Premium
Self‐weighted least absolute deviation estimation for infinite variance autoregressive models
Author(s) -
Ling Shiqing
Publication year - 2005
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2005.00507.x
Subject(s) - least absolute deviations , estimator , mathematics , autoregressive model , wald test , bounded function , statistic , statistics , series (stratigraphy) , star model , variance (accounting) , statistical inference , statistical hypothesis testing , time series , autoregressive integrated moving average , mathematical analysis , paleontology , accounting , business , biology
Summary. How to undertake statistical inference for infinite variance autoregressive models has been a long‐standing open problem. To solve this problem, we propose a self‐weighted least absolute deviation estimator and show that this estimator is asymptotically normal if the density of errors and its derivative are uniformly bounded. Furthermore, a Wald test statistic is developed for the linear restriction on the parameters, and it is shown to have non‐trivial local power. Simulation experiments are carried out to assess the performance of the theory and method in finite samples and a real data example is given. The results are entirely different from other published results and should provide new insights for future research on heavy‐tailed time series.