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2020 Spectral estimation for non-linear long range dependent discrete time trawl processes
Paul Doukhan, François Roueff, Joseph Rynkiewicz
Electron. J. Statist. 14(2): 3157-3191 (2020). DOI: 10.1214/20-EJS1742


Discrete time trawl processes constitute a large class of time series parameterized by a trawl sequence $(a_{j})_{j\in \mathbb{N}}$ and defined though a sequence of independent and identically distributed (i.i.d.) copies of a continuous time process $(\gamma (t))_{t\in \mathbb{R}}$ called the seed process. They provide a general framework for modeling linear or non-linear long range dependent time series. We investigate the spectral estimation, either pointwise or broadband, of long range dependent discrete-time trawl processes. The difficulty arising from the variety of seed processes and of trawl sequences is twofold. First, the spectral density may take different forms, often including smooth additive correction terms. Second, trawl processes with similar spectral densities may exhibit very different statistical behaviors. We prove the consistency of our estimators under very general conditions and we show that a wide class of trawl processes satisfy them. This is done in particular by introducing a weighted weak dependence index that can be of independent interest. The broadband spectral estimator includes an estimator of the long memory parameter. We complete this work with numerical experiments to evaluate the finite sample size performance of this estimator for various integer valued discrete time trawl processes.


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Paul Doukhan. François Roueff. Joseph Rynkiewicz. "Spectral estimation for non-linear long range dependent discrete time trawl processes." Electron. J. Statist. 14 (2) 3157 - 3191, 2020.


Received: 1 January 2020; Published: 2020
First available in Project Euclid: 21 August 2020

zbMATH: 07246815
MathSciNet: MR4137598
Digital Object Identifier: 10.1214/20-EJS1742

Primary: 62F12 , 62M10
Secondary: 60K35

Keywords: integer-valued time series , long memory parameter estimation , Trawl processes


Vol.14 • No. 2 • 2020
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