 Number of orders: pre - pandemic data 20.2868 15.8643 0.0650 Number of orders: post - pandemic data 37.4864 27.7062 0.1247 Table 3. Accuracy results according to the ARIMA model data RMSE MAE ACF1 Revenues forecast: pre - pandemic data 123645.3 90951.2 0.0243 Revenues forecast: post - pandemic data 218015 158084.5 0.0020 Number of orders: pre - pandemic data 20.2256 15.7006 0.0027 Number of orders: post - pandemic data 37.0503 27.5582 0.0007 Table 4. Accuracy results according to the neural network model data RMSE MAE ACF1 Revenues forecast: pre - pandemic data 123660.7 91029.67 0.0251 Revenues forecast: post - pandemic data 220112.3 158069.3 0.1134 Number of orders: pre - pandemic data 20.2868 15.8643 0.0650 Number of orders: post - pandemic data 37.4864 27.7062 0.1247 Table 5. Accuracy results according to the forecastHybrid data RMSE MAE ACF1 Revenues forecast: pre - pandemic data 109151.6 79836.51 0.0252 Revenues forecast: post - pandemic data 183004.4 133228.9 0.0842 Number of orders: pre - pandemic data 17.8029 13.7436 0.0356 Number of orders: post - pandemic data 33.2794 25.0714 0.0460 Table 6. Accuracy results according to the Theta data RMSE MAE ACF1 Revenues forecast: pre - pandemic data 123642.7 91222.12 0.0260 Revenues forecast: post - pandemic data 220112.3 158064.1 0.1135 Number of orders: pre - pandemic data 20.2868 15.8640 0.0650 Number of orders: post - pandemic data 37.4864 27.7061 0.1247 Table 7. Decline in model accuracy during the pandemic Theta forecastHybrid Nnar ARIMA ETS revenues 77.09% 70.07% 77.87% 91.77% 77.87% number of orders 47.87% 22.61% 47.87% 74.07% 47.87% Table 8. Order of models according to accuracy Order of models according to accuracy Total order RMSE MAE ACF1 Theta Revenues forecast: pre-pandemic data 2 4 4 4 Revenues forecast: post-pandemic data 3 2 4 3 forecastHybrid Revenues forecast: pre-pandemic data 1 1 3 1 Revenues forecast: post-pandemic data 1 1 2 1 NNAR Revenues forecast: pre-pandemic data 4 3 2 3 Revenues forecast: post-pandemic data 3 3 3 3 ARIMA Revenues forecast: pre-pandemic data 3 2 1 2 Revenues forecast: post-pandemic data 2 4 1 3 ETS Revenues forecast: pre-pandemic data 4 3 2 3 Revenues forecast: post-pandemic data 3 3 3 3 Theta Number of orders: pre-pandemic data 3 3 3 3 Number of orders: post-pandemic data 3 3 3 3 forecastHybrid Number of orders: pre-pandemic data 1 1 2 1 Number of orders: post-pandemic data 1 1 2 1 Table 9. Continued Order of models according to accuracy Total order RMSE MAE ACF1 NNAR Number of orders: pre-pandemic data 3 3 3 3 Number of orders: post-pandemic data 3 3 3 3 ARIMA Number of orders: pre-pandemic data 2 2 1 2 Number of orders: post-pandemic data 2 2 1 2 ETS Number of orders: pre-pandemic data 3 3 3 3 Number of orders: post-pandemic data 3 3 3 3 Figure 1. Decomposition of additive time series daily revenues Figure 2. Decomposition of additive time series daily number of orders Figure 3. Artificial neural networks Source: own processing according to Hyndman and Athanasopoulos (2021). Figure 4. ETS Forecast Figure 5. ARIMA forecast Figure 6. Neural networks forecast