Optimal Testing for Semi-Parametric AR Models-From Gaussian Lagrange Multipliers to Autoregression Rank Scores and Adaptive Tests

The autoregressive model has been selected because of its simplicity and pedagogical virtues. We nevertheless believe that several of the procedures described below will be new to many readers~despite the widespread use of AR models in everyday practice. And, the results described here can be expected to hold, with adequate modification, in much more general semiparametric situations: mixed ARMA models, random coefficient AR models, models with ARCH or GARCH innovation processes, nonlinear models, etc.