Validation of Stock Price Prediction Models in the Conditions of Financial Crisis

Vesela Mihova (), Ivan Georgiev, Elitsa Raeva, Slavi Georgiev and Velizar Pavlov
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Vesela Mihova: Department of Applied Mathematics and Statistics, University of Ruse, 8 Studentska Str., 7004 Ruse, Bulgaria
Ivan Georgiev: Department of Applied Mathematics and Statistics, University of Ruse, 8 Studentska Str., 7004 Ruse, Bulgaria
Elitsa Raeva: Department of Applied Mathematics and Statistics, University of Ruse, 8 Studentska Str., 7004 Ruse, Bulgaria
Slavi Georgiev: Department of Applied Mathematics and Statistics, University of Ruse, 8 Studentska Str., 7004 Ruse, Bulgaria
Velizar Pavlov: Department of Applied Mathematics and Statistics, University of Ruse, 8 Studentska Str., 7004 Ruse, Bulgaria

Mathematics, 2023, vol. 12, issue 1, 1-18

Abstract: The distribution laws of various natural and anthropogenic processes in the world around us are stochastic in nature. The development of mathematics and, in particular, of stochastic modeling allows us to study regularities in such processes. In practice, stochastic modeling finds a huge number of applications in various fields, including finance and economics. In this work, some particular applications of stochastic processes in finance are examined in the conditions of financial crisis, aiming to provide a solid approach for stock price forecasting. More specifically, autoregressive integrated moving average (ARIMA) models and modified ordinary differential equation (ODE) models, previously developed by some of the authors to predict the asset prices of four Bulgarian companies, are validated against a time period during the crisis. Estimated rates of return are calculated from the models for one period ahead. The errors are estimated and the models are compared. The return values predicted with each of the two approaches are used to derive optimal risk portfolios based on the Markowitz model, which is the second major aim of this study. The third aim is to compare the resulting portfolios in terms of distribution (i.e., weights of the stocks), risk, and rate of return.

Keywords: stochastic processes; time series; ARIMA; ODE; price forecasting (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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