fitRolling {gamlss.foreach}

Function to Fit Rolling Regression in gamlss

Description

Rolling regression is common in time series analysis when one step ahead forecasts is required. The function fitRolling() works as follows: A model is fitted first to the whole data set using gamlss(). Then the function fitRolling() can be used. The function uses a fixed size rolling widow i.e. 365 days. The model is refitted repeatedly for the different windows over time (like a local regression in smoothing). Each time one step ahead forecast of distribution parameters are saved together with the prediction global deviance. The result is presented as a matrix with time as rows and parameters and the prediction deviance as columns.

Usage

fitRolling(obj, data, window = 365, as.time = NULL)

Arguments

obj

a gamlss fitted model

data

the original data of the fitted model

window

the number of observation to include in the window (typically this will be a year)

as.time

if a column indicating time exist in the data set this can be specified here

Details

If the total observations are N and the window size n then we will need N-n different fits. The parallelization of the fits is achieved using the function foreach() from the package foreach.

Value

Returns a matrix containing as columns the one ahead prediction parameters of the distribution as well as the prediction global deviance.

Note

Do not forget to use registerDoParallel(cores = NUMBER) or cl <- makeCluster(NUMBER) and registerDoParallel(cl) before calling the function fitRolling() and closeAllConnections() after the fits. Where NUMBER depends on the machine used.

Author(s)

Mikis Stasinopoulos, [e-mail]

References

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.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC, doi:10.1201/9780429298547. An older version can be found in https://www.gamlss.com/.

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, doi:10.18637/jss.v023.i07.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC. doi:10.1201/b21973

Stasinopoulos, M. D., Rigby, R. A., and De Bastiani F., (2018) GAMLSS: a distributional regression approach, Statistical Modelling, Vol. 18, pp, 248-273, SAGE Publications Sage India: New Delhi, India. doi:10.1177/1471082X18759144

(see also https://www.gamlss.com/).

See Also

gamlss

Examples

# fitting the aids data 45 observations
m1 <- gamlss(formula = y ~ pb(x) + qrt, family = NBI, data = aids) 
# get rolling regression with a window of 30
# there are 45-40=15 fits to do
# declaring cores (not needed for small data like this)
registerDoParallel(cores = 2)
FF <- fitRolling(m1, data=aids, window=30)
FF
stopImplicitCluster()
# check the first prediction
m30_1 <-update(m1, data=aids[1:30,])
predictAll(m30_1, newdata=aids[31,],output="matrix")
FF[1,]
# plot all the data 
plot(y~x, data=aids, xlim=c(0,45), ylim=c(0, 700), col=gray(.8))
# the first 30 observations
points(y~x, data=aids[1:30,], xlim=c(0,45))
# One step ahead forecasts
lines(FF[,"mu"]~as.numeric(rownames(FF)), col="red")
lines(fitted(m1)~aids$x, col="blue")