Local power of a Cramér-von Mises type test for parametric autoregressive models of order one

  • Authors:

  • Joseph Ngatchou-Wandji;Níamane Laïb

  • Affiliations:

  • Université de Caen, Campus II Boulevard du Maréchal Juin, B.P. 5186, 14032 Caen, France;Université Paris-VI, L.S.T.A., 4 place Jussieu, 75252 Paris cedex 05, France

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2008

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Abstract

In this paper, we study the local power of a Cramer-von Mises type test for parametric autoregressive models, when the data are stationary and ergodic. Our test is based on the limiting distribution of the cumulative residual process associated to the null model. We prove the contiguity of the null hypothesis H"0 and a sequence of local alternatives that converges to H"0 at rate 1/n from a fixed direction. From this result, the limiting distribution of the test statistic and the power are computed under these local alternatives. Simulation experiments show that the test is powerful against some exponential models.