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СОЗДАНИЕ МАТЕМАТИЧЕСКИХ МОДЕЛЕЙ ПРОГНОЗИРОВАНИЯ ЭКОНОМИЧЕСКИХ ПОКАЗАТЕЛЕЙ
Т. В. Пен, Я. С. Ганжа
Сибирский государственный университет науки и технологий имени академика М. Ф. Решетнева Российская Федерация, 660037, г. Красноярск, просп. им. газеты «Красноярский рабочий», 31
E-mail: pen_tatiana@mail.ru
В представленной работе рассматривается процесс прогнозирования коэффициентов динамики рождаемости организации при помощи математического аппарата нейронных сетей и построения уравнения регрессии, а также сравнение полученных результатов в результате прогноза и выявления наилучшего из методов.
Ключевые слова: прогнозирование временных рядов, нейронные сети, метод обратного распространения ошибки, уравнение регрессии.
CREATION OF MATHEMATICAL MODELS FOR FORECASTING ECONOMIC
INDICATORS
T. V. Pen, Y. S. Ganzha
Reshetnev Siberian State University of Science and Technology 31, Krasnoyarskii rabochii prospekt, Krasnoyarsk, 660037, Russian Federation
E-mail: pen_tatiana@mail.ru
In the article presents the process of forecasting dynamics of organizations using the mathematical apparatus of neural networks and regression equation, then a comparison of the results obtained as a result of the forecast and identify the best method.
Keywords: forecasting of time series, neural net, backpropagation algorithm, regression equation.
The birth rate of organizations is the ratio of the number of registered organizations for the reporting period to the average number of organizations recorded by state statistics bodies according to state registration in the reporting period. Demographics of organizations is an indicator of the business climate in the country. Also, this indicator is directly related to the economic situation in the country, therefore, its forecasting is relevant.
The process of creating a forecast is carried out using the constructed model. The mathematical model seeks to find the dependence of the future value on the past within the process itself and on this dependence to calculate the predicted values for a certain period of time.
Time series models can be classified in two directions: statistical models and structural ones. In statistical models, the dependence of future values on the past is determined in the form of an equation, while in structural models, the dependence of the predicted values on the past is specified in the form of some structure and transition rules for it.
A natural way to handle the resulting dependencies is to build time series.
The determination of the coefficients of the regression equation, which is used to construct the forecast of the time series of statistical models, is carried out using the least squares method. The
Актуальные проблемы авиации и космонавтики - 2020. Том 2
residual functional is constructed and minimized by the parameters of the regression equation to be determined. The latter procedure provides a more accurate forecast [1,2].
The stochasticity of the indicators leads to time sequences for which sharp, spasmodic changes in the estimated values are possible. To increase the accuracy of estimating the coefficients of the regression equation, the smoothing procedure is applied [3].
Due to the obtained values, a forecast is generated for a certain period of time.
To build a structural model of time series, we use the mathematical apparatus: neural networks.
A neural network contains an input layer, hidden layers and an output layer. For time series, a multilayer perceptron is usually used.
Since the variables in question will only take positive values, a differentiable nonlinear logistic function is used as the activation function.
To train the neural network, the backpropagation method is implemented: supplying training data to the network inputs, backpropagation of errors, and correction of weights. This method is one of the most common methods of supervised learning of multilayer neural networks.
The backpropagation rule of the network is based on gradient descent. During the training period, weights are adjusted, which reduces the error.
Completion of training allows optimizing synoptic weighted connections, as well as establishing reliable connections between inputs and outputs. Сравним полученные значения.
Based on the results obtained, we can conclude that the predicted indicators of the neural network have a greater approximation to the initial values of the series than indicators obtained by the regression equation. A neural network provides a more adequate model for describing the economic indicators of a time series, while the regression equation averages the values.
Time Series Results
Based on the graph, we can conclude that the trend is decreasing, but in the future the indicator will stabilize. The approximation error during network training was 9.5%. This indicates that this model is suitable for predicting the birth rate of organizations.
References
1. Afanasyev V.N., Yuzbashev M.M. Time Series Analysis and Forecasting: A Textbook. - M.: Finance and Statistics, 2001.
2. Kremer N.Sh., Prutko B.A. Econometrics / Textbook for high schools. - M.: UNITY-DANA, 2005.
3. Panfilov I.A., Pen T.V. Modeling demand on the labor market in the IT industry / Proceedings of the conference "Russia and Europe: the connection of culture and the economy: Proceedings of the XI International Scientific and Practical Conference" - Part 2. / Otv. Editor Uvarina N.V. Prague, Czech Republic: Publishing House WORLD PRESS s.r.o., 2015. - S.207-209.
© Pen T. V., Ganzha Y. S., 2020
