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Актуальные проблемы авиации и космонавтики - 2022. Том 2
УДК 519.246.78
СРАВНЕНИЕ МЕТОДОВ РЕШЕНИЯ ЗАДАЧ ПРОГНОЗИРОВАНИЯ
ВРЕМЕННЫХ РЯДОВ
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 произведено сравнение методов прогнозирования временных рядов.
Ключевые слова: статистический анализ, нейронные сети, многослойный персептрон, линейный тренд, модели тренда.
COMPARISON OF METHODS FOR SOLVING PROBLEMS OF FORECASTING TIME SERIES
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, a comparison of methods for forecasting time series is made.
Keywords: statistical analysis, neural networks, multilayer perceptron, linear trend, trend models.
The task of time series forecasting has been and remains relevant, especially in recent times, when powerful tools for collecting and processing information have become available. Time series forecasting is an important scientific and technical problem, as it allows predicting the behavior of various factors in environmental, economic, social and other systems. In this paper, the problem of forecasting a time series by means of neural networks and using trend models, as well as performing a comparative analysis with the results, is considered.
The purpose of any forecasting is to create a model that allows you to look into the future and evaluate trends in changes in a particular factor. The quality of the forecast in this case depends on the presence of the prehistory of the variable factor, the measurement errors of the quantity under consideration, and other factors [1, 2].
To build a mathematical model, the data were taken from the website of the state statistics of the Krasnoyarsk Territory. The data reflects the dynamics of investments in fixed assets [3].
Investments in fixed assets reflect a set of costs aimed at the creation and reproduction of fixed assets, such as: construction, expansion of facilities, modernization, etc. As well as the acquisition by firms of new productive capital goods [4, 5].
The time series covers the period from 2005 to 2021 inclusive. The last year is a test year for the results of the constructed models. The period between observations is one month. There will be two hundred and four observations in total.
When analyzing the time series, various trend models were built: a linear trend model, an exponential trend model, a logarithmic trend model, and a power trend model.
Секция «Математические методы моделирования, управления и анализа данных»
Table 1
Received va ues
Trend equation R2 Statistical Significance (Student's t-test) Fisher's criterion Approximation error,%
Linear trend 0,96 Not confirmed Statistically significant 29,75%
Exponential trend 0,86 Confirmed Statistically significant 12,1%
Logarithmic trend 0,77 Not confirmed Statistically significant 67,4%
Power trend 0,95 Confirmed Statistically significant 16%
Thus, we can conclude that the exponential trend gives the best performance in forecast modeling.
Of course, the trend cannot fully reflect the behavior of the series, it only averages the predicted values, thereby showing the overall picture of the forecast.
In the next section, the forecasting method using the mathematical apparatus of neural networks will be considered. Such a method, based on the behavior of the series as a whole, will allow you to recreate the time series in such a way that, based on all previous values, build new ones [6].
When building a model using the mathematical apparatus of a neural network, it was found that the approximation error of the constructed model leaves 3.4%, which is significantly superior to using this model to create a forecast than using trend models.
Our next step is to create an ensemble of networks. The ensemble of networks is an averaging of the results obtained when choosing the best networks in terms of performance. This approach allows us to solve two problems at once: the tendency of the underlying neural network architecture to underfit, or the tendency of the underlying architecture to overfit.
The approximation error when using an ensemble of networks was 2.19%, thus it is the best model for making a forecast [7].
Table 2
Comparison of forecasting methods
Name of the forecasting method Approximation error,%
Linear trend 29,75%
Exponential trend 12,1%
Logarithmic trend 67,4%
Power trend 16%
Neural network (multilayer perceptron) 3,47%
Neural network (ensemble of networks) 2,19%
After analyzing the forecasting methods, we can conclude that the neural network gives more accurate results than the trend equation. If the trend equation tends to average the results and show the overall trend of the series, then the neural network tries to predict future values exactly. Therefore, if it is necessary to conduct a deep analysis and forecasting, then neural networks are used. And to identify the trend in general, trend models are suitable.
References
1. State statistics [Electronic resource] - 2021. - URL: http: // gks.ru/ (accessed date: 03/01/2021)
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.
äktva-ibhbie npoo-iembi авнацнн h kocmohabthkh - 2022. tom 2
3. Khaikin S. Neural networks: full course, 2nd edition; trans. from English - M .: Publishing Williams House, 2006.
4. 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.
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
