Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Stationary bootstrapping for structural break tests for a heterogeneous autoregressive model

  • Hwang, Eunju (Department of Applied Statistics, Gachon University) ;
  • Shin, Dong Wan (Department of Statistics, Ewha Womans University)
  • Received : 2017.01.18
  • Accepted : 2017.06.23
  • Published : 2017.07.31
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Abstract

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.

Keywords

Acknowledgement

Supported by : National Research Foundation of Korea

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