MixAR models for examples and testing
exampleModels.RdMixAR models for examples and testing.
Details
Coefficients of models from the examples in
Wong and Li (2000)
. Variations on these with different
noise distributions are used throughout the examples in mixAR.
The models are from classes inheriting from class "MixAR".
exampleModels is a list with the following components:
| WL_ibm WL_A WL_B WL_I WL_II WL_ibm_gen WL_ibm_t3v WL_ibm_tf WL_At WL_Bt_1 WL_Bt_2 WL_Bt_3 WL_Ct_1 WL_Ct_2 WL_Ct_3 |
Each component is a MixAR model, i.e. an object inheriting from class
"MixAR".
Source
Wong CS, Li WK (2000). “On a mixture autoregressive model.” J. R. Stat. Soc., Ser. B, Stat. Methodol. , 62(1), 95-115.
Examples
## use these instead of moWL, moWL_A, moWL_B, etc.
exampleModels$WL_ibm
#> An object of class "MixARGaussian"
#> Number of components: 3
#> prob shift scale order ar_1 ar_2
#> Comp_1 0.5439 0 4.8227 2 0.6792 0.3208
#> Comp_2 0.4176 0 6.0082 2 1.6711 -0.6711
#> Comp_3 0.0385 0 18.1716 1 1.0000
#>
#> Distributions of the error components:
#> standard Gaussian
#>
exampleModels$WL_A
#> An object of class "MixARGaussian"
#> Number of components: 2
#> prob shift scale order ar_1
#> Comp_1 0.5 0 5 1 0.5
#> Comp_2 0.5 0 1 1 1.1
#>
#> Distributions of the error components:
#> standard Gaussian
#>
exampleModels$WL_B
#> An object of class "MixARGaussian"
#> Number of components: 2
#> prob shift scale order ar_1
#> Comp_1 0.75 0 5 1 0.5
#> Comp_2 0.25 0 1 1 1.4
#>
#> Distributions of the error components:
#> standard Gaussian
#>
# what is the difference between A and B?
show_diff(exampleModels$WL_A, exampleModels$WL_B)
#> prob shift scale order ar_1
#> Comp_1 -0.25 0 0 1 0.0
#> Comp_2 0.25 0 0 1 -0.3
exampleModels$WL_I
#> An object of class "MixARGaussian"
#> Number of components: 3
#> prob shift scale order ar_1 ar_2 ar_3
#> Comp_1 0.4 0 1 2 0.9 -0.60
#> Comp_2 0.3 0 1 1 -0.5
#> Comp_3 0.3 -5 5 3 1.5 -0.74 0.12
#>
#> Distributions of the error components:
#> standard Gaussian
#>
exampleModels$WL_II
#> An object of class "MixARGaussian"
#> Number of components: 3
#> prob shift scale order ar_1 ar_2
#> Comp_1 0.4 5 1 2 0.9 -0.6
#> Comp_2 0.3 0 1 2 -0.7 0.0
#> Comp_3 0.3 -5 5 2 0.0 0.8
#>
#> Distributions of the error components:
#> standard Gaussian
#>
#show_diff(exampleModels$WL_I, exampleModels$WL_II)
exampleModels$WL_ibm_gen
#> An object of class "MixARgen"
#> Number of components: 3
#> prob shift scale order ar_1 ar_2
#> Comp_1 0.5439 0 4.8227 2 0.6792 0.3208
#> Comp_2 0.4176 0 6.0082 2 1.6711 -0.6711
#> Comp_3 0.0385 0 18.1716 1 1.0000
#>
#> Distributions of the error components:
#> Component 1: Standard normal distribution
#>
exampleModels$WL_ibm_t3v
#> An object of class "MixARgen"
#> Number of components: 3
#> prob shift scale order ar_1 ar_2
#> Comp_1 0.5439 0 4.8227 2 0.6792 0.3208
#> Comp_2 0.4176 0 6.0082 2 1.6711 -0.6711
#> Comp_3 0.0385 0 18.1716 1 1.0000
#>
#> Distributions of the error components:
#> Component 1: Student t with 3 df
#>
exampleModels$WL_ibm_tf
#> An object of class "MixARgen"
#> Number of components: 3
#> prob shift scale order ar_1 ar_2
#> Comp_1 0.5439 0 4.8227 2 0.6792 0.3208
#> Comp_2 0.4176 0 6.0082 2 1.6711 -0.6711
#> Comp_3 0.0385 0 18.1716 1 1.0000
#>
#> Distributions of the error components:
#> Component 1: Student t with 20 df
#> Component 2: Student t with 30 df
#> Component 3: Student t with 40 df
#>
#show_diff(exampleModels$WL_ibm_gen, exampleModels$WL_ibm_t3v)
