Tests of correlation among wavelet-based estimates for long memory processes. (English) Zbl 1132.62076
Summary: Long memory models have received a significant amount of attention in the theoretical literature as they cover a wide range of applications, including economics and telecommunications. In recent years, a semiparametric estimator of long memory parameter of stationary processes with long-range dependence, based on wavelet decomposition, has been proposed and studied by D. Veitch and P. Abry [IEEE Trans. Inf. Theory 45, No. 3, 878–897 (1999; Zbl 0945.94006)] under the idealized assumption of decorrelation among wavelet coefficients. The asymptotic statistical analysis of the wavelet-based estimator has been recently complemented taking into account the correlations among wavelet coefficients, at fixed scales as well as among different scales [J. M. Bardet et al., Stat. Inference Stoch. Process. 3, No. 1–2, 85–99 (2000; Zbl 1054.62579)].
The goal of the present article is to study the statistical properties of the wavelet-based estimator for a finite sample size and the correlation among the wavelet-based long memory estimates. The analysis is conducted by simulation, through the use of the circulant matrix method and shows that the correlation among wavelet coefficients has an impact on the moments of the wavelet-based estimator and on the correlation among the wavelet-based long memory estimates computed on non overlapping blocks of the original process.
The goal of the present article is to study the statistical properties of the wavelet-based estimator for a finite sample size and the correlation among the wavelet-based long memory estimates. The analysis is conducted by simulation, through the use of the circulant matrix method and shows that the correlation among wavelet coefficients has an impact on the moments of the wavelet-based estimator and on the correlation among the wavelet-based long memory estimates computed on non overlapping blocks of the original process.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62G10 | Nonparametric hypothesis testing |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 62M07 | Non-Markovian processes: hypothesis testing |
Software:
longmemoReferences:
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