spinar_penal_val {spINAR}

Validated penalized semiparametric estimation of INAR models

Description

Semiparametric penalized estimation of the autoregressive parameters and the innovation distribution of INAR(p) models, \code{p} \in \{1,2\}. The estimation is conducted by maximizing the penalized conditional likelihood of the model. Included is a possible validation of one or both penalization parameters. If no validation is wanted, the function coincides to the spinar_penal function of this package.

Usage

spinar_penal_val(
  x,
  p,
  validation,
  penal1 = NA,
  penal2 = NA,
  over = NA,
  folds = 10,
  init1 = 1,
  init2 = 1,
  progress = TRUE
)

Arguments

x

[integer]
vector with integer observations.

p

[integer(1)]
order of the INAR model, where \code{p} \in \{1,2\}.

validation

[logical(1)]
indicates whether validation is wanted.

penal1

[numeric(1)]
L_1 penalization parameter. It will be ignored if validation = TRUE and over \in \{"both", "L_1"\}. It is mandatory if validation = FALSE.

penal2

[numeric(1)]
L_2 penalization parameter. It will be ignored if validation = TRUE and over \in \{"both", "L_2"\}. It is mandatory if validation = FALSE.

over

[string(1)]
validation over "both" penalization parameters or only over "L_1" or "L_2". It is mandatory if validation = TRUE, otherwise it will be ignored.

folds

[integer(1)]
number of folds for (cross) validation.

init1

[numeric(1)]
initial value for penal1 in validation. Default value is init1 = 1.

init2

[numeric(1)]
initial value for penal2 in validation. Default value is init2 = 1

progress

[logical(1)]
Should a nice progress bar be shown? Turning it off, could lead to significantly faster calculation. Default is TRUE.

Value

If validation = FALSE, the function returns a vector containing the penalized estimated coefficients \code{alpha}_1,...,\code{alpha}_p and the penalized estimated entries of the pmf \code{pmf}_0, \code{pmf}_1... where \code{pmf}_i represents the probability of an innovation being equal to i.

If validation = TRUE, the function returns a named list, where the first entry contains the penalized estimated coefficients \code{alpha}_1,...,\code{alpha}_p and the penalized estimated entries of the pmf \code{pmf}_0, \code{pmf}_1,... where \code{pmf}_i represents the probability of an innovation being equal to i. The second (and if over = both also the third entry) contain(s) the validated penalization parameter(s).

Examples

# generate data
dat1 <- spinar_sim(n = 50, p = 1, alpha = 0.5,
                   pmf = c(0.3, 0.3, 0.2, 0.1, 0.1))


# penalized semiparametric estimation with validation over L1
spinar_penal_val(x = dat1, p = 1, validation = TRUE, penal2 = 0.1,
                 over = "L1")
# penalized semiparametric estimation with validation over both L1 and L2
spinar_penal_val(x = dat1, p = 1, validation = TRUE, over = "both")