MSGARCH (version 0.17.7)

pit: Probability Integral Transform.

Description

Method returning the predictive probability integral transform (PIT) in-sample or of a vector of points at t = T + 1.

Usage

pit(object, x, theta, y, do.norm = FALSE, do.its = FALSE)

Arguments

object

Model specification of class MSGARCH_SPEC created with create.spec or fit object of type MSGARCH_MLE_FIT created with fit.mle or MSGARCH_BAY_FIT created with fit.bayes.

x

Vector (of size N) of point at t = T + 1 to be evaluated (used when do.its = FALSE).

theta

Vector (of size d) or matrix (of size M x d) of parameter estimates (not require when using a fit object).

y

Vector (of size T) of observations (not require when using a fit object).

do.norm

Boolean indicating if the PIT value are transforms into standard Normal variate. (Default: do.norm = FALSE).

do.its

Boolean indicating if the in-sample pit is returned. (Default: do.its = FALSE)

Value

A list of class MSGARCH_PIT containing two components:

• pit: If do.its = FALSE: probability integral transform of the points x at t = T + 1 or Normal variate derived from the probability integral transform of x (vector of size N). If do.its = TRUE: In-sample probability integral transform or Normal variate derived from the probability integral transform of y (vector of size T or matrix of size M x T).
• x: If do.its = FALSE: Vector (of size N) of at point t = T + 1 evaluated. If do.its = TRUE: Vector (of size T) of observations.

The class MSGARCH_PIT contains the plot method only if do.its = FALSE.

Details

If a matrix of MCMC posterior draws estimates is given, the Bayesian probability integral transform is calculated. If do.its = FALSE, the points x are evaluated as t = T + 1 realization and the method uses the variance estimate at t = T + 1. If do.its = TRUE, y is evaluated using their respective variance estimate at each time t. The do.norm argument transforms the PIT value into Normal variate so that normality test can be done.

Examples

# load data
data("sp500")
sp500 = sp500[1:1000]

# create model specification
spec = MSGARCH::create.spec() 

# fit the model on the data with ML estimation using DEoptim intialization
set.seed(123)
fit = MSGARCH::fit.mle(spec = spec, y = sp500, ctr = list(do.init = FALSE))

# run pit method in-sample              
pit.its = MSGARCH::pit(object = fit, do.norm = FALSE, do.its = TRUE)                              

plot(pit.its)  
                                                                         
# generate random draws at T + 1 from model
set.seed(123)
sim.ahead = MSGARCH::simahead(object = fit, n = 1, m = 100)

x = sim.ahead$draws

# run pit method on random draws at T + 1 from model
pit = MSGARCH::pit(object = fit, x = x, do.norm = FALSE)

plot(pit)