TIME SERIES MODELS WITH NONNORMAL INNOVATIONS: SYMMETRIC LOCATION{SCALE DISTRIBUTIONS Moti L Tiku McMaster University and Wilfrid Laurier University Canada Wing-Keung Wong Department of Economics National University of Singapore and Guorui Bian Department of Statistics & Applied Probability National University of Singapore Abstract. We consider AR(q) models in time series with non-normal innovations represented by a member of a wide family of symmetric distributions (Student's t). We derive the MML (modi¯ed maximum likelihood estimators) of the parameters and show that they are remarkably e±cient. We use these estimators for hypothesis testing and show that the resulting tests are remarkably powerful. We study the robustness of the proposed estimators and tests to deviations from an assumed model. Skew distributions will be considered in part II of this paper. Keywords. Time Series; Student's t; Nonnormality; Robustness; Modi¯ed likelihood; Hypothesis testing; Power function 1