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The asymptotic distribution of the CADF unit root test in the presence of heterogeneous AR(\(p\)) errors

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Abstract

The CADF test of Pesaran (J Appl Econ 22:265–312, 2007) are among the most popular univariate tests for cross-section correlated panels around. Yet, the existing asymptotic analysis of this test statistic is limited to a model in which the errors are assumed to follow a simple AR(1) structure with homogenous autoregressive coefficients. One reason for this is that the model involves an intricate identification issue, as both the serial and cross-section correlation structures of the errors are unobserved. The purpose of the current paper is to tackle this issue and in so doing extend the existing analysis to the case of AR(\(p\)) errors with possibly heterogeneous coefficients.

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Notes

  1. The requirement that \(\overline{\gamma }\ne 0\) is intuitive; since CADF uses cross-section averages of the data to approximate \(f_t\) the common component must not average to zero.

  2. Without \(x\) CADF\(_{i}\) is identically the ADF test statistic applied to cross-section unit \(i\).

  3. The name is due to the fact that CIPS can be seen as a cross-section augmented version of the IPS panel unit root test of Im et al. (2003).

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Correspondence to Joakim Westerlund.

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Westerlund, J. The asymptotic distribution of the CADF unit root test in the presence of heterogeneous AR(\(p\)) errors. Stat Papers 57, 303–317 (2016). https://doi.org/10.1007/s00362-014-0655-x

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  • DOI: https://doi.org/10.1007/s00362-014-0655-x

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