COINTEGRATION RANK TESTING UNDER CONDITIONAL HETEROSKEDASTICITY
研究了条件异方差下传统协整秩检验的极限分布性质，提出并验证了野自助法在有限样本中的优越性，并应用于利率期限结构。
We analyze the properties of the conventional Gaussian-based cointegrating rank tests of Johansen (1996, Likelihood-Based Inference in Cointegrated Vector Autoregressive Models) in the case where the vector of series under test is driven by globally stationary, conditionally heteroskedastic (martingale difference) innovations. We first demonstrate that the limiting null distributions of the rank statistics coincide with those derived by previous authors who assume either independent and identically distributed (i.i.d.) or (strict and covariance) stationary martingale difference innovations. We then propose wild bootstrap implementations of the cointegrating rank tests and demonstrate that the associated bootstrap rank statistics replicate the first-order asymptotic null distributions of the rank statistics. We show that the same is also true of the corresponding rank tests based on the i.i.d. bootstrap of Swensen (2006, Econometrica 74, 1699–1714). The wild bootstrap, however, has the important property that, unlike the i.i.d. bootstrap, it preserves in the resampled data the pattern of heteroskedasticity present in the original shocks. Consistent with this, numerical evidence suggests that, relative to tests based on the asymptotic critical values or the i.i.d. bootstrap, the wild bootstrap rank tests perform very well in small samples under a variety of conditionally heteroskedastic innovation processes. An empirical application to the term structure of interest rates is given.