Modelling of Indian Stock Prices using Nonhomogeneous Poisson Processes with Time Trends

The financial sector in India has undergone radical reforms, particularly in the stock market segment, since early 1990s. Testing duration in stock markets concerns the ability to predict the turning points of bull and bear cycles. This article study some point process models to fit the data from Indian stock market cycles. We have considered the BSE 30 (SENSEX) data from January, 1991 to August, 2012 for bull and bear markets. The duration dependence of stock market cycles can help to pinpoint the peaks and troughs in these cycles. Upon carrying out various statistical procedures and goodness of fit tests, we found that the Nonhomogeneous Poisson Process models like Power Law Process, Modulated Power Law Process, Log-linear process and other models are some of the possible alternative models to describe the data. We provide estimates, confidence interval estimates and tests of hypothesis for the parameters involved in a particular model.