Project Description
The goal of this project is to develop a new parameter estimation method for time series data based on simulations rather than on the theoretical likelihood function, which is the traditional approach. Maximum likelihood estimation, the favored traditional method, has always been based on formulas that first have to be derived "by hand" by the statistician. But the computational power available nowadays makes this step unnecessary; everything can be done by the computer. The proposed method consists of:
(i) simulating many (thousands) realizations of a time series for a given set of parameters,
(ii) compare them with the actual data using, for example, the mean squared error (MSE) as goodness-of-fit measure, and
(iii) finding the parameters that minimize the MSE using a numerical optimization algorithm.
Every step of this process is based on numerical computations and simulations, not on written-down formulas.
Tasks and Responsibilites
The student will write the simulation programs mentioned above, which, with the supervisor's assistance if necessary, is a manageable task for an undergraduate student who has taken MthStat 564 or a similar course. Then, real-data analyses of some publicly available test-bed data sets will be performed.