A Global Wavelet Based Bootstrapped Test of Covariance Stationarity
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| Publicado en: | arXiv.org (May 21, 2024), p. n/a |
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| Autor principal: | |
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| Publicado: |
Cornell University Library, arXiv.org
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| Materias: | |
| Acceso en línea: | Citation/Abstract Full text outside of ProQuest |
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| Resumen: | We propose a covariance stationarity test for an otherwise dependent and possibly globally non-stationary time series. We work in a generalized version of the new setting in Jin, Wang and Wang (2015), who exploit Walsh (1923) functions in order to compare sub-sample covariances with the full sample counterpart. They impose strict stationarity under the null, only consider linear processes under either hypothesis in order to achieve a parametric estimator for an inverted high dimensional asymptotic covariance matrix, and do not consider any other orthonormal basis. Conversely, we work with a general orthonormal basis under mild conditions that include Haar wavelet and Walsh functions; and we allow for linear or nonlinear processes with possibly non-iid innovations. This is important in macroeconomics and finance where nonlinear feedback and random volatility occur in many settings. We completely sidestep asymptotic covariance matrix estimation and inversion by bootstrapping a max-correlation difference statistic, where the maximum is taken over the correlation lag \(h\) and basis generated sub-sample counter \(k\) (the number of systematic samples). We achieve a higher feasible rate of increase for the maximum lag and counter \(\mathcal{H}_{T}\) and \(\mathcal{K}_{T}\). Of particular note, our test is capable of detecting breaks in variance, and distant, or very mild, deviations from stationarity. |
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| ISSN: | 2331-8422 |
| Fuente: | Engineering Database |