VAR.Wald | R Documentation |

Wald test for zero parameter restrictions based on system VAR estimation

Bootstrap option is available: iid bootstrap or wild bootstrap

Bootstrap is conducted under the null hypothesis using estimated GLS estimation: see Kim (2014)

VAR.Wald(x, p, restrict, type = "const",bootstrap=0,nb=500)

`x` |
data matrix in column |

`p` |
VAR order |

`restrict` |
Restriction matrix under H0 |

`type` |
"const" for the AR model with intercept only, "const+trend" for the AR model with intercept and trend |

`bootstrap` |
0 for no bootstrap; 1 for iid bootstrap; 2 for wild bootstrap |

`nb` |
the number of bootstrap iterations |

Restriction matrix is of m by 3 matrix where m is the number of restrictions. A typical row of this matrix (k,i,j), which means that (i,j) element of Ak matrix is set to 0. Ak is a VAR coefficient matrix (k = 1,....p). Under H1, the model is full VAR.

The bootstrap test is conducted using the GLS estimation under the parameter restrictions implied by the null hypothesis: see Kim (2014) for details.

Kim (2014) found that the bootstrap based on OLS can show inferior small sample properties.

There are two versions of the bootstrap: the first is based on the iid resampling and the second based on wild bootstrapping.

The Wild bootstrap is conducted with Mammen's two-point distribution.

`Fstat` |
Wald test statistic |

`pval` |
p-value of the test based on F-distribution |

`Boot.pval` |
p-value of the test based on bootstrapping |

See Chapter 3 of Lutkepohl

Jae H. Kim

Lutkepohl, H. 2005, New Introduction to Multiple Time Series Analysis, Springer.

Kim, J.H. 2014, Testing for parameter restrictions in a stationary VAR model: a bootstrap alternative. Economic Modelling, 41, 267-273.

data(dat) #replicating Section 3.6.2 of Lutkepohl (2005) restrict = rbind( c(1,1,2),c(1,1,3), c(2,1,2),c(2,1,3)) VAR.Wald(dat,p=2,restrict,type="const")

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