HHJ: HHJ-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 Hall, Horowitz and Jing (1995), henceforth HHJ, for the selection of optimal block length sizes in the case of block bootstrap of Kunsch (1989).

HHJ(data, statistic, R = 100L, nsteps = 5L, type.est = "bias.variance",
  type.optm = 0, ran.gen = function(tser, n.sim, args) tser,
  ran.args = NULL, allow.parallel = TRUE, errorhandling = "try",
  n.try = 5L, m.init = "default", type.sub.blocks = "fast", 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.
`type.est`	A character describing the type of estimation being undertaken. Accepted values are: 'bias.variance', 'one.sided.distribution' and 'two.sided.distribution'. The default value is 'bias.variance'.
`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.
`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.
`errorhandling`	A character, accepted values are 'try' and 'pass'.
`n.try`	A positive integer indicating the maximum number of tries if errorhandling='try'. The default value is 3.
`m.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 HHJ algorithm. The default value is 'default', in which `m.init=round(n.obs.^(1/3))`
`type.sub.blocks`	A character, accepted values are: 'fast' and 'complete', the former implements a sampling scheme in the subsets of `m (or m.init)`, where only three subsets lengths are evaluated. In the latter all subsets lenghts are evaluated. For a large dataset the option 'complete' might take too long. For more details see the section "Details" bellow.
`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 Hall, Horowitz and Jing (1995) 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 tsboot function from the boot package is used. Additionaly, with the argument type.sub.blocks the user might use a sampling sche on the subsets of m.init. There is one sample from the quantile 1/3, another for the 2/3 and the last one for the 1/3-2/3.

A dataframe, the first column for the iteration step and the second 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.

Hall, P., Horowitz, J. L e Jing, B-Y. 1995. On blocking rules for the bootstrap with dependent data. Biometrika. 82, 1995, pp. 561-574.

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

## Not run: 
library(gamlss)
library(dboot)
db <- example_HHJ
fam <- "PO"
ord <- c(0,1)

library(doParallel)
no_cores <- if(detectCores()==1) 1 else detectCores() -1
registerDoParallel(no_cores)

HHJ(db,bootf,R = 10,nsteps=1,ord=ord,fam=fam,
export=c("garmaFit2"), packages=c("gamlss"))

HHJ(db,bootf,R = 10, errorhandling="pass",ord=ord,seed=124
fam=fam,export=c("garmaFit2"),  packages=c("gamlss"),n.try=3)

HHJ(db,bootf,R = 10,nsteps=2,ord=ord,fam=fam,
export=c("garmaFit2"),  packages=c("gamlss"),n.try=2)

HHJ(db,bootf,R = 10,nsteps=1,ord=ord,fam=fam,
export=c("garmaFit2"), packages=c("gamlss"),type.sub.blocks="complete")

HHJ(db,bootf,R = 10,nsteps=2,ord=ord,fam=fam,
export=c("garmaFit2"),  packages=c("gamlss"),type.optm=2)

HHJ(db,bootf,R = 10,nsteps=3,ord=ord,fam=fam,
export=c("garmaFit2"), packages=c("gamlss"),m.init=6)

HHJ(db,bootf,R = 10,nsteps=1,ord=ord,fam=fam,
export=c("garmaFit2"), packages=c("gamlss"),m.init=6,allow.parallel=FALSE)

## End(Not run)