In this article we extend the martingale difference test of Kuan and Lee (2004) to tests of conditional moment restrictions involving unknown parameters. The proposed test is asymptotically pivotal, easy to implement and capable of diagnostic checking misspecifications of quantile regressions....

The response surfaces of MOSUM critical values are computed, from which the finite sample and asymptotic critical values for different moving window bandwidths can easily be calculated. Results also show that the finite-sample critical values originally suggested by Bauer and Hackl and the...