A Score Type Test for General Autoregressive Models in Time Series

Original Papers

DOI: 10.1007/s10255-007-0384-1

Cite this article as:
Wu, J. & Zhu, L. Acta Mathematicae Applicatae Sinica, English Series (2007) 23: 439. doi:10.1007/s10255-007-0384-1


This paper is devoted to the goodness-of-fit test for the general autoregressive models in time series. By averaging for the weighted residuals, we construct a score type test which is asymptotically standard chi-squared under the null and has some desirable power properties under the alternatives. Specifically, the test is sensitive to alternatives and can detect the alternatives approaching, along a direction, the null at a rate that is arbitrarily close to n−1/2. Furthermore, when the alternatives are not directional, we construct asymptotically distribution-free maximin tests for a large class of alternatives. The performance of the tests is evaluated through simulation studies.


Autoregressive model goodness-of-fit maximin test model checking score type test time series 

2000 MR Subject Classification

62F05 62H15 

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  1. 1.College of Statistics and MathematicsZhejiang Gongshang UniversityHangzhouChina
  2. 2.Hong Kong Baptist UniversityHong KongChina
  3. 3.East China Normal UniversityShanghaiChina

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