In this package, it is possible to select models based on information criteria such as **BIC**, **AIC** and **ICL**.

The selection can be done for the two folliwng parameters:

- \(K\): The number of regimes;
- \(p\): The order of the polyniomial regression.

Letâ€™s select a RHLP model for the following time series \(Y\):

```
selectedrhlp <- selectRHLP(X = x, Y = y, Kmin = 2, Kmax = 6, pmin = 0, pmax = 3)
## The RHLP model selected via the "BIC" has K = 5 regimes
## and the order of the polynomial regression is p = 0.
## BIC = -1041.40789532438
## AIC = -1000.84239591291
```

The selected model has \(K = 5\) regimes and the order of the polynomial regression is \(p = 0\). According to the way \(Y\) has been generated, these parameters are what we expected.

Letâ€™s summarize the selected model:

```
selectedrhlp$summary()
## ---------------------
## Fitted RHLP model
## ---------------------
##
## RHLP model with K = 5 components:
##
## log-likelihood nu AIC BIC ICL
## -982.8424 18 -1000.842 -1041.408 -1040.641
##
## Clustering table (Number of observations in each regimes):
##
## 1 2 3 4 5
## 100 120 200 100 150
##
## Regression coefficients:
##
## Beta(K = 1) Beta(K = 2) Beta(K = 3) Beta(K = 4) Beta(K = 5)
## 1 0.1694561 7.06396 4.03646 -2.134881 3.495854
##
## Variances:
##
## Sigma2(K = 1) Sigma2(K = 2) Sigma2(K = 3) Sigma2(K = 4) Sigma2(K = 5)
## 1.268475 1.125061 1.085376 1.011946 1.046146
```