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Секция «Математические методы моделирования, управления и анализа данных»
УДК 519.246.78
ПРИМЕНЕНИЯ МАТЕМАТИЧЕСКОЙ МОДЕЛИ ПРОГНОЗИРОВАНИЯ В РАМКАХ РЕШЕНИЯ ЗАДАЧ СТРАТЕГИИ ЦИФРОВОЙ ТРАНСФОРМАЦИИ
И. А. Панфилов, Т.В. Пен
Сибирский государственный университет науки и технологий имени академика М. Ф. Решетнева Российская Федерация, 660037, г. Красноярск, просп. им. газ. «Красноярский рабочий», 31
E-mail pen_tatiana@mail.ru
В представленной работе рассматривается применение математического аппарата нейронные сети и Метод Хольта для прогнозирования временного ряда.
Ключевые слова: статистический анализ, нейронные сети, многослойный персептрон, метод Хольта.
APPLICATIONS OF THE MATHEMATICAL MODEL OF FORECASTING IN THE FRAMEWORK OF SOLVING THE PROBLEMS OF THE DIGITAL
TRANSFORMATION STRATEGY
I.A. Panfilov, T V. Pen
Reshetnev Siberian State University of Science and Technology 31, Krasnoyarskii rabochii prospekt, Krasnoyarsk, 660037, Russian Federation
E-mail pen_tatiana@mail.ru
In the presented work, the application of the mathematical apparatus of neural networks and the Holt Methodfor forecasting a time series is considered.
Keywords: statistical analysis, neural networks, multilayer perceptron, Holt method.
As part of the digital transformation strategy, a regional strategy for the digital transformation of key sectors of the economy, social sphere, and public administration for the period 2022-2024 in the Krasnoyarsk Territory was approved [1, 2].
During the implementation of the digital transformation strategy, the following technologies are expected to be introduced: methods for processing large amounts of data, artificial intelligence technologies, platform solutions, the Internet of things and the industrial Internet.
Based on the results of the implementation of the strategy in the field of digital transformation of the sectors of the economy, social sphere and public administration of the Krasnoyarsk Territory, the process of making managerial decisions will be improved based on data analysis and time series forecasting.
Forecasting time series is an indispensable condition for effective planning of the entire region, as based on the forecast, the rationale for the management decisions taken is carried out. Such planning, based on predicted values, can be called a strategic analysis of the edge. The main objective of such a strategic analysis is to organize the uniform work of all production and trade divisions of the Krasnoyarsk Territory [3].
Qualitative analysis of time series is always a topical issue, because mathematical modeling systems do not stand still, every year they expand and become more complex, and most often assumptions about development that are not supported by statistical or econometric analysis may turn out to be erroneous.
Актуальные проблемы авиации и космонавтики - 2022. Том 2
Consider a time series forecast model based on statistical data on the birth rate index of organizations. The birth rate of organizations is the ratio of the number of registered organizations for the reporting period to the average number of organizations registered by state statistics bodies according to state registration data in the reporting period. The demographics of organizations is an indicator of the business climate in a country. Also, this indicator is directly related to the economic situation in the country, therefore, its forecasting is relevant.
Let's make two mathematical models of time series forecasting. The first model will be calculated using the mathematical apparatus of the neural network. The second - according to the method of Holt Winters [4, 5].
The neural network contains an input layer, hidden layers and an output layer. For time series, a multilayer perceptron is usually used.
To train the neural network, the backpropagation method is implemented: feeding the training data to the network inputs, backpropagating the error, and adjusting the weights. This method is one of the most common methods of supervised learning of multilayer neural networks.
The backpropagation network learning rule is based on gradient descent. During the training period, the weights are adjusted to reduce the error.Завершение обучения позволяет оптимизировать синоптические взвешенные соединения, а также установить надежные связи между входами и выходами.
The Holt Winters method is used to predict time series when there is an established trend and seasonality in the data structure [6].
The Holt Winters model is one of the forecasting methods using the so-called exponential smoothing. Smoothing consists in creating a weighted moving average, the weight of which is determined according to the scheme - the older the information about the phenomenon under study, the lower the value for the current forecast.
To compare the two forecasting methods, we will use the statistics of the organization's birth rate from January 2000 to December 2020, 2021 will be a test year [7].
Table 1
Received values
Forecasted values Original series Holt method NN
January 8,2 9,30 7,03
February 8,3 8,86 7,7
March 10,2 6,26 8,58
April 11,4 6,46 8,88
May 8 6,63 8,81
June 8,8 6,28 8,39
July 8,7 6,49 9,01
August 7,8 6,32 8,64
September 8,1 4,92 8,96
October 9,3 4,39 9,22
November 8,2 9,30 9,17
December 9 8,86 8,6
Prediction Error 0,30 0,02
Based on the obtained results, it can be concluded that the predicted indicators of the neural network have a greater approximation to the initial values of the series than the indicators obtained using the Holt Winters method. The neural network provides a more adequate model for describing the economic indicators of the time series, which means it can be used to further predict the birth rate of organizations in the Krasnoyarsk Territory.
Let's apply a mathematical model to predict a time series several steps ahead.
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The graph shows that the trend is positive and the growth in the number of new organizations in the future will be stable.
References
1. State statistics [Electronic resource] - 2021. - URL: http: // gks.ru/ (accessed date: 03/01/2022)
2. Panfilov I.A., Pen T.V. Solution of forecasting problems using neural networks for regional operational control centers - Scientific. Conf "Actual Problems of Aviation and Cosmonautics 2021", p. 176-178.
3. Pen T.V., Panfilov I.A. Analysis and processing of economic statistical indicators using neural networks - Scientific. Conf "Economics and management of the national economy: genesis, current state and prospects of development 2018", p. 266-269.
4. Khaikin S. Neural networks: full course, 2nd edition; trans. from English - M.: Publishing Williams House, 2006.
5. Kremer N.Sh., Prutko B.A. Econometrics / Textbook for high schools. - M.: UNITY-DANA, 2005.
6. Redko, V.G. Evolution, Neural Networks, Intelligence: Models and Concepts evolutionary cybernetics / V.G. Redko. - M.: Lenand, 2015.
7. Shiryaev, V.I. Financial Markets: Neural Networks, Chaos and Nonlinear dynamics / V.I. Shiryaev. - M.: KD Librocom, 2016.
© Panfilov I.A., Pen T.V., 2022
