Robust Inference for Near-Unit Root Processes with Time-Varying Error Variances

Matei Demetrescu and Christoph Hanck

Econometric Reviews, 2016, vol. 35, issue 5, 751-781

Abstract: The autoregressive Cauchy estimator uses the sign of the first lag as instrumental variable (IV); under independent and identically distributed (i.i.d.) errors, the resulting IV t -type statistic is known to have a standard normal limiting distribution in the unit root case. With unconditional heteroskedasticity, the ordinary least squares (OLS) t statistic is affected in the unit root case; but the paper shows that, by using some nonlinear transformation behaving asymptotically like the sign as instrument, limiting normality of the IV t -type statistic is maintained when the series to be tested has no deterministic trends. Neither estimation of the so-called variance profile nor bootstrap procedures are required to this end. The Cauchy unit root test has power in the same 1/ T neighborhoods as the usual unit root tests, also for a wide range of magnitudes for the initial value. It is furthermore shown to be competitive with other, bootstrap-based, robust tests. When the series exhibit a linear trend, however, the null distribution of the Cauchy test for a unit root becomes nonstandard, reminiscent of the Dickey-Fuller distribution. In this case, inference robust to nonstationary volatility is obtained via the wild bootstrap.

Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1080/07474938.2014.976525

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