polyDlm | R Documentation |
Applies polynomial distributed lag models with one predictor.
polyDlm(x , y , q , k , show.beta = TRUE)
x |
A vector including the observations of predictor time series. This is not restricted to |
y |
A vector including the observations of dependent time series. This is not restricted to |
q |
An integer representing finite lag length. |
k |
An integer representing order of polynomial distributed lags. |
show.beta |
If |
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}.
The standard function summary()
prints model summary for the model of interest.
model |
An object of class |
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 |
Haydar Demirhan
Maintainer: Haydar Demirhan <haydar.demirhan@rmit.edu.au>
B.H. Baltagi. Econometrics, Fifth Ed. Springer, 2011.
R.C. Hill, W.E. Griffiths, G.G. Judge. Undergraduate Econometrics. Wiley, 2000.
data(seaLevelTempSOI)
model.poly = polyDlm(x = seaLevelTempSOI$LandOcean, y = seaLevelTempSOI$GMSL ,
q = 4 , k = 2 , show.beta = TRUE)
summary(model.poly)
residuals(model.poly)
coef(model.poly)
fitted(model.poly)
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