Structural break analysis for spectrum and trace of covariance operators

Aue, Alexander; Rice, Gregory; Sönmez, Ozan

doi:10.1002/env.2617

Cited by 19 publications

(9 citation statements)

References 31 publications

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“…The following calculation is similar to Lemma A.3 in Aue et al (2018b). Let X(m) i (t, s) = X i,m (t)X i,m (s) − EX 0 (t)X 0 (s),…”

Section: Proof Of Proposition 21mentioning

confidence: 97%

Two-sample tests for relevant differences in the eigenfunctions of covariance operators

Aue¹,

Dette²,

Rice³

2019

Preprint

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This paper deals with two-sample tests for functional time series data, which have become widely available in conjunction with the advent of modern complex observation systems. Here, particular interest is in evaluating whether two sets of functional time series observations share the shape of their primary modes of variation as encoded by the eigenfunctions of the respective covariance operators. To this end, a novel testing approach is introduced that connects with, and extends, existing literature in two main ways. First, tests are set up in the relevant testing framework, where interest is not in testing an exact null hypothesis but rather in detecting deviations deemed sufficiently relevant, with relevance determined by the practitioner and perhaps guided by domain experts. Second, the proposed test statistics rely on a self-normalization principle that helps to avoid the notoriously difficult task of estimating the long-run covariance structure of the underlying functional time series. The main theoretical result of this paper is the derivation of the large-sample behavior of the proposed test statistics. Empirical evidence, indicating that the proposed procedures work well in finite samples and compare favorably with competing methods, is provided through a simulation study, and an application to annual temperature data.

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“…The following calculation is similar to Lemma A.3 in Aue et al (2018b). Let X(m) i (t, s) = X i,m (t)X i,m (s) − EX 0 (t)X 0 (s),…”

Section: Proof Of Proposition 21mentioning

confidence: 97%

Two-sample tests for relevant differences in the eigenfunctions of covariance operators

Aue¹,

Dette²,

Rice³

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…(), among others, whereas Zhang and Shao () and Aue et al . () discussed statistical inference tools for the eigensystem of covariance operators.…”

Section: Inference For Covariance Operatorsmentioning

confidence: 99%

Testing Relevant Hypotheses in Functional Time Series via Self-Normalization

Dette

Kokot

Volgushev

2020

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary We develop methodology for testing relevant hypotheses about functional time series in a tuning‐free way. Instead of testing for exact equality, e.g. for the equality of two mean functions from two independent time series, we propose to test the null hypothesis of no relevant deviation. In the two‐sample problem this means that an L2‐distance between the two mean functions is smaller than a prespecified threshold. For such hypotheses self‐normalization, which was introduced in 2010 by Shao, and Shao and Zhang and is commonly used to avoid the estimation of nuisance parameters, is not directly applicable. We develop new self‐normalized procedures for testing relevant hypotheses in the one‐sample, two‐sample and change point problem and investigate their asymptotic properties. Finite sample properties of the tests proposed are illustrated by means of a simulation study and data examples. Our main focus is on functional time series, but extensions to other settings are also briefly discussed.

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“…A fully functional test has also been proposed by Sharipov and Wendler (2019), who use a non overlapping block bootstrap to obtain critical values. More recently, Aue et al (2020) propose statistical tests for detecting a change in the spectrum and in the trace of the covariance operator, respectively. All these references consider the problem of testing classical hypotheses of the form (1.1).…”

Section: Related Literaturementioning

confidence: 99%

Detecting relevant differences in the covariance operators of functional time series -- a sup-norm approach

Dette¹,

Kokot²

2020

Preprint

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In this paper we propose statistical inference tools for the covariance operators of functional time series in the two sample and change point problem. In contrast to most of the literature the focus of our approach is not testing the null hypothesis of exact equality of the covariance operators. Instead we propose to formulate the null hypotheses in the form that "the distance between the operators is small", where we measure deviations by the sup-norm. We provide powerful bootstrap tests for these type of hypotheses, investigate their asymptotic properties and study their finite sample properties by means of a simulation study.

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Structural break analysis for spectrum and trace of covariance operators

Cited by 19 publications

References 31 publications

Two-sample tests for relevant differences in the eigenfunctions of covariance operators

Two-sample tests for relevant differences in the eigenfunctions of covariance operators

Testing Relevant Hypotheses in Functional Time Series via Self-Normalization

Detecting relevant differences in the covariance operators of functional time series -- a sup-norm approach

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