Event Date
Speaker: Vaidotas Characiejus, Visiting Assistant Professor, Statistics, UC Davis
Title: Testing for periodicities in functional time series
Abstract: We develop a test for periodicities in functional time series when the length of the period is unknown. The observations are assumed to belong to an infinite-dimensional separable Hilbert space and the test is based on the asymptotic distribution of the maximum over all Fourier frequencies of the Hilbert-Schmidt norm of the periodogram operator. We show that under certain assumptions the appropriately standardized maximum of the periodogram belongs to the domain of attraction of the Gumbel distribution. The main ingredient of our proof is a Gaussian approximation developed by Chernozhukov, Chetverikov, and Kato (2017). Our results generalize a result of Davis and Mikosch (1999) to multivariate and functional time series and our results also complement the results of Hörmann, Kokoszka, and Nisol (2018), where the length of the period was assumed to be known. We illustrate the usefulness of our test by examining the air quality data from Graz, Austria and showing that our test is able to reveal a periodic component which is not a priori expected. We also demonstrate the finite sample performance of our test using a small simulation study. The talk is based on the joint work with Clément Cerovecki and Siegfried Hörmann.
Short bio : https://anson.ucdavis.edu/~vaidas/
Seminar Date/Time: Thursday May 28th, 4:10pm
This seminar will be delivered remotely via Zoom. To access the Zoom meeting for this seminar, please contact the instructor Shizhe Chen ([email protected]) or Pete Scully ([email protected]) for the meeting ID and password, stating your affiliation.