LFL: LFL-MBB optimal block lenght selection algorithm
In matheusbarroso/dboot: Dependent Bootstrap package

Description Usage Arguments Details Value Note Author(s) References Examples

This functions performs the data-based algorithm of Lahiri, Furukawa and Lee (2005), henceforth LFL, for the selection of optimal block length sizes in the case of block bootstrap of Kunsch (1989).

LFL(data, statistic, R = 100L, nsteps = 5L, l.init = NULL,
  type.optm = 0, type.est = "bias.variance", ran.gen = function(tser,
  n.sim, args) tser, ran.args = NULL, allow.parallel = TRUE, seed = 123,
  packages = NULL, export = NULL, ...)

`data`	A univariate or multivariate time series. It might be vector, matrix or data frame to be passed to statistic.
`statistic`	A function which when applied to data returns a vector containing the statistic of interest. Each time statistic is called it is passed a time series of length n which is of the same class as the original tseries. Any other arguments which statistic takes must remain constant for each bootstrap replicate and should be supplied through the . . . argument to tsboot.
`R`	A positive integer giving the number of bootstrap replicates required. The default value is 100.
`nsteps`	A positive integer with the number of steps (iterations) in the HHJ algorithm. The default value is 5.
`l.init`	A positive integer smaller then the number of observations (n.obs.) in `data` (i.e. the length of the time series), indicating the size of the subset in the LFL algorithm. The default value is 'default', in which m.init = round(c1n.obs.^(1/(r+4)))*
`type.optm`	0 for mean of the parameters vector or a positive integer giving the index of the desired parameter to optimize in the same order as provided by statistic. For more details see the section "Details" bellow.#'
`type.est`	A character describing the type of estimation being undertaken. Accepted values are: "bias.variance" and "distribution.quantile". The default value is 'bias.variance'.
`ran.gen`	This is a function of three arguments. The first argument is a time series, it is the result of selecting `n.sim` observations from `tseries` by some scheme and converting the result back into a time series of the same form as `tseries` (with length `n.sim`). The second argument to `ran.gen` is always the value `n.sim`, and the third argument is `ran.args`, which is used to supply any other objects needed by `ran.gen`.
`ran.args`	This will be supplied to `ran.gen` each time it is called. If `ran.gen` needs any extra arguments then they should be supplied as components of `ran.args`. Multiple arguments may be passed by making `ran.args` a list. If `ran.args` is `NULL` then it should not be used within `ran.gen` but note that `ran.gen` must still have its third argument.
`allow.parallel`	Logical TRUE/FALSE indicating whether parallel computation via the foreach package should be used. The default value is TRUE. OBS:paralllel backend must be registered prior to calling HHJ.
`seed`	Numeric, the seed to `set.seed()` for replicable examples.
`packages`	If `allow.parallel = TRUE`. A character vector with the lisf of packages required by `statisitc`.
`export`	If `allow.parallel = TRUE`. A character vector with the lisf of objects (functions, etc...) required by `statisitc`.
`...`	Extra argumetns to `statistic` may be supplied here. Beware of partial matching to the arguments of `tsboot2`.

This functions implements the iterative version of the Lahiri, Furukawa and Lee (2005) algorithm. Here some modifications are implemented in the fashion of Barroso (2017). Namely, a vectorized algorithm is implemented where the user might supply which parameter to optimize over or use a default value. The default value is obtained by minimizin the mean MSE vector (if a vector or parameters is returned by statistic). For the MBB step the tsboot2,a modification of the tsboot function from the boot package, is used.

A dataframe, the first column for the iteration step the second and third for the estimated optimal block length.

For bugs and further requests please refer to https://github.com/matheusbarroso/dboot

Matheus de Vasconcellos Barroso

Kunsch, Hans R. 1989. The Jakknife and the Bootstrap For General Stationary Observations. The Annals of Statistics. 1989, Vol. 17, 3, pp. 1217-1241.

Lahiri, Soumendra, Furukawa, Kyoji and Lee, Yd. 2007. A nonparametric plug-in rule for selecting optimal block lengths for block bootstrap methods. Statistical Methodology. July, 2007, Vol. 4, 3, pp. 292-321.

Barroso, Matheus de V. 2018. BOOTSTRAP METHODS FOR GENERALIZED AUTOREGRESSIVE MOVING AVERAGE MODELS

## Not run: 
library(dboot)
library(gamlss)
library(doParallel)
no_cores <- if(detectCores()==1) 1 else detectCores() -1
registerDoParallel(no_cores)
bootf <- function (db,ord,fam) {
 fit2 <- garmaFit2(yt~x-1,data=db,order=ord,family=fam,tail=0,control=list(iter.max=1000))
 return(fit2$coef)}
ord <- c(1,1) ; fam="GA"
db <- example_LFL

LFL(db,bootf,ord=ord,fam=fam,export=c("garmaFit2"),package=c("gamlss"))
## End(Not run)