Model selection for stock prices data

The geometric Brownian motion (GBM) is very popular in modeling the dynamics of stock prices. However, the constant volatility assumption is questionable and many models with nonconstant volatility have been developed. In the papers [7 M.L. Esquível and P.P. Mota, On some auto-induced regime switching double-threshold glued diffusions, J. Stat. Theory Pract. 8 (2014), pp. 760–771. doi: 10.1080/15598608.2013.854184.[Taylor &; Francis Online] , [Google Scholar],12 P. P. Mota and M.L. Esquível, On a continuous time stock price model with regime switching, delay, and threshold, Quant. Financ. 14 (2014), pp. 1479–1488. doi: 10.1080/14697688.2013.879990.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]] the authors introduce a regime switching process where in each regime the process is driven by GBM and the change in regime is defined by the crossing of a threshold. In this paper we used Akaike's and Bayesian information criteria to show that the GBM with regimes provides a better fit than the GBM. We also perform a forecasting comparison of the models for two selected companies.