Sieve-based inference for infinite-variance linear processes

Cavaliere, Giuseppe; Georgiev, Iliyan; Taylor, A. M. Robert

doi:10.1214/15-aos1419

Cited by 13 publications

(11 citation statements)

References 28 publications

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“…Regarding summability, Assumption

scriptA

.1 and the condition that

\sum_{j = 0}^{\infty} j {(||, ψ_{j})}^{δ / 2} < \infty

from Assumption

scriptA

.5 are sufficient for

{(\sum_{j = 0}^{\infty} ψ_{j} z^{j})}^{- 1}

to be bounded and bounded away from zero for | z |⩽1. The conditions placed on

ψ ((), z)

in Assumptions

scriptA

.1 and

scriptA

.5 imply Assumption 2 of Chang and Park () and coincide with Assumption A(b,d) of Cavaliere et al (), allowing us to use certain results from these papers.

□

…”

Section: Near‐integrated Local‐to‐finite Variance Processesmentioning

confidence: 95%

Unit Root Tests and Heavy‐Tailed Innovations

Georgiev

Rodrigues

Taylor

2017

Journal Time Series Analysis

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We evaluate the impact of heavy-tailed innovations on some popular unit root tests. In the context of a near-integrated series driven by linear-process shocks, we demonstrate that their limiting distributions are altered under infinite variance vis-à-vis finite variance. Reassuringly, however, simulation results suggest that the impact of heavy-tailed innovations on these tests are relatively small. We use the framework of Amsler and Schmidt (2012) whereby the innovations have local-to-finite variances being generated as a linear combination of draws from a thintailed distribution (in the domain of attraction of the Gaussian distribution) and a heavy-tailed distribution (in the normal domain of attraction of a stable law). We also explore the properties of ADF tests which employ Eicker-White standard errors, demonstrating that these can yield significant power improvements over conventional tests.JEL: C12, C22, C58.

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“…Regarding summability, Assumption

scriptA

.1 and the condition that

\sum_{j = 0}^{\infty} j {(||, ψ_{j})}^{δ / 2} < \infty

from Assumption

scriptA

.5 are sufficient for

{(\sum_{j = 0}^{\infty} ψ_{j} z^{j})}^{- 1}

to be bounded and bounded away from zero for | z |⩽1. The conditions placed on

ψ ((), z)

in Assumptions

scriptA

.1 and

scriptA

.5 imply Assumption 2 of Chang and Park () and coincide with Assumption A(b,d) of Cavaliere et al (), allowing us to use certain results from these papers.

□

…”

Section: Near‐integrated Local‐to‐finite Variance Processesmentioning

confidence: 95%

Unit Root Tests and Heavy‐Tailed Innovations

Georgiev

Rodrigues

Taylor

2017

Journal Time Series Analysis

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“…Loretan and Phillips (1994) in terms of financial time series. Least squares estimation of the autoregressive parameters in stationary AR models driven by heavy-tailed independent innovations has been studied by Davis and Resnick (1986) and bootstrap-based inference has been considered by Davis and Wu (1997) and Cavaliere et al (2016a). In terms of dependent heavy-tailed innovations, Mikosch and Stărică (2000), Lange (2011), and Zhang and Ling (2015) have investigated the properties of the least squares estimator.…”

Section: Introductionmentioning

confidence: 99%

Robust inference in conditionally heteroskedastic autoregressions

Pedersen

2019

Econometric Reviews

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We consider robust inference for an autoregressive parameter in a stationary autoregressive model with GARCH innovations when estimation is based on least squares estimation. As the innovations exhibit GARCH, they are by construction heavy-tailed with some tail index κ. The rate of consistency as well as the limiting distribution of the least squares estimator depend on κ. In the spirit of Ibragimov and Müller ("t-statistic based correlation and heterogeneity robust inference", Journal of Business & Economic Statistics, 2010, vol. 28, pp. 453-468), we consider testing a hypothesis about a parameter based on a Student's t-statistic for a fixed number of subsamples of the original sample. The merit of this approach is that no knowledge about the value of κ nor about the rate of consistency and the limiting distribution of the least squares estimator is required. We verify that the one-sided t-test is asymptotically a level α test whenever α ≤ 5% uniformly over κ ≥ 2, which includes cases where the innovations have infinite variance. A simulation experiment suggests that the finite-sample properties of the test are quite good.

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“…Lahiri (1995) arrives at the same conclusion for the moving block bootstrap when the random variables are dependent. Starting with the work of Athreya (1987), a number of important papers appeared on this topic in the last two decades; see Knight (1989), Arcones and Giné (1989), Arcones and Giné (1991), Giné and Zinn (1989), Giné and Zinn (1990), Hall (1990), Hall and LePage (1996), Athreya, Lahiri, and Wu (1998), Hall and Jing (1998), Romano and Wolf (1999), Politis, Romano, and Wolf (1999), Cavaliere, Georgiev, and Taylor (2013), Cornea-Madeira and Davidson (2015), Cavaliere, Georgiev, and Taylor (2016) and the references therein. The solutions to the failure of the naive bootstrap proposed in these papers are either based on a smaller resampling size (m out of n bootstrap and subsampling) or on a bootstrap sample size equal to the original sample size (parametric bootstrap, wild bootstrap, permutation bootstrap).…”

Section: Introductionmentioning

confidence: 99%

Link of Moments Before and After Transformations, With an Application to Resampling From Fat-Tailed Distributions

Abadir

Cornea‐Madeira

2018

Econom. Theory

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Let x be a transformation of y, whose distribution is unknown. We derive an expansion formulating the expectations of x in terms of the expectations of y. Apart from the intrinsic interest in such a fundamental relation, our results can be applied to calculating E(x) by the low-order moments of a transformation which can be chosen to give a good approximation for E(x). To do so, we generalize the approach of bounding the terms in expansions of characteristic functions, and use our result to derive an explicit and accurate bound for the remainder when a finite number of terms is taken. We illustrate one of the implications of our method by providing * We thank Essie Maasoumi, Natalia Markovich, Peter Phillips, Robert Taylor, Michael Wolf and three anonymous referees for their comments. This paper was invited at the 2nd conference of the International

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Sieve-based inference for infinite-variance linear processes

Cited by 13 publications

References 28 publications

Unit Root Tests and Heavy‐Tailed Innovations

Unit Root Tests and Heavy‐Tailed Innovations

Robust inference in conditionally heteroskedastic autoregressions

Link of Moments Before and After Transformations, With an Application to Resampling From Fat-Tailed Distributions

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