Asymptotic inference in time series regressions with a unit root and infinite variance errors

Callegari, Francesca; Cappuccio, Nunzio; Lubian, Diego

doi:10.1016/s0378-3758(02)00236-7

Cited by 17 publications

(10 citation statements)

References 34 publications

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“…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%

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: 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 literature is also extensive on unit‐root detection with infinite variance; for example, Ahn, et al. (2001), Callegari et al. (2003) and Hasan (2001).…”

Section: Introductionmentioning

confidence: 99%

“…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 (2003) and Hasan (2001). Knight (1989) finds the asymptotic distribution of M-estimators of the autoregressive parameter of an infinite-variance random walk.…”

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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Asymptotic inference in time series regressions with a unit root and infinite variance errors

Cited by 17 publications

References 34 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

Unit root bootstrap tests under infinite variance

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