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УДК 519.246.78
СОЗДАНИЕ МАТЕМАТИЧЕСКОЙ МОДЕЛИ ДЛЯ РЕШЕНИЯ ЭКОНОМИЧЕСКИХ ЗАДАЧ, ИСПОЛЬЗУЯ МАТЕМАТИЧЕСКИЙ АППАРАТ НЕЙРОННАЯ СЕТЬ
Т. В. Пен
Научный руководитель - И. А. Панфилов
Сибирский государственный университет науки и технологий имени академика М. Ф. Решетнева
Российская Федерация, 660037, г. Красноярск, просп. им. газ. «Красноярский рабочий», 31
Е-mail: pen_tatiana@mail.ru
В представленной работе рассматривается процесс создания модели прогнозирования экономических показателей при помощи математического аппарата нейронная сеть. При помощи использования модели в будущем появляется возможность произвести прогноз и на основе показателей принимать управленческие решения.
Ключевые слова: прогнозирование, математическая модель, экономические показатели, нейронная сеть.
CREATING A MATHEMATICAL MODEL FOR SOLVING ECONOMIC PROBLEMS
USING A NEURAL NETWORK
T. V. Pen Scientific Supervisor - I. A. Panfilov
Reshetnev Siberian State University of Science and Technology 31, Krasnoyarsky Rabochy Av., Krasnoyarsk, 660037, Russian Federation Е-mail: pen_tatiana@mail.ru
In the present paper, the process of creating a model of forecasting economic indicators using the mathematical apparatus of a neural network is considered. By using the model in the future, it is possible to make a forecast and make management decisions based on indicators.
Keywords: forecasting, mathematical model, economic indicators, neural network.
In the production process consumed various types of resources, whether tangible or intangible. They are necessary for the full functioning of the enterprise. The main capital of the company provides all these factors of production. It is investment in fixed assets that is the driving force in the development of an enterprise. Therefore, their prediction is relevant.
The period covering the time series, from 2001 to 2017 inclusive. Last year will be a test for the model. It is with him that we will compare the results obtained by various methods.
To predict time series, we use a structural model, namely, in the future, the creation of a model will be carried out using the mathematical apparatus of neural networks [1]. To analyze and build the neural network model, we will use the software package for statistical data analysis STATISTICAv.10 [2].
Since 2017 is a verification year, we will compare the values obtained with the actual values of the year [3].
Let us establish the percentage of the control sample, since it was previously stipulated that the last twelve values are verifiable, then we exclude the test sample.
The process of learning a neural network is called setting up the network architecture and weights of synaptic connections for the best solution to the task of forecasting. Neural network training is carried out on a test sample. In the process of learning, the network is adjusted in such a way as to best respond
Актуальные проблемы авиации и космонавтики - 2019. Том 2
to input signals. For the learning process of the neural network, the back propagation method will be used [4]. Training involves two passes through all layers of the network, namely, direct and reverse.
The control sample is used to stop the learning process of the neural network. In other words, when the error in the control sample begins to increase, this is a sign that the model is already being retrained and it is at this point that it is necessary to stop training.
Thus, it is possible to make a forecast for 2017, presented in Figure 1.
Fig. 1. Visual forecast for 2017
The error in the approximation of the constructed model was only 3.4 %, this indicates a qualitative construction of the model, which means that in the future it can be used to predict the economic indicator.
Now we will create a forecast, based on the model obtained, for 2018.
Fig.2. Capital investment ratio forecast
Thus, we can conclude that the neural network solves the task well, the forecast of indicators of "Investment in fixed capital" has reliable indicators, and management decisions can be made on its basis.
Thanks to the constructed mathematical model, using a neural network, we can conclude that the trend is positive, which indicates a stable economic situation in the country for 2018.
Библиографические ссылки
1. Afanasyev V.N., Yuzbashev M.M. Time Series Analysis and Forecasting: Tutorial. - M .: Finance and Statistics, 2001.
2. Software STATISTICAv10.0 [Electronic resource] - 2016. - URL: http://statsoft.ru (appeal date: 03/18/2017).
3. State statistics [Electronic resource] - 2018. - URL: http: // gks.ru/ (appeal date: 10/01/2018)
4. Khaikin S. Neural networks: a full course, 2nd edition; per. from English - M .: Publishing house "Williams", 2006.
© Panfilov I. A., Pen T. V., 2019
