THE USE OF THE COMBINED MODEL OF FORECASTING IN REAL TRADE CONDITIONS. Peter KAČMÁRY, Dušan MALINDŽÁK

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1 THE USE OF THE COMBINED MODEL OF FORECASTING IN REAL TRADE CONDITIONS Peter KAČMÁRY, Dušan MALINDŽÁK Technical University of Košice, Faculty of BERG, Logistics Institute of Industry and Transport, Park Komenského 14, Košice, Abstract: This paper describes the principle and calculation of combined model of forecasting, describes also the choice of methods, which should be used in the model, examples of forecasts creations by using historic time series from real trade environment and conclusions and summaries of achieved results. Key words: Forecast, combined model of forecasting, time series, method, trade. 1. INTRODUCTION The topic of this paper is based on some projects created in Slovak industrial companies, which main products vary from food through electrotechnics to other industrial components. The inherent market volatility has forced companies to the systematic increase of flexibility in planning process in all levels of managing. As it is generally known, especially in the time of crisis, good and flexible planning cannot be done efficiently without forecasting [1, 2, 3]. Nowadays there are plenty of methods, methodologies or techniques, which are used at creation of any kind of forecasting, but there are not so many to be properly used in the time of inherent market volatility. A forecast-updating firm might react earlier than a firm with no forecast updating. [4]. It initiates the thoughts to prepare some new methodology or techniques just to solve the company s problems [5]. The selection of methods depends on the market characteristics, the forecast period, the amount and character of historical data, etc. Not only these problems are mentioned and solved in the references [6, 7], but also there is described the principle of how the results of different methods of forecasting should be aggregated together to get one result. 1. The first main reason comes out from the need of verification of the forecasted results and the achievement of one objective result. There is not possible to avoid of a fatal error by creation of forecasting based only on one method. 2. The selection of methods should be focused not only on a group of methods (e.g. quantitative methods), but also use the method with other approaches forecasting solutions. If the method selected from a group, such as quantitative, it is necessary to use different methods, regardless of stochastic type or type of time series. For example, the proposed solution should include regression analysis as a quantitative method, Sales Force Polling to estimate sales as qualitative methods and any of the methods using such weights e.g. the method of Harmonic Weights. This article describes and applied two methods, which use the aggregate approach: the head of a snake method (based on the principles of regression analysis) and the method of harmonic weights. 3. The similarity of results from different methods (minimum two) increases the probability that the calculation or forecast creation is correct. The similarity means that the deviation of ± 10%, because forecast with a tolerance of ± 10% are considered as accurate. [8, 9]. The deviation up to ± maximum 25% means accepted forecast (it depends on character of usage or on the character of an enterprise indeed). Thus, the calculation is verified by the correlative usage of various methods.

