Estimation and inference for time-varying spectra of locally stationary SLEX processes : In Memory of Jonathan A. Raz
(2000) , 12 pages
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- Abstract
- Ombao et al (JASA, 2001) have proposed an automatic procedure to estimate the time-varying spectrum of a bivariate non-stationary process. This Auto-SLEX method uses the so-called Smooth Localized complex EXponential basis function which are simultaneously orthogonal and localized in both the time and frequency domain. In this paper we investigate the properties of the SLEX estimator under a new model of locally stationary SLEX processes which have a well defined time-varying SLEX spectrum. The SLEX model is a sequence of SLEX processes defined via a spectral representation with respect to the SLEX basis as stochastic building blocks and having spectra which are piecewise constant over time. In the asymptotic limit it allows for a smoothly-varying ”evolutionary” spectrum. Due to its special structure this new model allows for simple synthesis of non-stationary processes of finite length and, hence, can be used to perform statistical inference on the SLEX estimator. We propose two different bootstrap procedures for inference in the frequency domain for non-stationary processes. We evaluate the performance of these procedures via a small simulation study.
- Affiliations
University of Pittsburgh University of Pennsylvania
Citations
Guo, W., Ombao, H., & von Sachs, R. (2000). Estimation and inference for time-varying spectra of locally stationary SLEX processes : In Memory of Jonathan A. Raz (STAT Discussion Paper 0027). https://hdl.handle.net/2078.5/85581