## Bernoulli

• Bernoulli
• Volume 25, Number 4B (2019), 3496-3526.

### Moving block and tapered block bootstrap for functional time series with an application to the $K$-sample mean problem

#### Abstract

We consider infinite-dimensional Hilbert space-valued random variables that are assumed to be temporal dependent in a broad sense. We prove a central limit theorem for the moving block bootstrap and for the tapered block bootstrap, and show that these block bootstrap procedures also provide consistent estimators of the long run covariance operator. Furthermore, we consider block bootstrap-based procedures for fully functional testing of the equality of mean functions between several independent functional time series. We establish validity of the block bootstrap methods in approximating the distribution of the statistic of interest under the null and show consistency of the block bootstrap-based tests under the alternative. The finite sample behaviour of the procedures is investigated by means of simulations. An application to a real-life dataset is also discussed.

#### Article information

Source
Bernoulli, Volume 25, Number 4B (2019), 3496-3526.

Dates
Revised: July 2018
First available in Project Euclid: 25 September 2019

https://projecteuclid.org/euclid.bj/1569398775

Digital Object Identifier
doi:10.3150/18-BEJ1099

Mathematical Reviews number (MathSciNet)
MR4010963

Zentralblatt MATH identifier
07110146

#### Citation

Pilavakis, Dimitrios; Paparoditis, Efstathios; Sapatinas, Theofanis. Moving block and tapered block bootstrap for functional time series with an application to the $K$-sample mean problem. Bernoulli 25 (2019), no. 4B, 3496--3526. doi:10.3150/18-BEJ1099. https://projecteuclid.org/euclid.bj/1569398775

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#### Supplemental materials

• Supplement to “Moving block and tapered block bootstrap for functional time series with an application to the $K$-sample mean problem”. The online supplement [21] contains the proofs of Lemma A.2 and Theorem 2.2 as well as some additional numerical results.