Simulation of non-stationary event flow with a nested stationary component

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Abstract

A method for constructing an ensemble of time series trajectories with a nonstationary flow of events and a non-stationary empirical distribution of the values of the observed random variable is described. We consider a special model that is similar in properties to some real processes, such as changes in the price of a financial instrument on the exchange. It is assumed that a random process is represented as an attachment of two processes - stationary and non-stationary. That is, the length of a series of elements in the sequence of the most likely event (the most likely price change in the sequence of transactions) forms a non-stationary time series, and the length of a series of other events is a stationary random process. It is considered that the flow of events is non-stationary Poisson process. A software package that solves the problem of modeling an ensemble of trajectories of an observed random variable is described. Both the values of a random variable and the time of occurrence of the event are modeled. An example of practical application of the model is given.

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About the authors

Ruslan V. Pleshakov

Keldysh Institute of Applied Mathematics

Author for correspondence.
Email: ruslanplkv@gmail.com

PhD student

4, Miusskaya Sq., Moscow, 125047, Russian Federation

References

  1. A. D. Bosov and Y. N. Orlov, “Kinetic and hydrodynamic approach to the non-stationary time series forecasting on the base of Fokker-Planck equation [Kinetiko-gidrodinamicheskiy podkhod k prognozirovaniyu nestatsionarnykh vremennykh ryadov na osnove uravneniya FokkeraPlanka],” in Proceedings of MIPT [Trudy MFTI], 4. 2012, vol. 4, pp. 134- 140, in Russian.
  2. Y. N. Orlov and S. L. Fedorov, “Modeling and statistical analysis of functionals set on samples from a non-stationary time series,” in Preprints of IPM im. M. V. Keldysh, 43. 2014, in Russian.
  3. Y. N. Orlov, Kinetic methods for studying non-stationary time seriesy [Kineticheskiye metody issledovaniya nestatsionarnykh vremennykh ryadov]. Moscow: MIPT, 2014, in Russian.
  4. Y. N. Orlov and S. L. Fedorov, Methods of numerical modeling of nonstationary random walk processes [Metody chislennogo modelirovaniya protsessov nestatsionarnogo sluchaynogo bluzhdaniya]. Moscow: MIPT, 2016, in Russian.
  5. Y. N. Orlov and K. P. Osminin, “Sample distribution function construction for non-stationary time-series forecasting [Postroyeniye vyborochnoy funktsii raspredeleniya dlya prognozirovaniya nestatsionarnogo vremennogo ryada],” Mathematical modeling, no. 9, pp. 23-33, 2008, in Russian.
  6. D. S. Kirillov, O. V. Korob, N. A. Mitin, Y. N. Orlov, and R. V. Pleshakov, “On the stationary distributions of the Hurst indicator for the non-stationary marked time series [Raspredeleniya pokazatelya Hurst nestatsionarnogo markirovannogo vremennogo ryada],” in Preprints of IPM im. M. V. Keldysh, 11. 2013, in Russian.
  7. M. H. Numan Elsheikh, D. O. Ogun, Y. N. Orlov, R. V. Pleshakov, and V. Z. Sakbaev, “Averaging of random semigroups and quantization [Usredneniye sluchaynykh polugrupp i neodnoznachnost’ kvantovaniya gamil’tonovykh sistem],” in Preprints of IPM im. M. V. Keldysh, 19. 2014, in Russian.
  8. E. Bacry, S. Delattre, M. Hoffmann, and J. F. Muzy, “Modeling microstructure noise with mutually exciting point processes,” Quantitative Finance, vol. 13, no. 1, pp. 65-77, 2013.
  9. G. Bhardwaj and N. R. Swanson, “An empirical investigation of the usefulness of ARFIMA models for predicting macroeconomic and financial time series,” Journal of Econometrics, vol. 131, pp. 539-578, 2006. doi: 10.1016/j.jeconom.2005.01.016.
  10. P. Embrechts, T. Liniger, and L. Lin, “Multivariate Hawkes Processes: an Application to Financial Data,” Journal of Applied Probability, vol. 48A, pp. 367-378, 2011. doi: 10.1239/jap/1318940477.
  11. N. S. Kremer and B. A. Putko, Econometrica [Ekonometrika]. Moscow: UNITY-DANA, 2005, in Russian.
  12. D. E. Bestens, V. M. van der Berth, and D. Wood, Neural networks and financial markets: decision-making in trading operations [Neyronnyye seti i finansovyye rynki: prinyatiye resheniy v torgovykh operatsiyakh]. Moscow: TVP, 1998, in Russian.
  13. A. Zeifman, A. Korotysheva, K. Kiseleva, V. Korolev, and S. Shorgin, “On the bounds of the rate of convergence and stability for some queueing models [Ob otsenkakh skorosti skhodimosti i ustoychivosti dlya nekotorykh modeley massovogo obsluzhivaniya],” Informatics and Applications, vol. 8, no. 3, pp. 19-27, 2014, in Russian. DOI: 10.14357/ 19922264140303.
  14. V. I. Khimenko, “Scatterplots in Analysis of Random Streams of Events [Diagrammy rasseyaniya v analize sluchaynykh potokov sobytiy],” Informatsionno-upravlyayushchiye sistemy, no. 4, pp. 85-93, 2016, in Russian. doi: 10.15217/issn1684-8853.2016.4.85.
  15. M. V. Zhitlukhin, A. A. Muravlyov, and A. N. Shiryaev, “On confidence intervals for Brownian motion changepoint times,” Russian Mathematical Surveys, vol. 71, no. 1, pp. 159-160, 2016. doi: 10.1070/RM9702.
  16. R. V. Pleshakov, “NSTS Software package for modeling non-stationary non-equidistant time series,” 2018.

Copyright (c) 2020 Pleshakov R.V.

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