Description Usage Arguments Details Value References See Also Examples

`Wald_test`

performs a Wald test for a GMAR, StMAR, or G-StMAR model.

1 |

`gsmar` |
a class 'gsmar' object, typically generated by |

`A` |
a size |

`c` |
a length |

`h` |
the difference used to approximate the derivatives. |

Denoting the true parameter value by *θ_{0}*, we test the null hypothesis *Aθ_{0}=c*.
Under the null, the test statistic is asymptotically *χ^2*-distributed with *k*
(`=nrow(A)`

) degrees of freedom. The parameter *θ_{0}* is assumed to have the same form as in
the model supplied in the argument `gsmar`

and it is presented in the documentation of the argument
`params`

in the function `GSMAR`

(see `?GSMAR`

).

Note that this function does **not** check whether the specified constraints are feasible (e.g., whether
the implied constrained model would be stationary or have positive definite error term covariance matrices).

A list with class "htest" containing the following components:

`statistic` |
the value of the Wald statistics. |

`parameter` |
the degrees of freedom of the Wald statistic. |

`p.value` |
the p-value of the test. |

`alternative` |
a character string describing the alternative hypothesis. |

`method` |
a character string indicating the type of the test (Wald test). |

`data.name` |
a character string giving the names of the supplied model, constraint matrix A, and vector c. |

`gsmar` |
the supplied argument gsmar. |

`A` |
the supplied argument A. |

`c` |
the supplied argument c. |

`h` |
the supplied argument h. |

Kalliovirta L., Meitz M. and Saikkonen P. 2015. Gaussian Mixture Autoregressive model for univariate time series.

*Journal of Time Series Analysis*,**36**, 247-266.Meitz M., Preve D., Saikkonen P. 2021. A mixture autoregressive model based on Student's t-distribution.

*Communications in Statistics - Theory and Methods*, doi: 10.1080/03610926.2021.1916531Virolainen S. 2021. A mixture autoregressive model based on Gaussian and Student's t-distributions. Studies in Nonlinear Dynamics & Econometrics, doi: 10.1515/snde-2020-0060

`LR_test`

, `fitGSMAR`

, `GSMAR`

, `diagnostic_plot`

,
`profile_logliks`

, `quantile_residual_tests`

, `cond_moment_plot`

1 2 3 4 5 6 7 8 9 10 11 | ```
# GMAR p=1, M=2 model:
fit12 <- fitGSMAR(simudata, p=1, M=2, model="GMAR", ncalls=1, seeds=1)
# Test with Wald test whether the AR coefficients are the same in both
# regimes:
# There are 7 parameters in the model and the AR coefficient of the
# first regime is the 2nd element, whereas the AR coefficient of the second
# regime is in the 5th element.
A <- matrix(c(0, 1, 0, 0, -1, 0, 0), nrow=1, ncol=7)
c <- 0
Wald_test(fit12, A=A, c=c)
``` |

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