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SUMMARY: Vaidotas CHARACIEJUS\, ULB
DTSTART:20170310
DTEND:20170310
DESCRIPTION:Testing for white noise in functional time series
Abstract:
We propose a new procedure for white noise testing of a functional time series. Our approach is based on an explicit representation of the $L^2$-distance between the spectral density operator and its best ($L^2$)-approximation by a spectral density operator corresponding to a white noise process. The estimation of this distance can be accomplished by sums of periodogram kernels and it is shown that an appropriately standardized version of the estimator is asymptotically normally distributed under the null hypothesis (of functional white noise) and under the alternative. As a consequence we obtain a simple test (using the quantiles of the normal distribution) for the hypothesis of a white noise functional process. In particular the test does neither require the estimation of a long run variance (including a fourth order cumulant) nor resampling procedures to calculate critical values. Moreover\, in contrast to all other methods proposed in the literature our approach also allows to test for "relevant" deviations from white noise and to construct confidence intervals for a measure which measures the discrepancy of the underlying process from a functional white noise process.
LOCATION:ISBA C115 (Seminar Room Bernouilli)\, Voie du Roman Pays 20\, Louvain-la-Neuve 1348\, BE
DTSTAMP:20220523
UID:628bb9f73f37b
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