2 If some result(s) of forecasts differ(s) significantly, it is clear that an error should occur because: some of the methods was not correct selected for the given type of forecasted process; obtained data are not correct or sufficient for the forecast calculation; there are too high or too low number of data. The best way to verify the performance of the model of various forecasting methods or any prognostic model is by using historical data, by which the forecast is calculated and then verified with the real values. By this, it should be verified each model before applying in practice. One of methodologies that can aggregate various results from forecast calculations can be combined model of forecasting. The advantage of using of the combined model of forecasting is especially when there are conditions like unstable situation of observed events, uncertain decision about which method is the most accurate, error proof - when you want to minimise errors. It is expected that combining reduces errors [10]. This article tries to prove the about mentioned affirmation by the proposed model of combined forecast calculation. This calculation is based on the true historical data of the prices of crude oil in US dollars. However, the values are prices, it is an example of reaction of the certain methods and combined model of forecasting to the real market volatility during the near past. 2. THE COMBINED MODEL OF FORECASTING Combining forecasts (CF), sometimes referred to as composite forecasts, is a kind of the averaging of separate forecasts. These forecasts can be based on different data or different methods or both. The averaging is one by using a rule that can be represented e.g. by a simple average of the forecasts [10]. The following model or methodology is built on the multicriteria decision and the assessment conception. The principle is to rectify the results from many forecasts into one, which creates consensus of partial results. This correcting of results depends on the process for which it is calculated. This is ensured by the way of evaluating the results by weights, which ratio is configured according to the three variants, which represent the level of dynamics of the process. The summary of all weights is equal as it is in the following formula (1) [11]: (1) The description of the combined model has been described in previous CLC 2011 conference, but a little change was done in the calculation that the regression analysis (RA) was replaced by moving average (MA), because regression analysis is included in the head of a snake method. Other parameters were kept the same, also the simplicity of the calculation and the choice of methods. There are four methods coming into this consideration: exponential smoothing (ES), moving average (MA), harmonic weights (HW) and head of a snake (HS). The methods harmonic weights and head of a snake were detailed described in the article from the previous conference (CLC201), that is why, the description is skipped. Other method (exponential smoothing and moving average) are in the simplest form, description is also not included). The mentioned variants and the configured weights are in the following table 1 and figure 1: [11] Table 1: Forecasting methods evaluation by weights according to types of variants Forecasting methods: Weights I st variant of weights II nd variant of weights III rd variant of weights Harmonic weights (HW) w 1 = 0,1 0,3 0,4 Head of a Snake (HS) w 2 = 0,1 0,3 0,4 Moving average (MA) w 3 = 0,4 0,2 0,1 Expon. smoothing (ES) w 4 = 0,4 0,2 0,1

3 volume of consumption, sale, production, prices, etc , Jeseník, Czech Republic, EU y 80% 20% nd 2 variant of weights configurations >±20% ±10%{ { >±10% < ±20% st 1 variant of weights configuration 3rd variant of weights configuration time (t) Figure 1: Graphical means of variants [11] There are defined conditions of validation of these variants. The definition is important for a correct and objective choice of weight variants and can be varied for a different type of processes: 1 st variant: all time series values are scattered maximum ±10% according to a trend line correlation created by linear regression. In case of this correlation the process is considered as relatively stable, there are not the signs of sudden changes even at values in the last period. The weights are configured as for stable, non-dynamic process and that is why the higher weight is put to methods for stable environment [11]. 2 nd variant: values from the last period i.e. 20% of all time series values are scattered more than 10% but less than 20% according to a trend line correlation created by linear regression. In this case it is possible to consider the last period as slightly dynamic that is why the higher weight is put more to methods applicable to dynamic processes [11]. 3 rd variant: is similar to variant 2, but there is even higher scatter in the last period i.e. 20% of all time series values. Because the scatter is higher than 20% it is considered as dynamic dependency and that is why the weight configuration is changed again. The high accent is put to methods applicable to dynamic processes and it results to high volume of weight [11]. 3. THE FORECAST CALCULATION WITH THE COMBINED MODEL OF FORECASTING This chapter describes the example of the application of the combined model of forecasting. There are calculations, comparing of results and the verification of positive expectation, mentioned in introduction. This calculation can be applied in a wide range of time series analysis, in industrial or commercial sector. It means that the application of this model can be used to forecast the development of even prices of certain commodities. That is why the there were used historical data of available resources traded commodities for the demonstration of the general principle and practical work with this model. The following example is the forecast calculation of the future price of crude oil in U.S. dollars at commodity market.

