The vector error correction index model: representation, estimation and identification
将多元指数自回归模型扩展到(1,1)阶协整时间序列，提出向量误差修正指数模型(VECIM)，通过少量指数驱动变量差分，实现维度大幅缩减，并分解冲击为永久和暂时成分。
Summary This paper extends the multivariate index autoregressive model to the case of cointegrated time series of order (1,1). In this new modelling, namely the vector error-correction index model (VECIM), the first differences of series are driven by some linear combinations of the variables, namely the indexes. When the indexes are significantly fewer than the variables, the VECIM achieves a substantial dimension reduction with reference to the vector error correction model. We show that the VECIM allows one to decompose the reduced-form errors into sets of common and uncommon shocks, and that the former can be further decomposed into permanent and transitory shocks. Moreover, we offer a switching algorithm for optimal estimation of the VECIM. Finally, we document the practical value of the proposed approach by both simulations and an empirical application, where we search for the shocks that drive the aggregate fluctuations at different frequency bands in the US.