Testing for Co-integration in Vector Autoregressions with Non-Stationary Volatility

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Instrumental variable and variable addition based inference in predictive regressions (2015, methodology): “Under this assumption, an invariance principle holds (see e.g. Cavaliere et al., 2010) 1√ T T∑ t=1 ( ut vt ) ⇒ ( BH,u(r) BH,v(r) ) , where ( BH,u(r) BH,v(r) ) = ( 1 0 0 ∑ j≥0 bj )∫ r 0 H(s)dW(s) with W(s) a vector of two independent standard Wiener processes.”
Testing for linear vector autoregressive dynamics under multivariate generalized autoregressive heteroskedasticity (2009, methodology): “econometric literature after the seminal contributions by Engle (1982), Bollerslev (1986) and Taylor (1986) introducing (generalized) autoregressive conditionally heteroskedastic ((G)ARCH) processes and the stochastic volatility model, respectively.”
Bootstrap Determination of the Co-Integration Rank in Heteroskedastic VAR Models (2014, methodology): “For co-integrated VAR models with independent and identically distributed (i.i.d.) innovations, see, most notably, Swensen (2006) and Cavaliere, Rahbek and Taylor (2012); for VAR models with potentially heteroskedastic innovations, see Cavaliere, Rahbek and Taylor (2010a, 2010b).”