4 Price in US $ , Jeseník, Czech Republic, EU This example of the model application can be divided into two separate studies: 1. Forecasting based on daily data (calculated forecast points to the development of the price in the next trading day); 2. Forecasting based on monthly data mainly and partially on daily data (calculated forecast points to the development of the price in the last trading day of the month). Daily data are used only for the head of a snake method to calculate local trend (LT) 3.1 Case study 1 Daily data forecasting This case deals with daily forecasting, i.e. the period is a day and the result is the forecast for next day. Historical data are created by last daily price just before the closing trade in a stock exchange. These data reflects the daily changes of crude oil in US dollars per barrel from 1 st June 2012 till 18 th September 2012 the last known quarter of actual year (fig.2). 105 Crude oil price development Crude oil in USD LT GT 70 Date Figure 2: Diagram of daily crude oil prices development. Data source: [12] In the analysed data, there are not significant or chaotic changes in prices, this can be considered as relatively smooth time series. Maximum dispersion of data is 8,49% from the main trend line (GT) from all values. That is why it is used the variant no. 1 for weight configuration for the next calculation of combined forecast. Forecast was calculated for the first 15 working days in September. There are real values and forecasted values of prices and also the sign of the type of calculation according to the head of the snake method in the table 2.

5 Table 2: Real values and forecasts by the mentioned methods Date Real price HW HS F O R E C A S T S HS sign MA ES CF Sep 02, ,19 96,67 96,59 GT 95,39 97,02 96,29 Sep 03, ,86 96,38 96,06 LT 95,73 95,94 95,91 Sep 04, ,36 97,08 96,26 LT 96,50 97,14 96,79 Sep 05, ,78 95,47 95,87 LT 96,14 94,83 95,52 Sep 06, ,83 95,92 95,70 LT 96,00 96,07 95,99 Sep 07, ,34 94,91 95,41 LT 95,32 94,46 94,94 Sep 09, ,31 96,52 95,51 LT 95,65 96,90 96,22 Sep 10, ,25 96,47 95,60 LT 95,83 96,13 95,99 Sep 11, ,88 96,40 95,75 LT 96,30 96,29 96,25 Sep 12, ,96 97,06 96,15 LT 96,48 97,06 96,74 Sep 13, ,14 97,13 98,10 GT 96,70 96,93 96,97 Sep 14, ,99 98,37 98,30 GT 97,33 98,50 98,00 Sep 16, ,30 99,25 98,53 GT 98,03 99,14 98,64 Sep 17, ,30 99,56 98,76 GT 98,81 99,35 99,09 Sep 18, ,78 97,42 98,89 GT 98,53 96,69 97,72 Source: [12], own calculations The forecast accuracy is better visible, when using a kind of indicator of measurement of forecast error [13]. For this reason it is suitable mean absolute percentage error (MAPE) (2) and the results are in the table 3. (2) Table 3: MAPE of each method of forecast MAPE 1 (HW) MAPE 2 (HH) MAPE 3 (MA) MAPE 4 (ES) MAPE (CF) Source: own calculations 0,84% 0,93% 1,13% 0,95% 0,90% In this case, the harmonic weights method and then the combined model has the best result of forecasting. This is daily forecast calculation, that is why MAPE indicators are relatively low, but the target was to show the forecast accuracy. 3.2 Case study 2 Monthly data forecasting This is the case of monthly forecast calculation, i.e. the period of time series is a month and the result is the forecast for the end of next month. The head of a snake method requires an individual approach in this case, because the local trend (LT) is calculated by using daily data, while global trend (GT) is based on monthly data. Historical monthly data reflect monthly changes in the real price of crude oil in US dollars per barrel from 31 st August 2010 till 30 th September Graphical overview of the development of prices each month, GT and LT are shown in Fig. 3.

