vars (version 1.3-5)

normality: Normality, multivariate skewness and kurtosis test

Description

This function computes univariate and multivariate Jarque-Bera tests and multivariate skewness and kurtosis tests for the residuals of a VAR(p) or of a VECM in levels.

Usage

normality(x, multivariate.only = TRUE)

Arguments

x

Object of class varest; generated by VAR(), or an object of class vec2var; generated by vec2var().

multivariate.only

If TRUE (the default), only multivariate test statistics are computed.

Value

• A list of class varcheck with the following elements is returned:
• resid
  A matrix of the residuals.
• jb.uni
  A list of elements with class attribute htest containing the univariate Jarque-Bera tests. This element is only returned if multivariate.only = FALSE is set.
• jb.mul
  A list of elements with class attribute htest.
• containing the mutlivariate Jarque-Bera test, the multivariate Skewness and Kurtosis tests.

encoding

latin1

concept

• VAR
• VECM
• Vector autoregressive model
• Jarque-Bera
• Skewness
• Kurtosis
• Normality

Details

Multivariate and univariate versions of the Jarque-Bera test are applied to the residuals of a VAR. The multivariate version of this test is computed by using the residuals that are standardized by a Choleski decomposition of the variance-covariance matrix for the centered residuals. Please note, that in this case the test result is dependant upon the ordering of the variables.

References

Hamilton, J. (1994), Time Series Analysis, Princeton University Press, Princeton. Jarque, C. M. and A. K. Bera (1987), A test for normality of observations and regression residuals, International Statistical Review, 55: 163-172. L�tkepohl, H. (2006), New Introduction to Multiple Time Series Analysis, Springer, New York.

See Also

VAR, vec2var, plot

Examples

data(Canada)
var.2c <- VAR(Canada, p = 2, type = "const")
normality(var.2c)