Unit Root Tests With Infinite Variance Errors

Ahn, Sung K.; Fotopoulos, S.; He, Lijian

doi:10.1081/etc-100107000

Cited by 21 publications

(14 citation statements)

References 16 publications

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“…In contrast with the asymptotic distributions available in the infinite variance case (see Ahn et al, 2001), here they depend not only on the maximal moment exponent α but also on the nuisance parameters σ 2 1 and γ. The role played by U α (r) in shaping the asymptotic distribution of the test statistics depends on the magnitude of the weight γ.…”

Section: Unit Root Testsmentioning

confidence: 86%

“…errors, that the functional form of the asymptotic distribution of the least squares estimator and of the t-statistic depends on whether the maximal moment exponent α lies between zero and one, is equal to one or lies between one and two. The asymptotic distribution of additional unit root tests with infinite variance errors has been analyzed by Ahn et al (2001). As for tests of the null hypothesis of stationarity, Amsler and Schmidt (1999) have studied the asymptotic distribution of the KP SS test of Kwiatkowski et al (1992) and of the modified rescaled range (MRS) test of Lo (1991).…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic Null Distributions of Stationarity and Nonstationarity Tests Under Local-to-finite Variance Errors

Cappuccio

Lubian

2006

AISM

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The purpose of this paper is to investigate the asymptotic null distribution of stationarity and nonstationarity tests when the distribution of the error term belongs to the normal domain of attraction of a stable law in any finite sample but the error term is an i.i.d. process with finite variance as T ↑ ∞. This local-to-finite variance setup is helpful to highlight the behavior of test statistics under the null hypothesis in the borderline or near borderline cases between finite and infinite variance and to assess the robustness of these test statistics to small departures from the standard finite variance context. From an empirical point of view, our analysis can be useful in settings where the (non)-existence of the (second) moments is not clear-cut, such as, for example, in the analysis of financial time series. A Monte Carlo simulation study is performed to improve our understanding of the practical implications of the limi theory we develop. The main purpose of the simulation experiment is to assess the size distortion of the unit root and stationarity tests under investigation.

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Section: Unit Root Testsmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

Asymptotic Null Distributions of Stationarity and Nonstationarity Tests Under Local-to-finite Variance Errors

Cappuccio

Lubian

2006

AISM

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“…See Phillips (1990, p. 46) for further discussion and definitions of terms. See also Ahn, Fotopoulos, and He (2001) for a good expository treatment of these results and their application to unit root tests.…”

Section: Local-to-finite Variance Asymptoticsmentioning

confidence: 95%

Tests of Short Memory With Thick-Tailed Errors

Amsler

Schmidt

2012

Journal of Business & Economic Statistics

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In this article, we consider the robustness to fat tails of four stationarity tests. We also consider their sensitivity to the number of lags used in long-run variance estimation, and the power of the tests. Lo's modified rescaled range (MR/S) test is not very robust. Choi's Lagrange multiplier (LM) test has excellent robustness properties but is not generally as powerful as the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test. As an analytical framework for fat tails, we suggest local-to-finite variance asymptotics, based on a representation of the process as a weighted sum of a finite variance process and an infinite variance process, where the weights depend on the sample size and a constant. The sensitivity of the asymptotic distribution of a test to the weighting constant is a good indicator of its robustness to fat tails. This article has supplementary material online.

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“…Davis and Wu (1997b) propose the use of bootstrap to approximate the distribution of M‐estimators in the stationary case. The literature is also extensive on unit‐root detection with infinite variance; for example, Ahn, et al. (2001), Callegari et al.…”

Section: Introductionmentioning

confidence: 99%

Unit root bootstrap tests under infinite variance

Fernández

Romo

2011

Journal Time Series Analysis

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This article presents a family of new tests for unit roots based on M-estimators. Their robustness makes them very appealing when working with distributions that have infinite variance or heavy tails. These tests are completely automatic regardless of the complex distributions of this kind of estimators because the critical values are approximated using bootstrap, no additional parameter has to be estimated and the results obtained are very good in small samples. An exhaustive Monte Carlo study shows the high performance of these tests compared with others proposed in the literature when the variance is infinite.

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Unit Root Tests With Infinite Variance Errors

Cited by 21 publications

References 16 publications

Asymptotic Null Distributions of Stationarity and Nonstationarity Tests Under Local-to-finite Variance Errors

Asymptotic Null Distributions of Stationarity and Nonstationarity Tests Under Local-to-finite Variance Errors

Tests of Short Memory With Thick-Tailed Errors

Unit root bootstrap tests under infinite variance

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