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Semiparametric robust tests on seasonal or cyclical long memory time series. (English. English summary) Zbl 1023.62093

Let \(f\) be the spectral density of a time series and let at some frequencies \(\omega_i\in[0,\pi]\), \(i=1,\dots,H\), \(f(\omega_i\pm\lambda)\sim C\lambda^{-2d_i^{\pm}}\) as \(\lambda\to 0\). The author considers a hypothesis of the form \(H_0\): \(d_1^{+}=d_1^{-}=\dots=d_H^{-}\) or \(H_0\): \(d_i^{pm}=c_i^{\pm}\), \(i=1,\dots, d\), for some fixed \(c_i^{\pm}\). Lagrange multiplier (LM) tests are constructed for these hypotheses basing on the Whittle quasi-likelihood function. It is shown that the LM statistic is asymptotically \(\chi^2\) distributed. The test power is investigated under local alternatives. The performance of the test is compared with that of the Robinson test for some parametric models. The author’s conclusion is that the Robinson test performance is significantly worse. Results of simulations and an empirical application to a UK inflation series are presented.
Reviewer: R.E.Maiboroda

MSC:

62M15 Inference from stochastic processes and spectral analysis
62H15 Hypothesis testing in multivariate analysis
91B84 Economic time series analysis
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