gamlss.foreach (version 1.1-6)

fitRolling: 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)

Value

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

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

Author

Mikis Stasinopoulos,

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.

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, tools:::Rd_expr_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, tools:::Rd_expr_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. tools:::Rd_expr_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. tools:::Rd_expr_doi("10.1177/1471082X18759144")

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

See Also

gamlss

Examples

# \donttest{
# 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")
# }