2.2.4 ECM
If the time series is co-integrated, an ECM can be constructed. This model describes the long-term equilibrium and short-term fluctuations between variables and the modeling steps are as follows:
The first step is to perform a co-integration regression to the variables:
, (8)
to obtainingk 0、k 1、k 2 and the residual sequence ut ;
(9)
The second step is to make ecm (-1) =ut -1 as an error correction term and substitute the error correction model:
(10)
In the formula,is a constant term,andare the coefficients of the difference terms of each variable, which reflects the short-term dynamic changes of the model; ecm (-1) is an error correction term, which reflects the degree to which the former term deviates from the long-term equilibrium in short-term fluctuations; φ is the correction coefficient, also called the adjustment speed, usually a negative value;εt is a white noise sequence.