Interval approach of time series forecasting by neural networks for the decision support system

The article is devoted to the new method of preparation of time series data and its prediction made by neural networks. A detailed analysis of the methodology and comparison of the results with ARIMA method carried out. A full table of initial data and forecasting results for the export of goods and services for 2021 accompanies the article.


Introduction
Forecasting of time series of economic data is relevant and important for companies engaged in planning process in the various sectors of the economy.For example: logistics companies that planning optimal routes of cargo and seasonal loading of warehouse space, for industrial companies that are planning the production volume, for companies which entering to the new markets, international markets, that are planning the future sales growth and impact on competitors.
The availability of a fast and correct method of time series forecasting is usually the basis for building a modern, multi-parameter and proactive decision support system.

Method
The main algorithm of the method following:  The data of time series of exports of goods and services from 1960 to 2016 are loaded into the table, for 180 countries (Table 1), source of the data [1];  Data is prepared in a special way for a neural network: it organised in two columns, one input column and one output column.The data taken from the last ten years of the time series, and then it is coped the first five years into the input column, and the next five years into the output column.At the end, we have two columns of 895 rows each of 180 countries, like at the Table 2 [2].4,30E+11 4,10E+11 4,25E+11 4,42E+11 3,77E+11 3,94E+11   Brazil  3,00E+11 2,89E+11 2,88E+11 2,70E+11 2,32E+11 2,24E+11   Central African Republic  2,53E+08 2,53E+08 2,19E+08 2,22E+08 2,00E+08 2 The full table is available here [2]. Next the neural network training is carried out on the data and a model of the system is obtained (Fig. 5) [4];  Then before applying the model we changed the output column to the input, and the output of the model gives us the results of prediction for the next five years;  Next we checking the results and compare it with the well-known ARIMA [3] time series forecasting method (see full data table [2]).

Results
First, we describe the results of neural network training, and then the results of applying the neural network model to the time series data.On the Fig. 3 presented the result of neural network training of the initial data, from the Table 2.In addition, Figure 4 demonstrates the R-value of approximated model, which has a good value (R=0.9774).At this section, examine the results obtained by applying the resulting model to the output data.According to our methodology, we give a column of output data to the model input and get a forecast for five years ahead.
Figures 6 and 7 present the results of the model forecast to 2021 for two segments: for countries with high exports of goods and services, and for countries with low.The full table of the results is available here [2].The comparison of the accuracy of obtained time series forecasting results with the well-known ARIMA method [3] (Fig 8 ) gives a good similarity.

Conclusions
The time series forecasting by neural networks made in this new work has the following advantages: fast speed of creation and training of neural network, a small error of approximation (R-value) and a quick algorithm of obtaining the results from neural networks model.It also gives irrelevantly good results of prediction for different types of time series data: with seasonal component, cyclic component or without.
The comparison of neural networks with the ARIMA method gives a good correlation of both approach.

Fig. 4 .
Fig. 4. R-value of approximated data.The Fig 5 demonstrated the structure of neural network: one input, 10 hidden neurons and one output.

Fig. 6 .
Fig. 6.The result of the forecast of exports of goods and services to 2021, countries with high export, us dollar.

Fig. 7 .
Fig. 7.The result of the forecast of exports of goods and services to 2021, countries with low export, us dollar.

Fig. 9 .
Fig. 9. Forecast of exports of goods and services for low-exporting countries without segmentation.

Fig. 10 .
Fig. 10.Forecast of exports of goods and services for low-exporting countries with segmentation.

Table 1 .
A fragment of the initial data table, exports of goods and services for 180 countries, from 1960 to 2016, us dollar.

Table 2 .
A fragment of a table with two columns for training the neural network, Xinput column and Y-output.