The function restoration method by integrals for analysis  and forecasting of rare events in the economy

The article discusses a rare events analysis method, which is based on the study of the processes that generate these events. In the economy the most common process of event formation is the process of consumption or the disturbance accumulation, which can be modeled as a process of emptying or filling a capacity. The consumption process parameter will be the unsteady capacity emptying / filling rate function, which can be recovered from the available data. After restoring this function, you can analyze it, build a model and extrapolate it, then get a forecast of future events by starting again the process of event formation. I call this rare events research method the capacity method. To restore the emptying / filling rate function, an optimization problem has been solved, which is represented in the form of finding a special smoothing integrating cubic spline. Formulas are obtained in matrix form for the restoration (regression) of the desired function. Since the intervals between events can be different, it is necessary to proceed to basic splines (<em >B-splines), which do not depend on the initial data. Formulas in matrix form for constructing the corresponding <em >B-spline are obtained. Details are given of how to fill all the matrices. A mathematical method example of restoring a function from rare events and example of a future events forecast obtaining are given.

Keywords

rare events; sparse events; capacity method; consumption rate; recovery; regression; spline; B-spline; integrating spline; integro-differential spline; nonlinearity penalty.

Acknowledgment

This study was supported by the Russian Foundation for Basic Research (project 19-010-00154).

Received

09.07.2020

Publication date

04.09.2020

Number of characters

24571

Cite

GOST	Korablev Y. The function restoration method by integrals for analysis and forecasting of rare events in the economy // Ekonomika i matematicheskie metody – 2020. – V. 56. – Issue 3 C. 113-124 [Electronic resource]. URL: https://emm.jes.su/S042473880010485-2-1 (circulation date: 20.04.2024). DOI: 10.31857/S042473880010485-2
MLA	Korablev, Yuri "The function restoration method by integrals for analysis and forecasting of rare events in the economy." Ekonomika i matematicheskie metody 56.3 (2020):113-124. DOI: 10.31857/S042473880010485-2
APA	Korablev Y. (2020). The function restoration method by integrals for analysis and forecasting of rare events in the economy. Ekonomika i matematicheskie metody 56(3), pp.113-124 DOI: 10.31857/S042473880010485-2

