CEE 4221 Study Guide - Quiz Guide: Independent And Identically Distributed Random Variables, Cointegration, Unit Root
27 May 2016
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One way to get around this problem is to use both first difference and levels terms, e. g. yt = 1 xt + 2(yt-1- xt-1) + ut (2) yt-1- xt-1 is known as the error correction term. Providing that yt and xt are cointegrated with cointegrating coefficient , then (yt-1- xt-1) will be i(0) even though the constituents are i(1). We can thus validly use ols on (2). The granger representation theorem shows that any cointegrating relationship can be expressed as an equilibrium correction model. So what we want to test is the residuals of equation (3) to see if they are non-stationary or stationary. We can use the df / adf test on ut. So we have the regression with vt iid. However, since this is a test on the residuals of an actual model, , then the critical values are changed.
