ARDL (version 0.2.3)

uecm: Unrestricted ECM regression

Description

uecm is a generic function used to construct Unrestricted Error Correction Models (UECM). The function invokes two different methods. The default method works exactly like ardl. The other method requires an object of class 'ardl'. Both methods create the conditional UECM, which is the UECM of the underlying ARDL.

Usage

uecm(...)
# S3 method for ardl
uecm(object, ...)
# S3 method for default
uecm(formula, data, order, start = NULL, end = NULL, ...)

Value

uecm returns an object of class

c("dynlm", "lm", "uecm"). In addition, attributes 'order', 'data', 'parsed_formula' and 'full_formula' are provided.

Arguments

...

Additional arguments to be passed to the low level regression fitting functions.

object

An object of class 'ardl'.

formula

A "formula" describing the linear model. Details for model specification are given under 'Details'.

data

A time series object (e.g., "ts", "zoo" or "zooreg") or a data frame containing the variables in the model. In the case of a data frame, it is coerced into a ts object with start = 1, end = nrow(data) and frequency = 1. If not found in data, the variables are NOT taken from any environment.

order

A specification of the order of the underlying ARDL model (e.g., for the UECM of an ARDL(1,0,2) model it should be order = c(1,0,2)). A numeric vector of the same length as the total number of variables (excluding the fixed ones, see 'Details'). It should only contain positive integers or 0. An integer could be provided if all variables are of the same order.

start

Start of the time period which should be used for fitting the model.

end

End of the time period which should be used for fitting the model.

Mathematical Formula

The formula of an Unrestricted ECM conditional to an \(ARDL(p,q_{1},\dots,q_{k})\) is: $$\Delta y_{t} = c_{0} + c_{1}t + \pi_{y}y_{t-1} + \sum_{j=1}^{k}\pi_{j}x_{j,t-1} + \sum_{i=1}^{p-1}\psi_{y,i}\Delta y_{t-i} + \sum_{j=1}^{k}\sum_{l=1}^{q_{j}-1} \psi_{j,l}\Delta x_{j,t-l} + \sum_{j=1}^{k}\omega_{j}\Delta x_{j,t} + \epsilon_{t}$$ $$\psi_{j,l} = 0 \;\; \forall \;\; q_{j} \leq 1, \;\;\;\;\; \psi_{y,i} = 0 \;\; if \;\; p = 1$$ In addition, \(x_{j,t-1}\) and \(\Delta x_{j,t}\) cancel out becoming \(x_{j,t} \;\; \forall \;\; q_{j} = 0\)

Author

Kleanthis Natsiopoulos,

Details

The formula should contain only variables that exist in the data provided through data plus some additional functions supported by dynlm (i.e., trend()).

You can also specify fixed variables that are not supposed to be lagged (e.g. dummies etc.) simply by placing them after |. For example, y ~ x1 + x2 | z1 + z2 where z1 and z2 are the fixed variables and should not be considered in order. Note that the | notion should not be confused with the same notion in dynlm where it introduces instrumental variables.

See Also

ardl recm

Examples

data(denmark)

## Estimate the UECM, conditional to it's underlying ARDL(3,1,3,2) -----

# Indirectly
ardl_3132 <- ardl(LRM ~ LRY + IBO + IDE, data = denmark, order = c(3,1,3,2))
uecm_3132 <- uecm(ardl_3132)

# Directly
uecm_3132_ <- uecm(LRM ~ LRY + IBO + IDE, data = denmark, order = c(3,1,3,2))
identical(uecm_3132, uecm_3132_)
summary(uecm_3132)