Development of multi-forecasting model using Monte Carlo simulation coupled with wavelet denoising-ARIMA model

The analysis and prediction of stock market prices are crucial areas of research due to their complex, chaotic, and nonlinear features. As a result, making significant gains in stock market investments is a crucial task. However, expert and intelligent modeling techniques can help in achieving positive stock market returns. In this study, we use the Monte Carlo (MC) simulation method to generate multiple future values of the time series of closing prices of a particular stock of BSE using a combination of wavelet denoising and the autoregressive integrated moving average (ARIMA) model. The multiple future realizations of stock prices produced by the Monte Carlo (MC) simulation can help minimize risk and uncertainty in stock market investments. Firstly, we use wavelet analysis to detect significant noise levels in the time series at each scale in discrete wavelet decomposition, which is then eliminated by an appropriate wavelet denoising method. Next, the time series of denoised stock prices is fitted with a suitable ARIMA model, and the future values are obtained using this model. The future values of the denoised time series are simulated using MC simulation. The results of the study show that simulated forecasts obtained by MC simulation using the integrated wavelet-denoising-ARIMA model become more accurate with increasing simulation count than by applying a single ARIMA model to noisy stock price series. It has also been observed that MC simulation reduces the standard error of estimates to one half when the number of simulations is quadrupled.