| DATE: | Friday, November 10, 2006 |
| TIME: | 4:40-5:40 PM |
| PLACE: | LN 2205 |
| SPEAKER: | Hongwen Guo, Michigan State University |
| TITLE: | Regression model fitting with long memory |
In a simple linear regression model, when observations are disturbed by long range dependent heteroscedastic noise, the classical results fail to work. It is observed that in some cases the first order asymptotic distribution of the least squares estimator of the slope parameter is degenerate. In these cases, under some mild conditions, it is shown that the consistency rates of estimators depend on the dependent index h, H - the long memory parameters of regressor and error processes, respectively. Asymptotic distributions of the estimators are discussed in the model. In addition, in order to implement our results, an estimator of H based on pseudo residuals is shown to be log(n)-consistent. We also proposed a lack-of-fit test of a parametric regression model using a marked empirical process. The proposed lack-of-fit test is applied to fit a simple linear regression model to some currency exchange rate data sets that exhibit long memory. This is joint work with Prof. Hira Koul.