On limit theory for functionals of stationary increments Lévy driven moving averages
| Autor: | Claudio Heinrich, Andreas Basse-O'Connor, Mark Podolskij |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Asymptotic analysis Rank (linear algebra) fractional processes 01 natural sciences Lévy process 010104 statistics & probability Moving average Law of large numbers stable processes 60F05 FOS: Mathematics Ergodic theory 60G22 Limit (mathematics) 0101 mathematics Central limit theorem Mathematics self-similarity 010102 general mathematics Mathematical analysis Probability (math.PR) limit theorems 60F17 Statistics Probability and Uncertainty Mathematics - Probability 60G52 |
| Zdroj: | Basse-O'Connor, A, Heinrich, C & Podolskij, M 2019, ' On limit theory for functionals of stationary increments Lévy driven moving averages ', Electronic Journal of Probability, vol. 24, 79 . https://doi.org/10.1214/19-EJP336 Electron. J. Probab. |
| DOI: | 10.1214/19-EJP336 |
| Popis: | In this paper we present new limit theorems for variational functionals of stationary increments Lévy driven moving averages in the high frequency setting. More specifically, we will show the “law of large numbers” and a “central limit theorem”, which heavily rely on the kernel, the driving Lévy process and the properties of the functional under consideration. The first order limit theory consists of three different cases. For one of the appearing limits, which we refer to as the ergodic type limit, we prove the associated weak limit theory, which again consists of three different cases. Our work is related to [10, 7], who considered power variation functionals of stationary increments Lévy driven moving averages. However, the asymptotic theory of the present paper is more complex. In particular, the weak limit theorems are derived for an arbitrary Appell rank of the involved functional. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|