PredPdf function

Predictive density.

Method returning the predictive density (pdf).

PredPdf(object, ...)

## S3 method for class 'MSGARCH_SPEC'
PredPdf(
  object,
  x = NULL,
  par = NULL,
  data = NULL,
  log = FALSE,
  do.its = FALSE,
  nahead = 1L,
  do.cumulative = FALSE,
  ctr = list(),
  ...
)

## S3 method for class 'MSGARCH_ML_FIT'
PredPdf(
  object,
  x = NULL,
  newdata = NULL,
  log = FALSE,
  do.its = FALSE,
  nahead = 1L,
  do.cumulative = FALSE,
  ctr = list(),
  ...
)

## S3 method for class 'MSGARCH_MCMC_FIT'
PredPdf(
  object,
  x = NULL,
  newdata = NULL,
  log = FALSE,
  do.its = FALSE,
  nahead = 1L,
  do.cumulative = FALSE,
  ctr = list(),
  ...
)

Arguments

• object: Model specification of class MSGARCH_SPEC created with CreateSpec

  or fit object of type MSGARCH_ML_FIT created with FitML or MSGARCH_MCMC_FIT

  created with FitMCMC.

• ...: Not used. Other arguments to PredPdf.

• x: Vector (of size n). Used when do.its = FALSE.

• par: Vector (of size d) or matrix (of size nmcmc x d) of parameter estimates where d must have the same length as the default parameters of the specification.

• data: Vector (of size T) of observations.

• log: Logical indicating if the log-density is returned. (Default: log = FALSE)

• do.its: Logical indicating if the in-sample predictive is returned. (Default: do.its = FALSE)

• nahead: Scalar indicating the number of step-ahead evaluation. Valid only when do.its = FALSE. (Default: nahead = 1L)

• do.cumulative: Logical indicating if predictive density is computed on the cumulative simulations (typically log-returns, as they can be aggregated). Only available for do.its = FALSE. (Default: do.cumulative = FALSE)

• ctr: A list of control parameters:

  • nsim (integer >= 0) : Number indicating the number of simulation done for the evaluation of the density at nahead > 1. (Default: nsim = 10000L)

• newdata: Vector (of size T*) of new observations. (Default newdata = NULL)

Returns

A vector or matrix of class MSGARCH_PRED.

If do.its = FALSE: (Log-)predictive of the points x at t = T + T* + 1, ... ,t = T + T* + nahead (matrix of size nahead x n).

If do.its = TRUE: In-sample predictive of data if x = NULL

(vector of size T + T*) or in-sample predictive of x (matrix of size (T + T*) x n).

Details

If a matrix of MCMC posterior draws is given, the Bayesian predictive probability density is calculated. Two or more step-ahead predictive probability density are estimated via simulation of nsim paths up to t = T + T* + nahead. The predictive distribution are then inferred from these simulations via a Gaussian Kernel density. If do.its = FALSE, the vector x are evaluated as t = T + T* + 1, ... ,t = T + T* + nahead

realization.

If do.its = TRUE and x is evaluated at each time t up top time t = T + T*.

Finally, if x = NULL the vector data is evaluated for sample evaluation of the predictive denisty ((log-)likelihood of each sample points).

Examples

# create model specification
spec <- CreateSpec()

# load data
data("SMI", package = "MSGARCH")

# fit the model on the data by ML
fit <- FitML(spec = spec, data = SMI)

# run PredPdf method in-sample
pred.its <- PredPdf(object = fit, log = TRUE, do.its = TRUE)

# create a mesh
x <- seq(-3,3,0.01)

# run PredPdf method on mesh at T + 1
pred.x <- PredPdf(object = fit, x = x, log = TRUE, do.its = FALSE)