internally evaluated no need for specification here
control
a list of a number of control parameters for the fitting function penLags()
lags
the number of lags
from.lag
from which lag value to start, the default is zero which means include the original x in the basis
df
use this if you want to fix the degrees of freedom
lambda
use this if you would like to fix the smoothing parameter
start.lambda
initial starting value for lambda
order
the order of the penalty
plot
whether you would like a plot of the data
method
method of fitting if lambda or df are not specified
k
the penally used if method "GAIC" is used
...
for further arguments
Details
The idea of penalised lags is that we use a large amount of lags but we penalised their fitted coefficients and therefore we use few degrees of freedom.
The penally and method of fitting are the same as in the pb() function of gamlss. This function does not do the fitting this is achieved by the function gamlss.la() which uses the function penLags for the fitting
Value
a vector of zeros is returned, endowed with a number of attributes. The vector itself is used in the construction of the model matrix (contributing nothing), while the attributes are needed for the back-fitting algorithms of the additive fit.
Note
Note that an appropriate prior weight is needed in the gamlss fit
Benjamin M. A., Rigby R. A. and Stasinopoulos D.M. (2003) Generalised Autoregressive Moving Average Models. J. Am. Statist. Ass., 98, 214-223.
Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion),
Appl. Statist., 54, part 3, pp 507-554.
Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R.
Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).
Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.
Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.
See Also
penLags
Examples
## the data
dax <- EuStockMarkets[,"DAX"]
plot(dax)
## using a penalised autorgressive model
w <- wlag(dax, lag=20)
m1 <- gamlss(dax~ la(dax, lags=20, order=1, from.lag=1), weights=w)
lines(fitted(m1)~as.numeric(time(dax)), col=2)
wp(m1, ylim.all=1) # not very good model
## Not run:
## Try modelling the variance
m2 <- gamlss(dax~ la(dax, lags=20, order=1, from.lag=1),
sigma.fo=~la(dax^2, lags=10, order=1, from.lag=1), weights=w)
wp(m2, ylim.all=1)# maybe the tails
m3 <- gamlss(dax~ la(dax, lags=20, order=1, from.lag=1),
sigma.fo=~la(dax^2, lags=10, order=1, from.lag=1),
weights=w, family=TF)
wp(m3, ylim.all=1) # better model
plot(m3, ts=TRUE) # autocorrelation OK
## using FTSE to precict DAX
ftse <- EuStockMarkets[,"FTSE"]
# fitting using penLags
l1 <- penLags(dax, ftse, lags=30, plot=TRUE)
# similar model within gamlss
w <- wlag(ftse, lag=30)
g1 <- gamlss(dax~ la(ftse, lags=30, order=1), weights=w)
lines(fitted(m1)~as.numeric(time(dax)))
op <- par(mfrow=c(2,1))
# plotting the fitted coeficints of the AR terms
plot(coef(l1, "AR"), type="h")
plot(coef(g1$mu.coefSmo[[1]])[-1], type="h")
par(op)
g2 <- gamlss(dax~ la(ftse, lags=30, order=1)+la(dax, lags=20, order=1, from.lag=1) , weights=w)
g3 <- gamlss(dax~ la(ftse, lags=30, order=1)+la(dax, lags=20, order=1, from.lag=1) ,
sigma.fo=~la(dax^2, lags=10, order=1, from.lag=1), weights=w)
## End(Not run)