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, B ˜ ( ϑ ) with ϑ ∈ [ 0 , 1 ] . Since in general it is not easy, if at all possible, to find a time deformation g ( ϑ ) such that B ˜ ( g ( ϑ ) ) is a Brownian (bridge) process, tests based on B ˜ ( ϑ ) 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.