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1. Altman N.S. (1992). An introduction to kernel and nearest-neighbor nonparametric regression. The American Statistician, 46 (3), 175185. DOI:10.1080/00031305.1992.10475879
2. Bartsev S.I., Okhonin V.A. (1986). Adaptive information processing networks. Krasnoyarsk: Institute of Physics, Siberian Branch of the Academy of Sciences of the USSR. Preprint No. 59B (in Russian).
3. Biryukova T.K., Kireev V.I., Gershkovich M.M. (2016). Methods of numerical differentiation and recovery of grid functions by integrals, based on integro-differential splines. Computer mathematics systems and their applications. Materials of the XVII International scientific conference. Issue 17. Smolensk: Izdatel'stvo SmolGU, 106112 (in Russian).
4. Boor C. de (2001). A Practical Guide to Splines. Revised Edition. New-York: Springer.
5. Bowersox D.J., Closs D.J. (2008). Logistical management: The integrated supply chain process. 2th ed. Translated from the English N.N. Baryshnikova, B.S. Pinsker. Moscow: Olimp-Biznes. Originally published by McGraw-Hill Higher Education, 1996 (in Russian).
6. Cover T., Hart P. (1967). Nearest neighbor pattern classification. IEEE Transactions on Information Theory, 13 (1), 2127.
7. Croston J.D. (1972). Forecasting and stock control for intermittent demands. Operational Research Quarterly (19701977), 23 (3), 289303.
8. Dzanagova I.T., Khugaeva L.T. (2015). Method of operator series for constructing extremal models of rare events. Fundamental Research, 11 (6), 10811084 (in Russian).
9. Efron B., Tibshirani R.J. (1993). An introduction of the bootstrap. New York: Chapman & Hall.
10. Fedorova O.P. (2008). One variant of spline approximating a function. Tomsk State University Journal of Mathematics and Mechanics, 2 (3), 6166 (in Russian).
11. Fedorova O.P. (2016). Method of creation of a spline with the integral equal to integral of function of two variables on area of its definition. Science Almanac, 13 (15), 3135 (in Russian).
12. Green P.J., Silverman B.W. (1994). Nonparametric regression and generalized linear models. A roughness penalty approach. New York: Chapman & Hall.
13. Ivanko R.S. (2005). Short-term forecasting of non-stationary demand for wholesale. Abstract of thesis for Cand. Sc. (Economics). Moscow (in Russian).
14. Johnston F.R., Boylan J.E. (1996). Forecasting intermittent demand: A comparative evaluation of Croston's method. Comment. International journal of forecasting, 12 (2), 297298.
15. Kireev V.I, Biryukova T.K. (1998). Polynomial integro-differential one-dimensional and two-dimensional splines. Computational Technologies, 3, 3, 1934 (in Russian).
16. Kireev V.I, Biryukova T.K. (2014). Integro-differential information processing method and its application in numerical analysis. Moscow: IPI RAS (in Russian).
17. Kireev V.I. (1994). Integral method of approximation of functions by algebraic polynomials and biquadratic splines. Vestnik Moskovskogo aviatsionnogo institute, 1, 1, 4858 (in Russian).
18. Korablev Yu.A. (2015a). Capacity method determination consumption rate function. Economics and Management Systems, 15 (1.1), 140150 (in Russian).
19. Korablev Yu.A. (2015b). Argumentation of capacity method demand determination. Statistics and Economics, 5, 96101 (in Russian).
20. Korablev Yu.A. (2017a). Capacity method for analyzing rare sales in Excel. Ekonomika i Upravlenie: Problemy, Resheniya, 6, 3 (66), 224230 (in Russian).
21. Korablev Yu.A. (2017b). The causes analysis and error estimation of the anomalous pictures in the capacity method for the analysis of rare events. Ekonomika i Upravlenie: Problemy, Resheniya, 8 (6), 812 (in Russian).
22. Korablev Yu.A. (2018). The study of the capacitive method accuracy from the position in the chain of distributors. Ekonomika i Upravlenie: Problemy, Resheniya, 7 (5), 106121 (in Russian).
23. Korablev Yu.A. (2019b). Capacity method of analyzing rare events in the trade of various goods. Business. Education. Law. Bulletin of Volgograd Business Institute, 3, 121131. DOI: 10.25683/VOLBI.2019.48.313 (in Russian).
24. Korablev Yu.A. (2019a). Error of the capacity method of rare events analysis, remoteness from the end user. The News of KBSC of RAS, 3 (89), 4877. DOI: 10.35330/1991-6639-2019-3-89-48-77 (in Russian).
25. Lukinsky V., Zamaletdinova D. (2015a). Methods of inventory management: The calculation of inventory indicators for product groups related to rare events (Part I). Logistics, 1 (98), 2833 (in Russian).
26. Lukinsky V., Zamaletdinova D. (2015b). Methods of inventory management: the calculation of inventory indicators for product groups related to rare events (Part II). Logistics, 2 (99), 2427 (in Russian).
27. Quinn B.G., Fernandes J.M. (1991). A fast efficient technique for the estimation of frequency. Biometrika, 78, 3 (Sep.), 489497.
28. Quinn B.G., Hannan E.J. (2001). The estimation and tracking of frequency. Cambridge: Cambridge University Press.
29. Rumelhart D.E., Hinton G.E., Williams R.J. (1986). Learning internal representations by error propagation. In: Parallel distributed processing. 1, 318362. Cambridge: MIT Press.
30. Vozhzhov A.P., Lunyakov Î.V., Vozhzhov S.P. (2015). Safety stock determination with application of the Poisson processes to incoming and outgoing flows. In: Economics and management: Theory and practice, 1 (1), 3035 (in Russian).
31. Walker S.H., Duncan D.B. (1967). Estimation of the probability of an event as a function of several independent variables. Biometrika, 54 (1/2), 167178. DOI: 10.2307/2333860. JSTOR 2333860
32. Wentzel E.S., Ovcharov L.A. (2000). The theory of random processes and its engineering applications. Training manual for technical colleges. 2nd ed. Moscow: Vysshaja Shkola (in Russian).
33. Willemain T.R., Park D.S., Kim Y.B., Shin K.I. (2001). Simulation output analysis using the threshold bootstrap. European journal of operational research, 134 (1), 1728.