Bootstrap-assisted tests of symmetry for dependent data^*

* We are grateful to two referees and an Associate Editor for their constructive comments and suggestions

ABSTRACT

The paper considers the problem of testing for symmetry (about an unknown centre) of the marginal distribution of a strictly stationary and weakly dependent stochastic process. The possibility of using the autoregressive sieve bootstrap and stationary bootstrap procedures to obtain critical values and P-values for symmetry tests is explored. Bootstrap-assisted tests for symmetry are straightforward to implement and require no prior estimation of asymptotic variances. The small-sample properties of a wide variety of tests are investigated using Monte Carlo experiments. A bootstrap-assisted version of the triples test is found to have the best overall performance.

KEYWORDS:

• Autoregressive sieve bootstrap
• stationary bootstrap
• symmetry
• weak dependence

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

* We are grateful to two referees and an Associate Editor for their constructive comments and suggestions