Methodology of Modeling and Forecasting Nonlinear Processes in Finances

Petro I. Bidyuk, Scott Overmyer, Tatyana I. Prosyankina-Zharova, Oleksandr M. Terentiev


Background. Most of the models of financial and economic processes are characterized by considerable com­pu­ta­tio­nal complexity, and construction of predictions of acceptable quality for the required time horizon – by considerable efforts. Therefore, the development and implementation of effective tools for forecasting the modeling of fi­nancial and economic processes are one of the actual and practically meaningful tasks. The paper deals with the modeling and forecasting of nonlinear nonstationary processes in macroeconomics and finance using a methodology based on the principles of system analysis such as hierarchical modeling, consideration of the influence of uncertainties, opti­mi­za­tion of the characteristics of models using complex criteria, structural and parametric adaptation. The application of the pro­posed methodology will improve the quality of forecasting by studying the features of the analyzed process and adapting models to new data, etc.

Objective. The purpose of this article is to develop a methodology for predictive modeling of nonstationary processes in finance and macroeconomics using statistical data, as well as its implementation in the corresponding computer system.

Methods. The methodology is based on the technologies of preliminary processing of statistical data intended to eli­mi­nate possible uncertainties, the use of correlation analysis to evaluate structure of the model and choice of me­thods for estimating its parameters, calculating forecast estimates and generating alternative solutions. This allows us to objec­tively evaluate the results obtained at each stage of solving the problem of modeling nonlinear nonstationary processes in macroeconomics and finance. The paper proposes an original methodology for determining the structure of the model and its implementation in the information system for decision support.

Results. Appropriate models were built for the selected financial and macroeconomic processes. High quality of the final result of data analysis and forecasting is achieved due to implementation of evaluation of the results obtained using statistical quality criteria at each stage of data processing, modeling and forecasting, and also due to the possibility of adapting models to new data through analysis of statistical characteristics of the processes under study and application of combined criteria for the adequacy of models and quality of estimates of forecasts, and the convenient presentation of intermediate and final results.

Conclusions. The proposed methodology is used for forecasting modeling of some macroeconomic and financial pro­cesses in Ukraine. The obtained results show that it can be successfully used to solve practical problems of con­struc­ting models and prediction of nonlinear nonstationary processes under conditions of uncertainties of various types, which, as a rule, have to be considered during modeling and forecasting on the basis of statistical data.


nonlinear nonstationary process; uncertainties; mathematical modelling; forecasting; macroeconomic and financial processes

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O.M. Тrofymchuk et al., “Probabilistic and statistical uncertainty decision support systems”, Visnyk Natsional’noho Universytetu “L’vivs’ka politekhnika”. Ser. Komp’yuterni Nauky ta Informatsiyni Tekhnolohiyi, no. 826, pp. 237–248, 2015 (in Ukrainian).

F.X. Diebold. Elements of Forecasting. Ohio: Thomson South-Western, 2007.

Econometrics Theory and Practice: Frontiers of Analysis and Applied Research, D. Corbae et al., eds. Cambridge, UK: Cambridge University Press, 2010.

R.S. Tsay, Analysis of Financial Time Series. Hoboken: John Wiley & Sons, Inc., 2010.

S.O. Dovhii et al., Decision Support Systems Based on Statistical Probabilistic Methods. Kyiv, Ukraine: Logos, 2014 (in Ukrainian).

J. Pearl. Causality: Models, Reasoning, and Inference. Cambridge, UK: Cambridge University Press, 2009.

Bayesian Networks: A Practical Guide to Applications, O. Pourret et al., eds., Chichester, UK: John Wiley & Sons Ltd, 2008.

Optimization, Simulation and Control, A. Chinchuluun et al., eds. New York: Springer-Verlag New York, 2013. doi: 10.1007/978-1-4614-5131-0

R. Baldick, Applied Optimization: Formulation and Algorithms for Engineering Systems. Cambridge, UK: Cambridge University Press, 2006. doi: 10.1017/CBO9780511610868

J.B. Ramsey, “Tests for specification errors in classical linear least squares regression analysis”, J. Royal Statistical Soc. B, vol. 31, pp. 350–371, 1969.

Т. Teräsvirta et al., “Aspects of modeling nonlinear time series”, Handbook of Econometrics, vol. 4, pp. 2919–2957, 1994. doi: 10.1016/S1573-4412(05)80017-0

R.S. Tsay, “Nonlinearity tests for time series”, Biometrika, vol. 73, pp. 461–466, 1986. doi: 10.1093/biomet/73.2.461

D. Tjøstheim, “Some doubly stochastic time series models”, J. Time Series Analysis, vol. 1, no. 7, pp. 51–72, 1986. doi: 10.1111/j.1467-9892.1986.tb00485.x

D. Tjøstheim, “Nonlinear time series: a selective review”, Scandinavian J. Statistics, vol. 2, no. 21, pp. 97–130, 1994.

B.K. Stensholt and D.Tjøstheim, “Multiple bilinear time series models”, J. Time Series Analysis, vol. 2, no. 8, pp. 221–233, 1987. doi: 10.1111/j.1467-9892.1987.tb00434.x

R.S. Tsay, “Testing and modeling threshold autoregressive processes”, J. Am. Statistical Association, vol. 84, no. 405, pp. 231–240. 1989. doi: 10.1080/01621459.1989.10478760

Jr.W.N. Anderson et al., “Consistent estimates of the parameters of a linear system”, Annals Math. Stat., vol. 40, no. 6, pp. 2064–2075, 1969. doi: 10.1016/B978-0-12-012711-5.50007-9

Y. Yavin, “A discrete Kalman filter for a class of non-linear stochastic systems”, Int. J. System Sci., vol. 13, no. 11, pp. 1233–1246, 1982. doi: 10.1080/00207728208926425

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