exampleModels$WL_At
#> An object of class "MixARgen"
#> Number of components: 2
#> prob shift scale order ar_1
#> Comp_1 0.5 0 1 1 -0.5
#> Comp_2 0.5 0 2 1 1.1
#>
#> Distributions of the error components:
#> Component 1: Student t with 4 df
#> Component 2: Student t with 8 df
#>
exampleModels$WL_Bt_1
#> An object of class "MixARgen"
#> Number of components: 3
#> prob shift scale order ar_1 ar_2 ar_3
#> Comp_1 0.3 5 2.0 2 0.5 0.24
#> Comp_2 0.3 -5 1.0 1 -0.9
#> Comp_3 0.4 0 0.5 3 1.5 -0.74 0.12
#>
#> Distributions of the error components:
#> Component 1: Student t with 4 df
#> Component 2: Student t with 6 df
#> Component 3: Student t with 10 df
#>
exampleModels$WL_Bt_2
#> An object of class "MixARgen"
#> Number of components: 3
#> prob shift scale order ar_1 ar_2 ar_3
#> Comp_1 0.3 5 2.0 2 0.5 0.24
#> Comp_2 0.3 -5 1.0 1 -0.9
#> Comp_3 0.4 0 0.5 3 1.5 -0.74 0.12
#>
#> Distributions of the error components:
#> Component 1: Student t with 4 df
#> Component 2: Student t with 4 df
#> Component 3: Student t with 10 df
#>
exampleModels$WL_Bt_3
#> An object of class "MixARgen"
#> Number of components: 3
#> prob shift scale order ar_1 ar_2 ar_3
#> Comp_1 0.3 5 2.0 2 0.5 0.24
#> Comp_2 0.3 -5 1.0 1 -0.9
#> Comp_3 0.4 0 0.5 3 1.5 -0.74 0.12
#>
#> Distributions of the error components:
#> Component 1: Student t with 4 df
#> Component 2: Student t with 4 df
#> Component 3: Student t with 10 df
#>
## what is different between Bt_2 and Bt_1? (df of component 2)
show_diff(exampleModels$WL_Bt_2, exampleModels$WL_Bt_1)
#> prob shift scale order ar_1 ar_2 ar_3
#> Comp_1 0 0 0 2 0 0
#> Comp_2 0 0 0 1 0
#> Comp_3 0 0 0 3 0 0 0
#>
#> Distributions of the error components:
#>
#> Model 1:
#> Component 1: Student t with 4 df
#> Component 2: Student t with 4 df
#> Component 3: Student t with 10 df
#>
#> Model 2:
#> Component 1: Student t with 4 df
#> Component 2: Student t with 6 df
#> Component 3: Student t with 10 df
exampleModels$WL_Ct_1
#> An object of class "MixARgen"
#> Number of components: 3
#> prob shift scale order ar_1 ar_2 ar_3
#> Comp_1 0.3 5 2.0 2 0.5 0.24
#> Comp_2 0.3 -5 1.0 1 -0.9
#> Comp_3 0.4 0 0.5 3 1.5 -0.74 0.12
#>
#> Distributions of the error components:
#> Component 1: Student t with 4 df
#> Component 2: Student t with 7 df
#> Component 3: Standard normal distribution
#>
exampleModels$WL_Ct_2
#> An object of class "MixARgen"
#> Number of components: 3
#> prob shift scale order ar_1 ar_2 ar_3
#> Comp_1 0.3 5 2.0 2 0.5 0.24
#> Comp_2 0.3 -5 1.0 1 -0.9
#> Comp_3 0.4 0 0.5 3 1.5 -0.74 0.12
#>
#> Distributions of the error components:
#> Component 1: Student t with 4 df
#> Component 2: Student t with 7 df
#> Component 3: Standard normal distribution
#>
exampleModels$WL_Ct_3
#> An object of class "MixARGaussian"
#> Number of components: 3
#> prob shift scale order ar_1 ar_2 ar_3
#> Comp_1 0.3 5 2.0 2 0.5 0.24
#> Comp_2 0.3 -5 1.0 1 -0.9
#> Comp_3 0.4 0 0.5 3 1.5 -0.74 0.12
#>
#> Distributions of the error components:
#> standard Gaussian
#>
## The models were created with something like:
moWLprob <- c(0.5439,0.4176,0.0385)
moWLsigma <- c(4.8227,6.0082,18.1716)
moWLar <- list(c(0.6792,0.3208), c(1.6711,-0.6711), 1)
moWL <- new("MixARGaussian", prob = moWLprob, scale = moWLsigma,
arcoef = moWLar)
moWLgen <- new("MixARgen", prob = moWLprob, scale = moWLsigma,
arcoef = moWLar, dist = list(dist_norm))
## clean up a bit
rm(moWLprob, moWLsigma, moWLar, moWL, moWLgen)