tstests (version 1.0.0)

hongli_test: The Non-Parametric Density Test of Hong and Li

Description

Implements the Non-Parametric Density Test of Hong and Li (2005).

Usage

hongli_test(x, lags = 4, conf_level = 0.95, ...)

Value

An object of class “tstest.hongli” which has a print and “as_flextable” method.

Arguments

x

a series representing the PIT transformed actuals given the forecast values.

lags

the number lags to use for testing the joint hypothesis.

conf_level

the confidence level for generating the critical values which serve as thresholds for deciding on the null hypothesis.

...

none.

Details

A novel method to analyze how well a conditional density fits the underlying data is through the probability integral transformation (PIT) discussed in Rosenblatt (1952) and used in the berkowitz_test. Hong and Li (2005) introduced a nonparametric portmanteau test, building on the work of Ait-Sahalia (1996), which tests the joint hypothesis of i.i.d and uniformity for a series of PIT transformed data. To achieve this, it tests for misspecification in the conditional moments of the model transformed standardized residuals, and is distributed as N(0, 1) under the null of a correctly specified model. These moment tests are reported as ‘M(1,1)’ to ‘M(4,4)’ in the output, with ‘M(1,2)’ related to ARCH-in-mean effects, and ‘M(2,1)’ to leverage, while ‘W’ is the Portmanteu type test statistic for general misspecification (using p lags) and also distributed as N(0, 1) under the null of a correctly specified model. Only upper tail critical values are used in this test. The interested reader is referred to the paper for more details.

References

Hong2005tstests

Examples

library(tsdistributions)
data(garch_forecast)
x <- pdist('jsu', q = garch_forecast$actual, mu = garch_forecast$forecast,
sigma = garch_forecast$sigma, skew = garch_forecast$skew,
shape = garch_forecast$shape)
print(hongli_test(x), include.decision = TRUE)