Inference in Autoregression under Heteroskedasticity

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HETEROSKEDASTIC TIME SERIES WITH A UNIT ROOT (2009, background): “Other related work is considered by Phillips and Xu (2006), Xu and Phillips (2008), and Xu (2008), who show that nonconstant volatility can have a large impact on standard estimation and testing procedures in stable autoregressions.”
Adaptive Estimation of Autoregressive Models with Time-Varying Variances (2008, background): “Lemma A(ii) of Phillips and Xu (2006a) shows that for every continuous point r of gð Þ; limT!”
Testing for Co-integration in Vector Autoregressions with Non-Stationary Volatility (2010, unknown): “All results given in this section carry over straightforwardly to the case of either a restricted constant term (D1t = 1, D2t = 0) or a restricted linear trend (D1t = t, D2t = 1), as are considered in Swensen (2006). For example, the limiting null distributions of the Qr statistic in these two cases”