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Multidimensional parameter estimation of heavy‐tailed moving averages
- Source :
- Ljungdahl, M M & Podolskij, M 2022, ' Multidimensional parameter estimation of heavy-tailed moving averages ', Scandinavian Journal of Statistics, vol. 49, no. 2, pp. 593-624 . https://doi.org/10.1111/sjos.12527
- Publication Year :
- 2021
- Publisher :
- Wiley, 2021.
-
Abstract
- In this paper we present a parametric estimation method for certain multi-parameter heavy-tailed Levy-driven moving averages. The theory relies on recent multivariate central limit theorems obtained in [3] via Malliavin calculus on Poisson spaces. Our minimal contrast approach is related to the papers [14, 15], which propose to use the marginal empirical characteristic function to estimate the one-dimensional parameter of the kernel function and the stability index of the driving Levy motion. We extend their work to allow for a multi-parametric framework that in particular includes the important examples of the linear fractional stable motion, the stable Ornstein-Uhlenbeck process, certain CARMA(2, 1) models and Ornstein-Uhlenbeck processes with a periodic component among other models. We present both the consistency and the associated central limit theorem of the minimal contrast estimator. Furthermore, we demonstrate numerical analysis to uncover the finite sample performance of our method.
- Subjects :
- Statistics and Probability
Estimation theory
Numerical analysis
05 social sciences
limit theorems
Estimator
Poisson distribution
Malliavin calculus
01 natural sciences
Lévy process
parametric estimation
heavy tails
010104 statistics & probability
symbols.namesake
Lévy processes
Moving average
0502 economics and business
symbols
Applied mathematics
low frequency
0101 mathematics
Statistics, Probability and Uncertainty
050205 econometrics
Mathematics
Central limit theorem
Subjects
Details
- ISSN :
- 14679469 and 03036898
- Volume :
- 49
- Database :
- OpenAIRE
- Journal :
- Scandinavian Journal of Statistics
- Accession number :
- edsair.doi.dedup.....b17a8514154f770f0cc711848ca393e2