A Comparison of Sequential and Information‐based Methods for Determining the Co‐integration Rank in Heteroskedastic VAR Models
研究了在异方差VAR系统中，信息准则（AIC、BIC）与Johansen序贯方法（基于渐近或自助法似然比检验）估计协整秩的表现，发现BIC和自助序贯检验整体最优，但自助法更可靠，避免了BIC在小样本中高估秩的倾向。
Abstract In this article, we investigate the behaviour of a number of methods for estimating the co‐integration rank in VAR systems characterized by heteroskedastic innovation processes. In particular, we compare the efficacy of the most widely used information criteria, such as Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) , with the commonly used sequential approach of Johansen [ Likelihood‐based Inference in Cointegrated Vector Autoregressive Models (1996)] based around the use of either asymptotic or wild bootstrap‐based likelihood ratio type tests. Complementing recent work done for the latter in Cavaliere, Rahbek and Taylor [ Econometric Reviews (2014) forthcoming], we establish the asymptotic properties of the procedures based on information criteria in the presence of heteroskedasticity (conditional or unconditional) of a quite general and unknown form. The relative finite‐sample properties of the different methods are investigated by means of a Monte Carlo simulation study. For the simulation DGPs considered in the analysis, we find that the BIC‐based procedure and the bootstrap sequential test procedure deliver the best overall performance in terms of their frequency of selecting the correct co‐integration rank across different values of the co‐integration rank, sample size, stationary dynamics and models of heteroskedasticity. Of these, the wild bootstrap procedure is perhaps the more reliable overall as it avoids a significant tendency seen in the BIC‐based method to over‐estimate the co‐integration rank in relatively small sample sizes.