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

Cappuccio, Nunzio; Lubian, Diego

doi:10.1007/s10463-006-0060-x

Cited by 7 publications

(3 citation statements)

References 31 publications

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“…Amsler and Schmidt (1999) derived the asymptotic distribution of the KPSS statistic with no lags ( = 0), which is exactly as in Equation (5) except that G * α,c (r) replaces U * α (r) in the numerator of the expression for the asymptotic distribution. That is, Cappuccio and Lubian (2007) also derived these results for the KPSS and MR/S tests, as well as the LM test and several other tests. We will therefore omit the proofs here.…”

Section: Local-to-finite Variance Asymptoticsmentioning

confidence: 97%

“…The parameterization was first suggested and the proofs of the asymptotic results given in the current article were presented by Amsler and Schmidt (1999), but that paper was never published. These results were used, and some of them were proved again, by Callegari, Cappuccio, and Lubian (2003) and Cappuccio and Lubian (2007). Those articles quoted Amsler and Schmidt (1999) but gave a somewhat self-contained presentation of the results.…”

Section: Local-to-finite Variance Asymptoticsmentioning

confidence: 99%

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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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Section: Local-to-finite Variance Asymptoticsmentioning

confidence: 97%

Section: Local-to-finite Variance Asymptoticsmentioning

confidence: 99%

Tests of Short Memory With Thick-Tailed Errors

Amsler

Schmidt

2012

Journal of Business & Economic Statistics

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“…This local-to-finite variance setup is helpful to highlight the behavior of test statistic under the null hypothesis in the borderline or near borderline cases between finite variance, and assess the robustness of our test statistic to small departure from the standard finite variance context. One refer Callegari et al (2003), Cappuccio and Lubian (2007) for more detailed discussions about this sequence. (2) is generated by (9), and Assumption 2.2 holds, then the null distribution of (6) is given bỹ (2) is generated by (9), then under Assumption 2.2 the result of Theorem 3.3 is still hold.…”

Section: Local-to-finite Variance Casementioning

confidence: 99%

Monitoring Change in Persistence Against the Null of Difference-Stationarity in Infinite Variance Observations

Chen

2014

Communications in Statistics - Simulation and Computation

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In this article, we propose a moving kernel-weighted variance ratio statistic to monitor persistence change in infinite variance observations. We focus on I (1) to I (0) persistence change for sequences in the domain of attraction of a stable law and local-to-finite variance sequences. The null distribution of the monitoring statistic and its consistency are proved. In particular, a bootstrap procedure is proposed to determine the critical values for the derived asymptotic distribution depends on unknown tail index. The small sample performances of proposed monitoring procedure are illustrated by both simulation and application to a high frequency financial data.

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The power of unit root tests under local-to-finite variance errors

Cappuccio¹,

Lubian

Mistrorigo

2015

Chaos, Solitons & Fractals

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We study the power of four popular unit root tests in the presence of a local-to-finite variance DGP. We characterize the asymptotic distribution of these tests under a sequence of local alternatives, considering both stationary and explosive ones . We supplement the theoretical analysis with a small simulation study to assess the finite sample power of the tests. Our results suggest that the finite sample power is affected by the $\alpha$-stable component for low values of $\alpha$ and that, in the presence of this component, the DW test has the highest power under stationary alternatives. We also document a strange behavior of the $DW$ test which, under the explosive alternative, suddenly falls from 1 to zero for very small changes in the autoregressive parameter suggesting a discontinuity in the power function of the $DW$ test

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

Cited by 7 publications

References 31 publications

Tests of Short Memory With Thick-Tailed Errors

Tests of Short Memory With Thick-Tailed Errors

Monitoring Change in Persistence Against the Null of Difference-Stationarity in Infinite Variance Observations

The power of unit root tests under local-to-finite variance errors

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