BIC based model selection for MixAR models

BIC calculations for mixture autoregressive models.

Usage

mixAR_BIC(y, model, fix = NULL, comp_loglik = TRUE, index)
BIC_comp(x, y)

Arguments

y

a time series.

model

the model for which to calculate BIC, an object inheriting from class MixAR. Alternatively, an output list from fit_mixAR.

fix

If fix = "shift" shift parameters are not included in calculation of BIC. Default is NULL, i.e. shift parameters are included.

comp_loglik

Should the loglikelihood be calculated? Default is TRUE. If FALSE and model is output of fit_mixAR, then the loglikelihood is not recalculated.

index

Discard the first 1:index observations. If missing, index is set to the largest AR order.

x

a list containing a combination of MixAR objects and/or output lists from fit_mixAR.

Details

mixAR_BIC calculates the BIC criterion of a given MixAR object with respect to a specified time series.

If index is specified, it has to be at least equal to the largest autoregressive order. The function calculates BIC on the last (index + 1):n data points.

BIC_comp calculates the value of BIC for the models listed in x with respect to the specified time series y.

If the distributions of the components contain estimated parameters, then their number is included in the number of parameters for the calculation of BIC.

Value

If comp_loglik = TRUE, the function calculates BIC based on the given model, data and index. If comp_loglik = FALSE and model is output from fit_mixAR, it returns object vallogf from that list.

Author

Davide Ravagli

Examples

model1 <- new("MixARGaussian", prob = c(0.5, 0.5), scale = c(1, 2),
              arcoef = list(-0.5, 1.1))

model2 <- new("MixARGaussian", prob = c(0.5, 0.3, 0.2), scale = c(1, 3, 8),
              arcoef = list(c(-0.5, 0.5), 1, 0.4))

set.seed(123)
y <- mixAR_sim(model1, 400, c(0, 0, 0), nskip = 100)

mixAR_BIC(y, model1)
#> [1] 1770.964

model_fit1 <- fit_mixAR(y, model1)
model_fit2 <- fit_mixAR(y, model2, crit = 1e-4)

mixAR_BIC(y, model_fit1)
#> [1] 1766.659
mixAR_BIC(y, model_fit2)
#> [1] 1782.464

BIC_comp(list(model1, model2, model_fit1, model_fit2), y)
#> Best model:  1 1 
#> [1] 1770.964 2151.311 1766.659 1782.464

mixAR_BIC(y, model_fit1, index = 20)
#> [1] 3.439512
mixAR_BIC(y, model_fit2, index = 20)
#> [1] 3.456183