dLagM (version 1.0.2)

polyDlm: Implement finite polynomial distributed lag model

Description

A function that applies polynomial distributed lag models with one predictor.

Usage

polyDlm(x , y , q , k , show.beta = TRUE , show.summary = TRUE)

Arguments

x

A vector including the observations of predictor time series. This is not restricted to ts objects.

y

A vector including the observations of dependent time series. This is not restricted to ts objects.

q

An integer representing finite lag length.

k

An integer representing order of polynomial distributed lags.

show.beta

If TRUE, generates original beta parameters and associated t-tests and prints the results.

show.summary

If TRUE, prints standard model summary for the model of interest.

Value

model

An object of class lm.

designMatrix

The design matrix composed of transformed z-variables.

designMatrix.x

The design matrix composed of original x-variables.

beta.coefficients

Estimates and t-tests of original beta coefficients. This will be generated if show.beta is set to TRUE.

Details

Finite distributed lag models, in general, suffer from the multicollinearity due to inclusion of the lags of the same variable in the model. To reduce the impact of this multicollinearity, a polynomial shape is imposed on the lag distribution (Judge and Griffiths, 2000). The resulting model is called Polynomial Distributed Lag model or Almond Distributed Lag Model.

Imposing a polynomial pattern on the lag distribution is equivalent to representing \(\beta\) parameters with another $k$th order polynomial model of time. So, the effect of change in \(X_{t-s}\) on the expected value of \(Y_{t}\) is represented as follows:

$$ \frac{\partial E(Y_{t})}{\partial X_{t-s}}=\beta_{s}=\gamma_{0}+\gamma_{1}s+\gamma_{2}s^{2}+\cdots+\gamma_{k}s^{k} $$

where \(s=0,\dots,q\) (Judge and Griffiths, 2000). Then the model becomes:

$$ Y_{t} = \alpha +\gamma_{0}Z_{t0}+\gamma_{1}Z_{t1}+\gamma_{2}Z_{t2}+\cdots +\gamma_{k}Z_{tk} + \epsilon_{t}. $$

References

B.H. Baltagi. Econometrics, Fifth Ed. Springer, 2011.

R.C. Hill, W.E. Griffiths, G.G. Judge. Undergraduate Econometrics. Wiley, 2000.

Examples

# NOT RUN {
data(warming)
model.poly = polyDlm(x = warming$NoMotorVehicles , y = warming$Warming , 
q = 2 , k = 2 , show.beta = TRUE ,  show.summary = TRUE)
# }