Publication Date

5-2014

Date of Final Oral Examination (Defense)

3-7-2014

Type of Culminating Activity

Thesis

Degree Title

Master of Science in Mathematics

Department

Mathematics

Supervisory Committee Chair

Jaechoul Lee, Ph.D.

Supervisory Committee Member

Leming Qu, Ph.D.

Supervisory Committee Member

Partha Mukherjee, Ph.D.

Abstract

In a complex and dynamic world, the assumption that relationships in a system remain constant is not necessarily a well-founded one. Allowing for time-varying parameters in a regression model has become a popular technique, but the best way to estimate the parameters of the time-varying model is still in discussion. These parameters can be autocorrelated with their past for a long time (long memory), but most of the existing models for parameters are of the short memory type, leaving the error process to account for any long memory behavior in the response variable. As an alternative, we propose a long memory stochastic parameter regression model, using a fractionally integrated (ARFIMA) noise model to take into account long memory autocorrelations in the parameter process. A fortunate consequence of this model is that it deals with heteroscedasticity without the use of transformation techniques. Estimation methods involve a Newton-Raphson procedure based on the Innovations Algorithm and the Kalman Filter, including truncated versions of each to decrease computation time without a noticeable loss of accuracy. Based on simulation results, our methods satisfactorily estimate the model parameters. Our model provides a new way to analyze regressions with a non-stationary long memory response and can be generalized for further application; the estimation methods developed should also prove useful in other situations.

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