ghyp: lik.ratio.test – R documentation

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lik.ratio.test

Likelihood-ratio test

Description

This function performs a likelihood-ratio test on fitted generalized hyperbolic distribution objects of class mle.ghyp.

Usage

lik.ratio.test(x, x.subclass, conf.level = 0.95)

Arguments

`x`	An object of class `mle.ghyp`.
`x.subclass`	An object of class `mle.ghyp` whose parameters form a subset of those of `x`.
`conf.level`	Confidence level of the test.

Details

The likelihood-ratio test can be used to check whether a special case of the generalized hyperbolic distribution is the “true” underlying distribution.

The likelihood-ratio is defined as

Lambda = (sup{L(theta | X) : theta in Theta_0})/ (sup{L(theta | X) : theta in Theta}).

Where L denotes the likelihood function with respect to the parameter θ and data X, and Θ_0 is a subset of the parameter space Θ. The null hypothesis H0 states that θ \in Θ_0. Under the null hypothesis and under certain regularity conditions it can be shown that -2 \log(Λ) is asymtotically chi-squared distributed with ν degrees of freedom. ν is the number of free parameters specified by Θ minus the number of free parameters specified by Θ_0.

The null hypothesis is rejected if -2 \log(Λ) exceeds the conf.level-quantile of the chi-squared distribution with ν degrees of freedom.

Value

A list with components:

`statistic`	The value of the L-statistic.
`p.value`	The p-value for the test.
`df`	The degrees of freedom for the L-statistic.
`H0`	A boolean stating whether the null hypothesis is `TRUE` or `FALSE`.

Author(s)

David Luethi

References

Linear Statistical Inference and Its Applications by C. R. Rao
Wiley, New York, 1973

Examples

data(smi.stocks)

  sample <- smi.stocks[, "SMI"]

  t.symmetric <- fit.tuv(sample, silent = TRUE, symmetric = TRUE)
  t.asymmetric <- fit.tuv(sample, silent = TRUE)

  # Test symmetric Student-t against asymmetric Student-t in case
  # of SMI log-returns
  lik.ratio.test(t.asymmetric, t.symmetric, conf.level = 0.95)
  # -> keep the null hypothesis

  set.seed(1000)
  sample <- rghyp(1000, student.t(gamma = 0.1))

  t.symmetric <- fit.tuv(sample, silent = TRUE, symmetric = TRUE)
  t.asymmetric <- fit.tuv(sample, silent = TRUE)

  # Test symmetric Student-t against asymmetric Student-t in case of
  # data simulated according to a slightly skewed Student-t distribution
  lik.ratio.test(t.asymmetric, t.symmetric, conf.level = 0.95)
  # -> reject the null hypothesis

  t.symmetric <- fit.tuv(sample, silent = TRUE, symmetric = TRUE)
  ghyp.asymmetric <- fit.ghypuv(sample, silent = TRUE)

  # Test symmetric Student-t against asymmetric generalized
  # hyperbolic using the same data as in the example above
  lik.ratio.test(ghyp.asymmetric, t.symmetric, conf.level = 0.95)
  # -> keep the null hypothesis

ghyp

Generalized Hyperbolic Distribution and Its Special Cases

v1.6.1

GPL (>= 2)

Authors

Marc Weibel, David Luethi, Wolfgang Breymann

Initial release

2020-04-27