Whittle parameter estimation for vector ARMA models with heavy-tailed noises

She, Rui; Mi, Zichuan; Ling, Shiqing

doi:10.1016/j.jspi.2021.12.003

Cited by 4 publications

(2 citation statements)

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“…Resnick (1985, 1986) showed the limiting distribution of the LSE of the parameters in a heavy-tailed AR model is the functional of two stable random variables with the rate of convergence much faster than √ n, see Davis, Knight, and Liu (1992). Mikosch et al (1995) studied the Whittle estimators for the heavy-tailed ARMA model and this result was extended by She, Mi and Ling (2021) for model (1.1). Davis, Mikosch and Pfaffel (2016) studied the sample covariance matrix of a heavy-tailed multivariate time series.…”

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Statistical Inference for Heavy-tailed and Partially Nonstationary Vector ARMA Models

Guo,

Ling

2025

STAT SINICA

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This paper studies the full rank least squares estimator (FLSE) and reduced rank least squares estimator (RLSE) of the heavy-tailed and partially nonstationary ARMA model with the tail index α ∈ (0, 2). It is shown that the rate of convergence of the FLSE related to the long-run parameters is n (sample size) and that related to the short-term parameters are n 1/α L(n) and n, respectively, when α ∈ (1, 2) and ∈ (0, 1). Its limiting distribution is a stochastic integral in terms of two stable random processes when α ∈ (0, 2) for the long-run parameters and is a functional of some stable processes when α ∈ (1, 2) for the short-run parameters. Based on FLSE, we derive the asymptotic properties of the RLSE. The finite-sample properties of the estimation are examined through a simulation study and an application to three U.S. interest rate series is given.

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