Lag-cointegration Analysis Of Multivariate Time Series

Generally speaking, a large number of empirical researches on macro-economics and finance-economics are taken in time series, and nonstationarity has already been general characteristic of many time series in macro-economics and finance-economics. There are three approaches that can transform nonstationary time series into stationary time series. One approach is to take function item such as trend item and period item from the expression of time series. One approach is to make difference to time series. The other approach is to build the cointegration relation between self and other time series. With an introduction to cointegration, Granger proposed that we should construct the stationary relationship among nonstationary random variables in the macro-economics models, and its result is rational in statistics. The suggestion has radically changed the mode of forming macro-economics experience models.However the discussion about the traditional cointegration has a common trait, whether it is over integration component, fractional integration, linear cointegration or nonlinear cointegration. It only refers to vector series in the same period, not vector series in the different period. The cointegration test would be refused for the variables in the same period, or through their cointegration exists, the fitting result would be not good. Finally we couldn't yet reveal the long stationary relationship among the variables.Having synthesized multivariate statistic analysis, cointegration analysis and lag analysis of time series, the paper takes analysis of lag cointegration and constructs the synthetical model for multivariate time series system in order to get good forecast and control effect.Finally we build a mixed alert model through multivariate statistic analysis and lag cointegration to forecast the trend of commodity price. In fact the model is much more ascendant than the other models in forecasting, and it can be applied in many fields.