ttest0 {garchx}

T-tests and Wald-tests under nullity

Description

The permissible parameter-space of GARCH-models is bounded from below by 0. This means non-standard inference is required when one or more parameters are 0 under the null hypothesis, a frequent situation in empirical applications. The functions ttest0 and waldtest0 perform t-tests and Wald-tests when one or more parameters is 0. In the latter test, the Wald-test, the critical values are obtained by simulation, see Francq and Thieu (2018).

Usage

  ttest0(x, k = NULL)
  waldtest0(x, r = 0, R = NULL, level = c(0.1,0.05,0.01),
    vcov.type = NULL, quantile.type = 7, n = 20000)

Arguments

x

an object of class 'garchx'

k

NULL (default) or a vector of integers with the coefficients to test. If NULL, then all coefficients apart from the intercepts are tested

r

vector with restrictions

R

NULL (default) or a full-rank matrix. If NULL, then R is specified such that a test of all coefficients - apart from the intercept - is equal to the restriction r. If length(r)==1, then it is recycled so that its dimension match that of R

level

vector of significance levels whose critical values should be computed

vcov.type

NULL or a character that determines the type of coefficient-covariance to use, see vcov.garchx

quantile.type

integer, the algorithm used to compute the quantile, see quantile

n

integer, the numer of simulations used to estimate the critical values

Details

The ttest0 function performs a t-test of coefficient k with 0 as null. Under this null the parameter is on the boundary of the admissible parameter space, and so the distribution is non-standard under the null. The function ttest0 returns the result(s) of these non-standard t-test(s), see Francq and Thieu (2018). If k=NULL, the default, then a test for each coefficient apart from the intercept is undertaken.

The waldtest0 function performs a Wald-test of the restrictions in r, when one or more of its elements are 0, see Francq and Thieu (2018).

Value

ttest0:

a matrix with the t-tests

waldtest0:

a list with the test-statistic and the critical values

Author(s)

Genaro Sucarrat, http://www.sucarrat.net/

References

Christian Francq and Le Quien Thieu (2018): 'QML inference for volatility models with covariates', Econometric Theory, doi:10.1017/S0266466617000512

See Also

garchx, quantile, vcov.garchx, rmnorm

Examples

##simulate and estimate a garch(1,1):
set.seed(123)
y <- garchxSim(1000)
mymod <- garchx(y)

##t-tests:
ttest0(mymod)

##wald-test:
waldtest0(mymod)