Bootstrap specification tests for linear covariance stationary processes

This paper discusses goodness-of-fit tests for linear covariance stationary processes based on the empirical spectral distribution function. We can show that the limiting distribution of the tests are functionals of a Gaussian process, say, with [0,1]. Since in general it is not easy, if at all possible, to find a time deformation g() such that is a Brownian (bridge) process, tests based on will have limited value for the purpose of statistical inference. To circumvent the problem, we propose to bootstrap the test showing its validity. We also provide a Monte-Carlo experiment to examine the finite sample behaviour of the bootstrap.