GAS (version 0.1.1)

PIT_test: Goodness of Fit for Conditional Densities

Description

This function implements density goodness of fit procedure of Diebold et al. (1998).

Usage

PIT_test(U, G=20, alpha=0.05, plot=F)

Arguments

U

numeric vector of Probability Integral Transformation.

G

numeric number of bins of the empirical cumulative density function of the PIT.

alpha

numeric. test confidence level.

plot

boolean. Plot the result ?.

Value

list with elements: (i) Hist and (ii) IID. The fist element Hist concerns the test of the unconditional assumption of uniformity of the PIT, it is a list with elements:

• test: statistic test.
• crit: The critical value of the test.
• pvalue: the pvalue of the test.
• hist : the histogram, evaluated using the hist function.
• confidence : approximated asymptotic confidence level.

The second element IID concerns the iid assumption, it is a list with elements:

• test: a named numeric vector with elements: test1, test2, test3, test4 representing the Lagrange Multiplier test for the first four conditional moments of the PITs.
• crit: The critical value of the test.
• pvalue: a named numeric vector with elements: pvalue1, pvalue2, pvalue3, pvalue3 representing the pvalues of the Lagrange Multiplier test for the first four conditional moments of the PITs.

Details

This function implements density goodness of fit procedure of Diebold et al. (1998). The test relays on the result that, if the series of estimated conditional distributions is the true one, then the PIT series evaluated accordingly are iid Unif(0, 1) distributed. The test of the iid Uniform(0, 1) assumption consists of two parts. The first part concerns the independent assumption, and it tests if all the conditional moments of the data, up to the fourth one, have been accounted for by the model, while the second part checks if the conditional distribution assumption is reliable by testing if the PITs are Uniform over the interval (0, 1). See also Jondeau and Rockinger (2006) and Vlaar and Palm (1993).

References

Diebold, F. X., Gunther, T. A., & Tay, A. S. (1998). Evaluating Density Forecasts with Applications to Financial Risk Management. International Economic Review, 863-883.

Jondeau, E., & Rockinger, M. (2006). The copula-garch model of conditional dependencies: An international stock market application. Journal of international money and finance, 25(5), 827-853.

Vlaar, P. J., & Palm, F. C. (1993). The message in weekly exchange rates in the European monetary system: mean reversion, conditional heteroscedasticity, and jumps. Journal of Business & Economic Statistics, 11(3), 351-360.

Examples

data("StockIndices")

GASSpec = UniGASSpec(Dist = "std", ScalingType = "Identity",
                     GASPar = list(location = FALSE, scale = TRUE,
                                   shape = FALSE))

FTSEMIB = StockIndices[, "FTSEMIB"]

Fit = UniGASFit(GASSpec, FTSEMIB)

U = pit(Fit)

Test = PIT_test(U, G=20, alpha=0.05, plot=TRUE)