Non-parametric tests in AR models with applications to climatic data

Abstract

New non-parametric tests of the order of the autoregression in a time series model were recently developed by Hallin and JurecAE kova . The main tool of these tests is the autoregression rank scores. After a brief description of the tests, their performance on simulated AR(1) time series is illustrated with the normal, Laplace and Cauchy innovation densities and they are applied to series of daily maximum temperatures recorded in three stations in south Moravia. #

Regression Rank-Scores Tests against Heavy-Tailed Alternatives

“…This in turn implies that the Pitman ef®ciencies of the tests based on RR scores coincide with those of the corresponding rank tests being used under â 0 (or under known â). We believe that the regularity conditions leading to our results could still be weakened; simulation studies (see Hallin et al 1997) show that the tests work well even under densities not covered by our conditions.…”

“…Hallin and Jurec Ïkova  (1996) considered the tests of the linear hypotheses in the autoregressive models, based on autoregression rank scores, and derived their asymptotic properties under the innovation densities with exponentially decreasing tails. The good performance of the tests is illustrated in Hallin et al (1997) on the simulated AR series with the normal, Laplace and Cauchy innovation densities; the tests are then applied to the dataset of daily maximum temperatures, measured in three stations in South Moravia in the period 1961±90. The tests of independence of two time series based on autoregression rank scores, extensions of the Spearman rank correlation and other tests, are constructed in Hallin et al (1999).…”

A Conversation With Marc Hallin

“…This marked the beginning of my long‐standing association with Czech statistics. For example, with Jana Jurečková I worked on regression and autoregression rank scores (Hallin et al , 1997; Hallin & Jurečková, 1999; Hallin et al , 2007), while with Jean‐Marie Dufour, Ivan Mizera (now a Full Professor in Prague after retiring from the University of Alberta) and I developed generalised runs tests for heteroscedastic time series (Dufour et al , 1998). Jana also visited me at ULB for several months on a Francqui Chair.…”

Testing the tail index in autoregressive models

“…The residuals then were modeled as autoregressive series of order p = 1 (see Hallin et al 1997). Table 5 gives results of testing for all three time series for some selected values Table 6 gives the conclusions under a…”