Stationary bootstrapping for structural break tests for a heterogeneous autoregressive model

Eunju Hwang, Dong Wan Shin

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We consider an infinite-order long-memory heterogeneous autoregressive (HAR) model, which is motivated by a long-memory property of realized volatilities (RVs), as an extension of the finite order HAR-RV model. We develop bootstrap tests for structural mean or variance changes in the infinite-order HAR model via stationary bootstrapping. A functional central limit theorem is proved for stationary bootstrap sample, which enables us to develop stationary bootstrap cumulative sum (CUSUM) tests: a bootstrap test for mean break and a bootstrap test for variance break. Consistencies of the bootstrap null distributions of the CUSUM tests are proved. Consistencies of the bootstrap CUSUM tests are also proved under alternative hypotheses of mean or variance changes. A Monte-Carlo simulation shows that stationary bootstrapping improves the sizes of existing tests.

Original languageEnglish
Pages (from-to)367-382
Number of pages16
JournalCommunications for Statistical Applications and Methods
Issue number4
StatePublished - 1 Jul 2017

Bibliographical note

Publisher Copyright:
© 2017 The Korean Statistical Society, and Korean International Statistical Society.


  • CUSUM test
  • Heterogeneous autoregressive(∞) model
  • Stationary bootstrap
  • Structural changes


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