6 Price in US $ , Jeseník, Czech Republic, EU 140 Crude oil price development Crude oil in USD GT LT 0 Date Figure 3: Diagram of monthly crude oil prices development. Data source: [12] The analysed data from the mentioned interval shows that the maximum dispersion of data is 23,84% from the main trend line (GT) from all values. That is why, compared to the first case, it is used the variant no. 2 for weight configuration for this calculation of combined forecast. Combined forecast and other partial forecasts were calculated for May, June, July, August and September There are real values and forecasted values of prices and also the sign of the type of calculation according to the head of the snake method in the table 4. MAPE indexes are in the table 5. Table 4: Real values and forecasts by the mentioned methods F O R E C A S T S HS Date Real price HW HS sign MA ES CF May 31, ,57 106,07 106,01 LT 104,95 106,00 105,81 Jun 29, ,02 84,44 73,42 LT 98,13 80,74 83,13 Jul 31, ,75 83,41 75,18 LT 92,14 86,30 83,27 Aug 31, ,44 86,97 96,56 LT 86,45 88,18 89,99 Sep 28, ,03 97,19 104,03 LT 89,74 98,92 98,10 Source: [12], own calculations Table 5: MAPE of each method of forecast MAPE 1 (HW) MAPE 2 (HH) MAPE 3 (MA) MAPE 4 (ES) MAPE (CF) 8,65% 12,72% 10,90% 9,93% 8,55% Source: own calculations The MAPE (CF) result proved that the use of combined forecast can play an important role for the various kinds of business forecasts.

7 4. CONCLUSION I would like to highlight the importance of combined forecasting model even in its simple form, as it was presented in chapter 3.1 and 3.2 to the conclusion of this article in this Article. In the first case of the calculation of the daily forecasts the combined forecast did not achieve the best MAPE, because it is mainly due to the very low values of MAPE of separate forecasts and due to very small deviations of values (prices) from two consecutive days. In spite of that the combined forecast can be considered as successful. In the second case, there were higher MAPEs values, the combined forecast has the best (lowest) MAPE indicator. It shows that there is the compensation of error rates from separate forecasts at the large dispersion of values of the time series, which is already considered as dynamic change. ACKNOWLEDGEMENT This paper was created within the VEGA grant project No. 1/0036/12 Methods development and new approaches to design of input, interoperable and output warehouses and their location in mining, metallurgy and building industries. REFERENCES [1] MALINDŽÁK, D. Production Logistics I. Štroffek, Košice, Slovakia, [2] CHRISTOPHER, M. Logistics and Supply Chain Management: creating value-added networks. Pearson Education Limited, Harlow, UK, s.e [3] BOWERSOX, D. J. Logistic Strategic Planning for the 1990s. Concil of Logistics Management Fall 1987 Annual Conference Proceedings, Oak Brook, IL, USA, 1987, vol.1, p [4] WANG, Y., TOMLIN, B. To Wait or Not to Wait: Optimal Ordering Under Lead Time Uncertainty and Forecast Updating. Naval Research Logistics. Hoboken, NJ, USA, vol.: 56 p [5] BINDZÁR, P., MALINDŽÁK, D. Optimalizácia počtu dopravných pásov s ohľadom na ich typ a logistické parametre v ťažobnom podniku. In: Acta Montanistica Slovaca. Roč. 14, č. 4 (2008), s ISSN [6] MALINDŽÁK, D. Jr.: A Mixed Mode Modelling Approach to Using Forecasting and Simulation in the Slovakian Coal Industries.PhD thesis. Technical University of Košice, Košice, Slovak Republic, [7] MAKRIDAKIS, S., WHEELWRIGHT, C.S. Forecasting Methods for Management, New York: Wiley [8] CHAMAN L. J., MALEHORN J. Benchmarking Forecasting Practices: A Guide to Improving Forecasting Performance, Graceway Publishing Company, Inc.,, New York, USA [9] Institute of Business Forecasting & Planning, Discusion forum [10] ARMSTRONG, J.S. Combining forecast. Principles of forecasting: a handbook for researchers and practitioners, Kluwer Academic Publishing, Norwell, MA, USA, 2001, p [11] KAČMÁRY, P., MALINDŽÁK, D., DORČÁK, D. Trade and production forecast in the time of economic crisis. In proceedings from Carpathian Logistics Congress Technical University of Košice, Košice [12] ForexPros Financial Markets Worlwide, [13] ROSOVÁ, A. Sústava ukazovateľov distribučnej logistiky, logistiky dopravy a materiálového toku ako jeden z nástrojov controllingu v logistike podniku.in: Acta Montanistica Slovaca. Roč. 15, mimoriadne č. 1 (2010), s ISSN