archBootTest: Combined LM test for ARCH errors in VAR models.

In VARtests: Tests for Error Autocorrelation, ARCH Errors, and Cointegration in Vector Autoregressive Models

Description

Performs the bootstrap combined Lagrange multiplier (LM) test for autoregressive conditional heteroskedastic (ARCH) errors in vector autoregressive (VAR) models of Catani and Ahlgren (2016).

The tests of Eklund and Teräsvirta (2007), as well as the Multivariate LM test for ARCH as described for example in Lütkepohl (2006, sect. 16.5), are also included if the arguments ET respectively MARCH are set to TRUE. The bootstrap procedure for those are the same as in Catani and Ahlgren (2016).

Usage

archBootTest(fit, h = 2, B = 499, CA = TRUE, ET = TRUE, MARCH = TRUE,
             dist = "norm", skT.param = c(0, 1, 0, 5))
## S3 method for class 'archBootTest'
print(x, ...)

Arguments

fit	an object of class "VARfit" that was returned by the VARfit function, or an object of class "verest" from the function VAR in the vars package.
h	the lag length of the alternative VAR(h) model for the errors.
B	the number of bootstrap simulations.
CA	if TRUE, the Catani and Ahlgren (2017) test will run.
ET	if TRUE, the Eklund and Teräsvirta (2007) test will run.
MARCH	if TRUE, the Multivariate LM test for ARCH will run. See e.g. Lütkepohl (2006, sect. 16.5).
dist	the error distribution. Either "norm" for the standard normal distribution, or "skT" for the skew-t distribution. The parameters of the skew-t distribution can be set with the skT.param argument. Can also be a function that returns random draws as an (N-p) x K matrix or a vector of length (N-p) * K.
skT.param	a vector of four parameters for the skew-t distribution in case "skT" was used for the dist argument. The function rmst is used to draw the errors and the parameters are passed as skT.param = c(xi, Omega, alpha, nu)
x	Object with class attribute ‘archBootTest’.
...	further arguments passed to or from other methods.

Details

See the pdf version of the manual at the package's CRAN page for mathematical details of the test.

Value

a list of class "ACtest".

fit	the fit argument object.
inputType	the type of object of fit.
h	the lag length h of the alternative VAR(h) model for the errors.
B	the number of bootstrap simulations.
K	the number of series/equations in the fitted VAR model.
CA	the CA input argument.
ET	the ET input argument.
MARCH	the MARCH input argument.
dist	the dist argument object.
standardizedResi	the Cholesky-standardized residuals.
CA_LM	the combined LM statistic of Catani and Ahlgren (2016), computed as 1 - min(P(CA_LMi)).
CA_bootPV	the bootstrap P. value of the combined LM test of Catani and Ahlgren (2016).
CA_LMi	the LM statistics of Catani and Ahlgren (2016) for each time series.
CA_LMijStar	an (N-p) x K matrix of the bootstrap LM statistics for each time series (columns) and bootstrap sample (rows), for the Catani and Ahlgren (2016) test.
CA_uniBootPV	a vector of length K with the univariate bootstrap P. values for each time series, for the Catani and Ahlgren (2016) test.
ET_LM	the LM statistic of the Eklund and Teräsvirta (2007) test.
ET_PV	the P.value of the Eklund and Teräsvirta (2007) LM test statistic.
ET_bootPV	the bootstrap P.value of the Eklund and Teräsvirta (2007) test.
ET_LMStar	the bootstrap LM test statistics for the Eklund and Teräsvirta (2007) test.
MARCH_LM	the LM statistic of the Multivariate LM test for ARCH. See e.g. Lütkepohl (2006, sect. 16.5).
MARCH_PV	the P.value of the MARCH LM test statistic.
MARCH_bootPV	the bootstrap P.value of the MARCH test.
MARCH_LMStar	the bootstrap LM test statistics for the MARCH test.
description	who ran the test and when.
time	computation time taken to run the test.
call	how the function ACtest() was called.

References

Catani, P. and Ahlgren, N. (2016). Combined Lagrange multiplier test for ARCH in vector autoregressive models, Economics and Statistics, <doi:10.1016/j.ecosta.2016.10.006>.

Dufour, J.-M., Khalaf, L., and Beaulieu, M.-C. (2010). Multivariate residual-based finite-sample tests for serial dependence and arch effects with applications to asset pricing models, Journal of Applied Econometrics, 25 (2010) 263–285.

Eklund, B. and Teräsvirta, T. (2007). Testing constancy of the error covariance matrix in vector models, Journal of Econometrics, 140, 753-780.

Engle, R.F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, 987-1007.

Lütkepohl, H. (2006), New Introduction to Multiple Time Series Analysis, Springer, New York.

See Also

VARfit to estimate a VAR(p).

Examples

fit <- VARfit(y = VodafoneCDS, p = 3, const = TRUE, trend = FALSE)
test <- archBootTest(fit = fit, h = 5, B = 199, CA = TRUE, ET = TRUE, MARCH = TRUE, dist = "norm")

VARtests documentation built on May 2, 2019, 5:03 a.m.