Saddlepoint approximations to the distribution of the estimator of the parameter in a non-stationary AR(1) model

ABRIL, JUAN CARLOS; ABRIL, MARÍA DE LAS MERCEDES

Londres

Conferencia; 4th International Conference of the ERCIM WG on COMPUTING & STATISTICS (ERCIM’11); 2011

Birkbeck College, University of London

Usually, we approximate the distribution of a statistic whose exact distribution can not be obtained conveniently. When the first moments are known, a usual procedure is to fit a law of a Pearson or Edgeworth type with those moments. Both methods are usually satisfactory in practice, but have the disadvantage that errors in the "tails" of the distribution are often comparable with the frequencies themselves. Edgeworth's approach in particular, can take negative values in these regions. The aim of this paper is an application of the saddlepoint approximations to the non-stationary AR (1) models. In particular, we want to investigate the saddlepoint approximations to the distribution of coefficient estimates in non-stationary AR (1) models.