Ground-level ozone: Evidence of increasing serial dependence in the extremes

Dupuis, Debbie J.; Trapin, Luca

doi:10.1214/18-aoas1183

Cited by 2 publications

(13 citation statements)

References 35 publications

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“…• Method 2 (M2): Use the marginal likelihood to estimate the marginal parameters first, and proceed to a PL-based estimation of the trawl parameter in the second stage, similarly to Dupuis and Trapin (2019).…”

Section: Inferencementioning

confidence: 99%

“…Examples of trawl functions include the exponential function , that is,

g (u) = \exp (ρ u)

for some fixed

ρ > 0

(Dupuis & Trapin, 2019; Noven et al, 2018), or the weighted sum of exponentials such that

g (u) = \sum_{i = 1}^{d} w_{i} \exp (ρ_{i} u)

for some integer

d \geq 2

ρ_{1} > \dots > ρ_{d} > 0

and nonnegative weights such that

\sum_{i = 1}^{d} w_{i} = 1

(Barndorff‐Nielsen et al, 2014, example 5). See Barndorff‐Nielsen et al (2014) for additional trawl sets.…”

Section: The Latent Trawl Model For Extremesmentioning

confidence: 99%

“…In this section, we introduce the four inference strategies of interest: for a target parameter vector denoted

θ = {(ξ, σ, κ, ρ)}^{⊤} \in ℝ^{3 + p}

, we either estimate the full parameter vector at once (Noven et al, 2018) or take a two‐stage approach where one infers the marginal parameters

(ξ, σ, κ)

and then estimates the trawl parameter

ρ

(Dupuis & Trapin, 2019). We present two corresponding schemes based on the PL function first, and then introduce the novel AM methods formalized as a GMM approach as listed below: Method 1 (M1): Use the PL to estimate the full parameter vector in a single stage as in Noven et al (2018).…”

Section: Inferencementioning

confidence: 99%

“…So far, two inference approaches have been considered for the LTME: Noven et al (2018) used a (single-stage) pairwise likelihood (PL) method (M1), whereas Dupuis and Trapin (2019) proposed a three-stage approach consisting of first estimating the exceedance rate parameter, then the marginal GPD parameters, followed by the parameters associated with the trawl process using PL. We will discuss a two-stage variant of this estimation method, where the exceedance rate and the GPD parameters are estimated jointly, followed by the estimation of the trawl parameters using PL (M2).…”

Section: Introductionmentioning

confidence: 99%

“…setting have been extensively studied (Davison & Smith, 1990; Smith, 1985). Somewhat recent developments allowing for general serial dependencies (Francq & Zakoïan, 2013), involving Markov chains (Bortot & Gaetan, 2014; Bortot & Gaetan, 2016), or parametrizable latent serial dependence (Dupuis & Trapin, 2019; Noven et al, 2018) have rendered those approaches more flexible and reliable for applications, notably through a mixture representation of the GPD as an exponential distribution with a Gamma‐distributed process as the rate (Hogg & Klugman, 1983; Smith & Miller, 1986).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Asymptotic theory for the inference of the latent trawl model for extreme values

Courgeau

Veraart

2022

Scandinavian J Statistics

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This article develops statistical inference methods and their asymptotic theory for the latent trawl model for extremes, which captures serial dependence in the time series of exceedances above a threshold. We review two methods based on pairwise likelihood and show that they underestimate the serial dependence in the extremes. We propose two generalized method of moments procedures based on auto-covariance matching to overcome this shortcoming. Out of those four inference approaches, two are single-stage strategies while the others have two stages, and we provide central limit theorems in the sense of weakly approaching sequences of distributions for all of them. This additional flexibility ensures good behavior between the estimators and estimates of the limiting distribution.In an empirical illustration using London air pollution data, we find that the two-stage auto-covariance matching scheme yields a high-quality inference. It comprises two interpretable steps and correctly captures the serial dependence structure of extremes while performing on par with other methods in terms of marginal fit.

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Section: Inferencementioning

confidence: 99%

“…Examples of trawl functions include the exponential function , that is,