Uniform limit theorems for the integrated periodogram of weakly dependent time series and their applications to Whittle's estimate
| dc.creator | Bardet, Jean-Marc | |
| dc.creator | Doukhan, Paul | |
| dc.creator | León, José Rafael | |
| dc.date | 2007-01-25 | |
| dc.date.accessioned | 2026-07-07T09:32:32Z | |
| dc.date.available | 2026-07-07T09:32:32Z | |
| dc.description | We prove uniform convergence results for the integrated periodogram of a weakly dependent time series, namely a law of large numbers and a central limit theorem. These results are applied to Whittle's parametric estimation. Under general weak-dependence assumptions we derive uniform limit theorems and asymptotic normality of Whittle's estimate for a large class of models. For instance the causal $θ$-weak dependence property allows a new and unified proof of those results for ARCH($\infty$) and bilinear processes. Non causal $η$-weak dependence yields the same limit theorems for two-sided linear (with dependent inputs) or Volterra processes. | |
| dc.identifier | https://arxiv.org/abs/math/0701739 | |
| dc.identifier | http://arxiv.org/abs/math/0701739 | |
| dc.identifier | Journal of Time Series Analysis (2008) à paraître | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158812 | |
| dc.subject | Statistics Theory | |
| dc.subject | 60F17, 60F25, 62M09, 62M10, 62M15 | |
| dc.title | Uniform limit theorems for the integrated periodogram of weakly dependent time series and their applications to Whittle's estimate | |
| dc.type | text |