symmetry_test: Perform symmetry tests

In symmetry: Testing for Symmetry of Data and Model Residuals

Perform symmetry tests

Description

This is a generic function used to perform symmetry tests on numeric vectors or objects of class lm (linear models) and objects of class fGARCH (GARCH mdels fitted with the fGarch package).

Usage

symmetry_test(x, ...)

## Default S3 method:
symmetry_test(
  x,
  stat,
  mu = NULL,
  bootstrap = TRUE,
  B = 1000,
  boot_method = c("sign", "reflect"),
  trim = 0,
  k = 0,
  ...
)

## S3 method for class 'lm'
symmetry_test(
  x,
  stat,
  B = 1000,
  boot_method = c("sign", "reflect"),
  k = 0,
  ...
)

## S3 method for class 'fGARCH'
symmetry_test(
  x,
  stat,
  B = 1000,
  burn = 0,
  boot_method = c("sign", "reflect"),
  k = 0,
  approximate = FALSE,
  ...
)

Arguments

x	an object of class numeric, lm or fGARCH
...	not used
stat	a character vector indicating the test statistic to be used (see Available Test Statistics)
mu	the centre parameter around which to test symmetry
bootstrap	a logical indicating whether to use bootstrap
B	the number of bootstrap replications
boot_method	the method of bootstrap sample generation (see Details)
trim	the trim value used for estimating the centre (as used in "mean")
k	the k parameter of the statistic, ignored if the test statistic doesn't depend on a parameter (see Test Statistics)
burn	the number of elements to remove from the beginning of the time series for testing
approximate	a logical indicating whether to use the faster approximate bootstrap method (see Details)

Details

The tests are performed using bootstrap procedures or using asymptotic results, where applicable. Currently, two methods of generating a bootstrap sample from the null distribution are available. The "sign" method generates the bootstrap sample by multiplying the existing sample by -1 or 1 at random (with equal probabilities), essentially randomizing the sign of the data, giving a symmetric distribution. The "reflect" method reflects the sample around zero and samples length(x) elements with replacement. In practice, it has been shown that the "sign" method is almost always better, thus is the default.

For numeric data, the tests can be performed around a known (parameter "mu") or unknown centre. When the centre is known, the bootstrap method gives the same results as a Monte Carlo simulation of the p value, for tests which are distribution free. For unknown centre (when mu = NULL), bootstrap must be used and the estimate of the centre used is the trimmed mean, with trim parameter "trim". By default, the mean is taken (trim = 0).

For linear models, the tests are based on a bootstrap procedure as in \insertCiteAllisonsymmetry and are used to test the symmetry of the residuals around zero.

For GARCH models (must be fitted with the 'fGarch' package), the tests are also based on bootstrap and test for symmetry of the residuals around zero. An approximation of the bootstrap procedure is available where the residuals are treated as iid data, which is much faster and has been shown to give similar results to the default bootstrap procedure (described in \insertCiteKlar2012symmetry).

For a comparison of the performance of various tests of symmetry around an unknown centre, see \insertCiteUNKcentresymmetry).

Value

An object of class "htest" containing the results of the testing.

References

\insertAllCited

Examples

set.seed(1)

# IID samples
x <- rnorm(50)
symmetry_test(x, "MOI", bootstrap = FALSE, k = 3, mu = 0)
symmetry_test(x, "MOI", bootstrap = TRUE, k = 3, mu = 0)
symmetry_test(x, "MOI", bootstrap = TRUE, k = 3)
x <- rsl(50, alpha = 1.5)
symmetry_test(x, "MOI", bootstrap = FALSE, k = 3, mu = 0)
symmetry_test(x, "MOI", bootstrap = TRUE, k = 3, mu = 0)
symmetry_test(x, "MOI", bootstrap = TRUE, k = 3)

# Linear models
lin_model <- lm(dist ~ speed, cars)
symmetry_test(lin_model, "B1")

# Garch models
library(fGarch)
specskew19 = fGarch::garchSpec(model = list(omega = 0.1,
                                    alpha = 0.3,
                                    beta = 0.3,
                                    skew = 1.9),
                                    cond.dist = "snorm")

x <- fGarch::garchSim(specskew19, n = 500)
g <- fGarch::garchFit(~garch(1,1), x, cond.dist = "QMLE",
              include.mean = FALSE, trace = FALSE)
symmetry_test(g, "FM", B=400, burn = 100) # slower
symmetry_test(g, "FM", B=400, burn = 100, approximate = TRUE)

symmetry documentation built on March 31, 2023, 7:30 p.m.