TESTING FOR WHITE NOISE AGAINST MULTIMODAL SPECTRAL ALTERNATIVES

E. Reschenhofer and I. M. Bomze

Journal of Time Series Analysis, 1992, vol. 13, issue 5, 435-439

Abstract: Abstract. The test for white noise proposed by Reschenhofer (Biometrika 76 (1989) 629–32) is adaptive in that the form of its test statistic depends on the data. It proceeds (i) by using the real part of the finite Fourier transform of the data for the selection of the form of the test statistic and (ii) by applying the selected test statistic to the imaginary part. In this paper it is shown that independently of using information contained in the real part to construct a test statistic for the imaginary part, information contained in the imaginary part can be used to construct a test statistic for the real part. Because of the independence of these tests, they can easily be combined. Then a further test is proposed which again is adaptive but where both the real and imaginary parts contribute simultaneously to a single test statistic.

Date: 1992
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