| Autor: |
Sen, Kemal, Preuss, Philip, Dette, Holger |
| Rok vydání: |
2013 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
In this paper we consider the problem of measuring stationarity in locally stationary long-memory processes. We introduce an $L_2$-distance between the spectral density of the locally stationary process and its best approximation under the assumption of stationarity. The distance is estimated by a numerical approximation of the integrated spectral periodogram and asymptotic normality of the resulting estimate is established. The results can be used to construct a simple test for the hypothesis of stationarity in locally stationary long-range dependent processes. We also propose a bootstrap procedure to improve the approximation of the nominal level and prove its consistency. Throughout the paper, we will work with Riemann sums of a squared periodogram instead of integrals (as it is usually done in the literature) and as a by-product of independent interest it is demonstrated that the two approaches behave differently in the limit. |
| Databáze: |
arXiv |
| Externí odkaz: |
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