Testing proportionality for autoregressive processes
In this paper, we introduce a new hypothesis test to determine wether or not two autoregressive spectral densities are proportional. A test for autoregressive coefficient nullity or randomness is deduced. We also derive the exact asymptotic behavior for these tests under parametric alternatives and show that, given a significance level, our tests are the most powerful (MP) tests among all tests.
proportionality autoregressive process spectral density randomness distribution homogeneity test power of a test