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On October 5, 2021, a business meeting was held between representatives of the EPAM Systems IT Company Denis Grinev and Sergey Garashchuk with the Rector of the State University “Odessa Polytechnic” Gennadii Alexandrovich Oborskiy.
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THE APPLICATION OF CORRELATION FUNCTION IN FORECASTING STOCHASTIC PROCESSES
One of the most important applications of the correlation function is establishing a prediction model for stochastic process. Stationary property makes predicting the stochastic process entirely possible based on the correlation function. This predictive model is interested in cases, where the observation data are assumed to have no measurement errors. We provided some processing to make the forecasting model usable. It is proposed to calculate the value of the standardized correlation function in accordance with the actual observed sample and to estimate the necessary values of averaged correlation function that they cannot be calculated from the sample. We replaced the unknown values by their estimates, which we found using one of the predictive tools suitable for the time series. Theoretically, for the stationary stochastic processes, the correlation function and the standardized correlation function depend only on the time distance between two sections, without depending on the specific time value of each section. However, in this application, when we consider an observation process to be a stationary stochastic process, it means that we have approximated this observation process with a stationary stochastic process. Therefore, when calculating for a specific observation sample, the values of the sample correlation function and the sample standardized correlation function between two sections can fluctuate according to time values of each section, although time distance between two sections unchanged. The sample standardized correlation function of a section has been computed as the arithmetic mean of all values of the sample standardized correlation function between two sections. In this article, the prediction model is linear interpolation and extrapolation model and it is obtained by least squares method. The task for application of this model is to give the highest indexes of daily average temperature in July during last three years 2017-2019 in some localities in northern Vietnam using this forecasting model. The data has been compiled from the data source of the General Department of Meteorology and Hydrology of Vietnam. For processes occurring in the atmosphere and hydrosphere, their hypothesis of stationarity is relatively well satisfied in a time and distance that is not very large. Because of that, we selected the aforementioned data set to apply to the forecasting model. The calculation results are obtained by Matlab software.
Tran Kim Thanh
, Dr. of Philosophy
( email@example.com )
Tran The Vinh
, Doctor of Philosophy
( firstname.lastname@example.org )
stationary stochastic process; correlation function; forecasting model; temperature
Kannan D., & Lakshmikantham V. (2001). “Handbook of stochastic analysis and application”.
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Reference – 808 Pages. ISBN 9780824706609 - CAT# DK1885.
Gusti Ngurah Agung. (2018). “Advanced Time Series Data Analysis”.
, (December 2018). ISBN: 9781119504733.
Peter Michael Inness & Steve Dorling. (2012). “Operational Weather Forecasting. Series: Advancing Weather and Climate Science”. Wiley-Blackwell. (November 2012, 2018). ISBN: 9781118447642.
David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm & Kipp Martin. (2013). “Quantitative Methods for Business”.
South-Western; 12th International Edition.
Library of Congress Control Number: 2011936338. Book only ISBN-13: 978-0-8400-6234-5. Book only ISBN-10: 0-8400-6234-6.
Laurence D. Hoffmann & Gerald L. (2012). “Bradley. Applied Calculus for Business, Economics, and the Social and Life Sciences”.
McGraw-Hill Education; 11th edition (January 6, 2012).
ISBN-10: 0073532371. ISBN-13: 978-0073532370.
Kazakevits, D. I. (1971). “Fundamentals of the Random Function Theory and their use in Hydrometeorology”,
In Russian Gidrometeoizdat
. Leningragad: Russian Federation.
Lindgren, Georg. (2006). “Lectures on Stationary Stochastic Processes”. Lund University, Lund, Sweden. DOI: https://doi.org/10.1002/9780470012505.tas030.
Lindgren, Georg Rootzen, Holger & Sandsten, Maria. (2013). “Stationary Stochastic Processes for Scientists and Engineers”.
1st Edition.Reference, 1060 Pages. ISBN 9781466586185 - CAT# K20279.
Nguyen Duy Tien & Dang Hung Thang. (2005). “Probability Models and Applications. Part II - Stationary Processes and Applications”. Hanoi National University; 2th edition (2005). GT.005745. Press.Reference – 126 Pages (in Vietnamese).
Ross, S. M. (2009). “Introduction to Probability Models”.
; 10th edition. (Published December 17, 2009). Reference – 808 Pages. ISBN-10: 0123756863. ISBN-13: 978-0123756862.
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Geostatistics with Applications in Earth Sciences
, pp 62-77.
Dordrecht. Print ISBN978-1-4020-9379-1. Online ISBN978-1-4020-938. DOI https://doi.org/10.1007/978-1-4020-9380-7_4.
Long Teng Matthias Ehrhardt & Michael Günther. (2016).“Modelling Stochastic Correlation”.
Journal of Mathematics in Industry
, Volume 6, Article number: 2. DOI https://doi.org/10.1186/s13362-016-0018-4.
Teng, L, Van Emmerich C, Ehrhardt M. & Günther, M. A. (2016). “Versatile Approach for Stochastic Correlation using Hyperbolic Functions”. Int J. Comput Math. 2016; 93(3):524-39. DOI: https://doi.org/10.1080/00207160.2014.1002779.
Van Emmerich C. (June 2006). “Modeling Correlation as a Stochastic Process”. Preprint 06/03, University of Wuppertal. [Electronic resource]. Access mode:
. – Active Link –(June 2006).
Dang Hung Thang. (2009). “Stochastic Process and Stochastic Calculus”. Lesson of Hanoi National University (Vietnam). [Electronic resource] Access mode:
– Active Link 2009 (in Vietnamese)
General Department of Meteorology and Hydrology of Vietnam. (2019). “Average Daily Temperature in the years from 2008 to 2017 at the Measurement Stations of the Northern Region Vietnam: Bac Ninh, Cao Bang, Cua Ong, Ha Dong, Hai Duong, Lao Cai, Lang Son, Luc Ngan, Mong Cai, Van Ly, Vinh Yen”.In statistical data of General Department of Meteorology and Hydrology of Vietnam. Hanoi, Vietnam.
Vol. 2 № 4, 2019
24 Oct 2021
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