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## Sup-tests for linearity in a general nonlinear AR(1) model

** ** Christian Francq, Lajos Horvath and Jean-Michel Zakoļan
** Keywords: **Diagnostic checking; Exponential autoregressive (EXPAR) model; Lagrange Multiplier (LM) tests; Least Squares Estimator; Likelihood Ratio (LR); Non Linear models; Supremum Tests; Smooth Transition Autoregressive (STAR); Threshold AR (TAR); Wald test

** Abstract: **We consider linearity testing in a general class of nonlinear time
series model of order 1, involving a nonnegative nuisance parameter
which (i) is not identified under the null hypothesis and (ii) gives
the linear model when equal to zero. This paper studies the
asymptotic distribution of the Likelihood Ratio test and
asymptotically equivalent supremum tests. The asymptotic
distribution is described as a functional of chi-square processes
and is obtained without imposing a positive lower bound for the
nuisance parameter.
The finite sample properties of the sup-tests are studied by simulations.

MPRA working paper

R code used to obtain Figure 1