当测试co-integrations,恩格尔格兰杰首次提出了两步方法:第一步是测试是否名义汇率和相对价格水平都是集成的一个。第二步,如果两个变量都是我(1)过程,然后测试是否回归的残差(3 – 5)是固定的。应该是我(0)和固定是否存在协整关系,然后购买力平价条件。
Relative purchasing power parity may overcome these problems, the relative purchasing power parity refers to the movements of exchange rate between the two countries are equal to the level of relative price changes, formally:Co-integration technique was originally proposed by Engel and Granger (1987) and expanded and improved by many people. Although the concept of long term PPP means that short term exchange rate can deviate from the equilibrium level, only when such deviation (the real exchange rate ) is stationary, the long-term PPP will hold. If there exists a stationary series indicating a linear relationship between two time series which are both integrated of order one, then there is co-integration relationship between the two time series. At this point the non-stationarity of one series can be fully offset by the other series, so the long-term relationship can be established between these two serious. If the nominal exchange rate and relative price levels have a stationary, invertible, non-deterministic ARMA expression after d time’s differentials, we can say that they are integrated of order d, or I (d). If the real exchange rate is random walk process, then there is a linear combinationis usually an I (d) process. Conversely, if PPP holds, then there exists parameter which makes the above combination a stationary process.
When testing co-integrations, Engel and Granger first proposed a two-step method: The first step is to test whether the nominal exchange rate and relative price level are both integrated of order one. The second step, if the two variables are both I (1) process, then test whether the residuals of regression (3-5) are stationary. should be I(0) and stationary if there is a co-integration relationship between and , and then PPP condition holds.