The Non-Parametric Density Test of Hong and Li
Implements the Non-Parametric Density Test of Hong and Li (2005).
hongli_test(x, lags = 4, conf_level = 0.95, ...)
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.An object of class tstest.hongli which has a print and as_flextable method.
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.
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)
\insertRef Hong2005tstests