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http://dx.doi.org/10.5351/CSAM.2017.24.4.367

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)
Publication Information
Communications for Statistical Applications and Methods / v.24, no.4, 2017 , pp. 367-382 More about this Journal
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
heterogeneous autoregressive(${\infty}$) model; stationary bootstrap; structural changes; CUSUM test;
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