NON‐PARAMETRIC APPROACH IN TIME SERIES ANALYSIS

Abstract. Suppose that {X_t} is a Gaussian stationary process with spectral density f(Λ). In this paper we consider the testing problem , where K(Λ) is an appropriate function and c is a given constant. This test setting is unexpectedly wide and can be applied to many problems in time series. For this problem we propose a test based on K{f_n(Λ)}dΛ where f_n(Λ) is a non‐parametric spectral estimator of f(Λ), and we evaluate the asymptotic power under a sequence of non‐parametric contiguous alternatives. We compare the asymptotic power of our test with the other and show some good properties of our test. It is also shown that our testing problem can be applied to testing for independence. Finally some numerical studies are given for a sequence of exponential spectral alternatives. They confirm the theoretical results and the goodness of our test.