Invariance principles for tempered fractionally integrated processes
| Autor: | Farzad Sabzikar, Donatas Surgailis |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Invariance principle Limit distribution Applied Mathematics Probability (math.PR) 010102 general mathematics Mathematical analysis 01 natural sciences Statistics::Computation 010104 statistics & probability Autoregressive model Moving average Modeling and Simulation FOS: Mathematics Tempering Unit root Limit (mathematics) 0101 mathematics Mathematics::Representation Theory Mathematics - Probability Autoregressive fractionally integrated moving average Mathematical physics Mathematics |
| Zdroj: | Stochastic Processes and their Applications. 128:3419-3438 |
| ISSN: | 0304-4149 |
| DOI: | 10.1016/j.spa.2017.11.004 |
| Popis: | We discuss invariance principles for autoregressive tempered fractionally integrated moving averages in α -stable ( 1 α ≤ 2 ) i.i.d. innovations and related tempered linear processes with vanishing tempering parameter lim N → ∞ λ ∕ N = λ ∗ . We show that the limit of the partial sums process takes a different form in the weakly tempered ( λ ∗ = 0 ), strongly tempered ( λ ∗ = ∞ ), and moderately tempered ( 0 λ ∗ ∞ ) cases. These results are used to derive the limit distribution of the ordinary least squares estimate of AR(1) unit root with weakly, strongly, and moderately tempered moving average errors. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect