A class of CUSUM tests using empirical distributions for tail changes in weakly dependent processesA class of CUSUM tests using empirical distributions for tail changes in weakly dependent processes
- Other Titles
- A class of CUSUM tests using empirical distributions for tail changes in weakly dependent processes
- Authors
- 김준형; 황은주
- Issue Date
- Mar-2020
- Publisher
- 한국통계학회
- Keywords
- weak dependence; tail index; CUSUM test; limit theory; GARCH process
- Citation
- Communications for Statistical Applications and Methods, v.27, no.2, pp.163 - 175
- Journal Title
- Communications for Statistical Applications and Methods
- Volume
- 27
- Number
- 2
- Start Page
- 163
- End Page
- 175
- URI
- https://scholarworks.bwise.kr/gachon/handle/2020.sw.gachon/60145
- ISSN
- 2287-7843
- Abstract
- We consider a wide class of general weakly-dependent processes, called ψ-weak dependence, which unify almost all weak dependence structures of interest found in statistics under natural conditions on process parameters, such as mixing, association, Bernoulli shifts, and Markovian sequences. For detecting the tail behavior of the weakly dependent processes, change point tests are developed by means of cumulative sum (CUSUM) statistics with the empirical distribution functions of sample extremes. The null limiting distribution is established as a Brownian bridge. Its proof is based on the ψ-weak dependence structure and the existence of the phantom distribution function of stationary weakly-dependent processes. A Monte-Carlo study is conducted to see the performance of sizes and powers of the CUSUM tests in GARCH(1, 1) models; in addition, real data applications are given with log-returns of financial data such as the Korean stock price index.
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