ardl {ARDL}

ARDL model regression

Description

A simple way to construct complex ARDL specifications providing just the model order additional to the model formula. It uses dynlm under the hood. ardl is a generic function and the default method constructs an 'ardl' model while the other method takes a model of class 'uecm' and converts in into an 'ardl'.

Usage

ardl(...)

## S3 method for class 'uecm'
ardl(object, ...)

## Default S3 method:
ardl(formula, data, order, start = NULL, end = NULL, ...)

Arguments

...

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

object

An object of class 'uecm'.

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 ARDL model. 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.

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.

Value

ardl returns an object of class c("dynlm", "lm", "ardl"). In addition, attributes 'order', 'data', 'parsed_formula' and 'full_formula' are provided.

Mathematical Formula

The general form of an ARDL(p,q_{1},\dots,q_{k}) is:

y_{t} = c_{0} + c_{1}t + \sum_{i=1}^{p}b_{y,i}y_{t-i} + \sum_{j=1}^{k}\sum_{l=0}^{q_{j}}b_{j,l}x_{j,t-l} + \epsilon_{t}

Author(s)

Kleanthis Natsiopoulos, [e-mail]

See Also

uecm, recm

Examples

data(denmark)

## Estimate an ARDL(3,1,3,2) model -------------------------------------

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

## Add dummies or other variables that should stay fixed ---------------

d_74Q1_75Q3 <- ifelse(time(denmark) >= 1974 & time(denmark) <= 1975.5, 1, 0)

# the date can also be setted as below
d_74Q1_75Q3_ <- ifelse(time(denmark) >= "1974 Q1" & time(denmark) <= "1975 Q3", 1, 0)
identical(d_74Q1_75Q3, d_74Q1_75Q3_)
den <- cbind(denmark, d_74Q1_75Q3)
ardl_3132_d <- ardl(LRM ~ LRY + IBO + IDE | d_74Q1_75Q3,
                    data = den, order = c(3,1,3,2))
summary(ardl_3132_d)
compare <- data.frame(AIC = c(AIC(ardl_3132), AIC(ardl_3132_d)),
                      BIC = c(BIC(ardl_3132), BIC(ardl_3132_d)))
rownames(compare) <- c("no dummy", "with dummy")
compare

## Estimate an ARDL(3,1,3,2) model with a linear trend -----------------

ardl_3132_tr <- ardl(LRM ~ LRY + IBO + IDE + trend(LRM),
                     data = denmark, order = c(3,1,3,2))

# Alternative time trend specifications:
# time(LRM)                 1974 + (0, 1, ..., 55)/4 time(data)
# trend(LRM)                (1, 2, ..., 55)/4        (1:n)/freq
# trend(LRM, scale = FALSE) (1, 2, ..., 55)          1:n

## Subsample ARDL regression (start after 1975 Q4) ---------------------

ardl_3132_sub <- ardl(LRM ~ LRY + IBO + IDE, data = denmark,
                      order = c(3,1,3,2), start = "1975 Q4")

# the date can also be setted as below
ardl_3132_sub2 <- ardl(LRM ~ LRY + IBO + IDE, data = denmark,
                       order = c(3,1,3,2), start = c(1975,4))
identical(ardl_3132_sub, ardl_3132_sub2)
summary(ardl_3132_sub)

## Ease of use ---------------------------------------------------------

# The model specification of the ardl_3132 model can be created as easy as order=c(3,1,3,2)
# or else, it could be done using the dynlm package as:
library(dynlm)
m <- dynlm(LRM ~ L(LRM, 1) + L(LRM, 2) + L(LRM, 3) + LRY + L(LRY, 1) + IBO + L(IBO, 1) +
           L(IBO, 2) + L(IBO, 3) + IDE + L(IDE, 1) + L(IDE, 2), data = denmark)
identical(m$coefficients, ardl_3132$coefficients)

# The full formula can be extracted from the ARDL model, and this is equal to
ardl_3132$full_formula
m2 <- dynlm(ardl_3132$full_formula, data = ardl_3132$data)
identical(m$coefficients, m2$coefficients)

## Post-estimation testing ---------------------------------------------

# See examples in the help file of the uecm() function