| Title |
Asymptotic results on nearly nonstationary processes / |
| Translation of Title |
Beveik nestacionarių procesų asimptotiniai rezultatai. |
| Authors |
Markevičiūtė, Jurgita |
| Full Text |
|
| Pages |
145 |
| Keywords [eng] |
First order nearly nonstationary autoregressive process ; Hölder space ; functional limit theorems ; epidemic change. |
| Abstract [eng] |
We study some Hölderian functional central limit theorems for the polygonal partial sum processes built on a first order nearly nonstationary autoregressive process and its least squares residuals Innovations are i.i.d. centered and at least square-integrable innovations. Two types of models are considered. For the first type model we prove that the limiting process depends on Ornstein – Uhlenbeck one. In the second type model, the convergence to Brownian motion is established in Hölder space in terms of the rate of coefficient and the integrability of the residuals. We also investigate some epidemic change in the innovations of the first order nearly nonstationary autoregressive process . We build the alpha-Hölderian uniform increments statistics based on the observations and on the least squares residuals to detect the short epidemic change in the process under consideration. Under the assumptions for innovations we find the limit of the statistics under null hypothesis, some conditions of consistency and we perform a test power analysis. |
| Type |
Doctoral thesis |
| Language |
English |
| Publication date |
2013 |
