Statistics Seminar: Ke Zhu (Harvard) -- A bootstrapped spectral test for adequacy in weak ARMA models

Abstract:

This paper proposes a Cramér–von Mises (CM) test statistic to check
the adequacy of weak ARMA models. Without posing a martingale
difference assumption on the error terms, the asymptotic null
distribution of the CM test is obtained. Moreover, this CM test is
consistent, and has nontrivial power against the local alternative of
order n^{−1/2}. Due to the unknown dependence of error terms and the
estimation effects, a new block-wise random weighting method is
constructed to bootstrap the critical values of the test statistic.
The new method is easy to implement and its validity is justified. The
theory is illustrated by a small simulation study and an application
to S&P 500 stock index.