The cointegrated processes Y1t and Y2t are assumed to be in long-term stationary relationship. This sets conditions for a hypothesis that there is a mechanism of adjustment that returns Y1t and Y2t to their long-term relationship in case of their error.
Given below is the general case of the model:
Where:
Yt. Endogenous variable.
Ny. Endogenous variable lag.
x1,t, …, xn,t. Exogenous variables.
Nx. Exogenous variable lag.
ut. Standard error.
ck, al, dl,k, γ. Estimated coefficients of error correction model.
cCI. Cointegration equation constant.
cExog. Trend in source data (in autoregression).
The analyzed model may contain a non-zero average, or a trend. Cointegration equations may also contain a constant and a trend.
Denote: 
The following model types may exist:
A model with no trend in autoregression, and no constant in cointegration equation:
A model with no trend in autoregression, and with constant in cointegration equation:
A model with trend in autoregression and constant in cointegration equation:
See also:
Library of Methods and Models | Cointegrated Processes | Vector Error Correction Model | Modeling Container: Error Correction Model | Time Series Analysis: Error Correction Model | IModelling.Ecm | ISmErrorCorrectionModel