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Asymptotic distribution of a robust wavelet-based NKK periodogram | ||
| Caspian Journal of Mathematical Sciences | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 21 تیر 1405 | ||
| نوع مقاله: Research Articles | ||
| شناسه دیجیتال (DOI): 10.22080/cjms.2026.30976.1803 | ||
| نویسندگان | ||
| Manganaw N'DAAM* ؛ Tchilabalo Abozou Kpanzou؛ Edoh Katchekpele | ||
| Department of Mathematics, Faculty of Science and Technology, University of Kara, Kara, Togo | ||
| تاریخ دریافت: 11 دی 1404، تاریخ بازنگری: 02 تیر 1405، تاریخ پذیرش: 07 تیر 1405 | ||
| چکیده | ||
| This paper investigates the asymptotic distribution of a robust wavelet-based NKK periodogram constructed via least absolute deviations (LAD) harmonic regression at a fixed maximal scale. This statistic serves as a wavelet-domain analogue of the Laplace periodogram, specifically designed for long-memory processes. Under suitable regularity conditions, we establish the asymptotic normality of the LAD estimator and derive the explicit limiting distribution of the NKK periodogram. We show that this limit can be expressed as a quadratic form of a Gaussian vector, which reduces to a scaled chi-square distribution in the independent case. A key feature of the analysis is the exploitation of the decorrelation properties of wavelet coefficients at coarse scales. The proposed framework accommodates heavy-tailed innovations and, at the theoretical level, does not rely on the existence of finite second moments, thereby extending robust spectral methods beyond the classical Gaussian setting. Finally, Monte Carlo simulations based on ARFIMA models with heavy-tailed Student-t innovations (with $\nu = 5$ degrees of freedom) support the theoretical findings and illustrate the convergence of the finite-sample distribution toward the derived asymptotic law. | ||
| کلیدواژهها | ||
| Long memory؛ Wavelet-based periodogram؛ Least absolute deviations؛ Heavy-tailed distributions | ||
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