Exact Tests and Confidence Sets in Linear Regressions with Autocorraled Errors

This Paper Proposes a General Method to Build Exact Tests and Confidence Sets in Linear Regressions with First-Order Autoregressive Gaussian Disturbances. Because of a Nuisance Parameter Problem, We Argue That Generalized Bounds Tests and Conservative Confidence Sets Provide Natural Inference Procedures in Such a Context. Given an Exact Confidence Set for the Autocorrelation Coefficient, We Describe How to Obtain a Simular Simultaneous Confidence Set for the Autocorrelation Coefficient and Any Sub-Vector of Regression Coefficients. Conservative Confidence Sets for the Regression Coefficients Are Then Deduced by a Projection Method. for Any Hypothesis Which Specifies Jointly the Value of the Autocorrelation Coefficient and Any Set of Linear Restrictions on the Regression Coefficients, We Get Exeact Similar Tests. for Testing Bounds-Type Procedures. Exact Confidence Sets for the Autocorrelation Coefficient Are Built by "Inverting" Autocorrelatin Tests. the Method Is Illustrated with a Money Demand Equation.