Description Usage Arguments Details Value Note Author(s) References Examples

Fits an error correction model for univriate response.

1 |

`y` |
a response of a numeric vector or univariate time series. |

`X` |
an exogenous input of a numeric vector or a matrix for multivariate time series. |

`output` |
a logical value indicating to print the results in R console.
The default is |

An error correction model captures the short term relationship between the
response `y`

and the exogenous input variable `X`

. The model is defined as

*dy[t] = bold{β}[0]*dX[t] + β[1]*ECM[t-1] + e[t],*

where *d* is an operator of the first order difference, i.e.,
*dy[t] = y[t] - y[t-1]*, and *bold{β}[0]* is a coefficient vector with the
number of elements being the number of columns of `X`

(i.e., the number
of exogenous input variables), and* ECM[t-1] = y[t-1] - hat{y}[t-1]* which is the
main term in the sense that its coefficient *β[1]* explains the short term
dynamic relationship between `y`

and `X`

in this model, in which *hat{y}[t]* is estimated from the linear regression model
*y[t] = bold{α}*X[t] + u[t]*. Here, *e[t]* and *u[t]* are both error terms
but from different linear models.

An object with class "`lm`

", which is the same results of `lm`

for
fitting linear regression.

Missing values are removed before the analysis. In the results, `dX`

or
`dX1`

, `dX2`

, ... represents the first difference of each exogenous input
variable `X`

, and `dy`

is the first difference of response `y`

.

Debin Qiu

Engle, Robert F.; Granger, Clive W. J. (1987). Co-integration and error correction:
Representation, estimation and testing. *Econometrica*, 55 (2): 251-276.

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