A novel stochastic ProFiVaS model based on decomposition of stochastic Vasicek differential equation for modeling and simulating of financial indicators - Karadede, Yusuf (Expert systems with applications, 2024)
[Display omitted] The main purpose of this study is to develop a new discrete time stochastic ProFiVaS model based on decomposition of stochastic Vasicek differential equation which follows bouncing autoregressive AR1, with fixed variance and trend for modeling and simulating of international financial time series forecasting. This study offers the four discrete time stochastic models. The first model is determined as autoregressive integrated moving average-Arima1,1,1, and the parameter estimates of this model are found using the maximum likelihood method (MLM). Monte Carlo simulation is applied to the obtained parameters. This model is named MoCArima for short. Second, the MoCArima model whose parameters are estimated with particle swarm optimization (PSO) is determined as Proposed Monte Carlo (MC) Arima1,1,1, and is briefly named as ProMoCArima. The third model is determined as Fixed Variance Stochastic Model which has a bouncing autoregressive AR1 structure with constant variance and trend component. This model is briefly named as FiVaS. The parameter estimates are found using the MLM. The fourth model is determined as the Proposed Fixed Variance Stochastic Model. This model is briefly named as ProFiVaS. Structurally the same as the third model. The parameter estimates of both trend and stochastic parts of the FiVaS model are found by the PSO. Proposed models are applied to forecasting international different financial indicators to show its superiority and applicability. The performance and usage efficiency of the proposed four stochastic models are examined on a total of six different international financial data types, five of which are stock index data BIST100 (Türkiye), S&P500 (USA), DAX (Germany), FTSE100 (UK), NIKKEI225 (Japan), and one of which is the exchange rate EURO/USD. The ProFiVaS among all models provides the best performance on the all indices. The ProFiVaS can easily be extended to any real-world time series prediction requirements. The proposed models can be extended to all stationary and non-stationary linear or nonlinear autoregression models opening the door to modeling data types obtained from different sector fields. A part of the future plan of this work is to design a decision support system software that assigns a value of 1 when an investor needs to invest in a financial indicator, and 0 otherwise.