Identifying the instances of jumps in a discrete time series sample of a jump diffusion model is a challenging task. We have developed a novel statistical technique for jump detection and volatility estimation in a return time series data using a threshold method. Since we derive the threshold and the volatility estimator simultaneously by solving an implicit equation, we obtain unprecedented accuracy across a wide range of parameter values. Using this method, the increments attributed to jumps have been removed from a large collection of historical data of Indian sectorial indices. Subsequently, we test the presence of regime switching dynamics in the volatility coefficient using a new discriminating statistic. The statistic is shown to be sensitive to the transition kernel of the regime switching model. We perform the testing using bootstrap method and find a clear indication of presence of multiple regimes of volatility in the data.
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