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Parameter estimation in stochastic volatility models with missing data using particle methods and the em algorithm

The main concern of financial time series analysis is how to forecast future values of financial variables, based on all available information. One of the special features of financial variables; such as stock prices and exchange rates, is that they show changes in volatility, or variance, over time. Several statistical models have been suggested to explain volatility in data, and among them Stochastic Volatility models or SV models have been commonly and successfully used. Another feature of financial variables I want to consider is the existence of several missing data. For example, there is no stock price data available for regular holidays, such as Christmas, Thanksgiving, and so on. Furthermore, even though the chance is small, stretches of data may not available for many reasons. I believe that if this feature is brought into the model, it will produce more precise results. 
The goal of my research is to develop a new technique for estimating parameters of SV models when some parts of data are missing. By estimating parameters, the dynamics of the process can be fully specified, and future values can be estimated from them. SV models have become increasingly popular in recent years, and their popularity has resulted in several different approaches proposed regarding the problem of estimating the parameters of the SV models. However, as of yet there is no consensus on this problem. In addition there has been no serious consideration of the missing data problem. A new statistical approach based on the EM algorithm and particle filters is presented. Moreover, I expand the scope of application of SV models by introducing a slight modification of the models.