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

The selection is done on two parameters which are:

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

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

```
selectedhmmr <- selectHMMR(X = x, Y = y, Kmin = 2, Kmax = 6, pmin = 0, pmax = 3)
## The HMMR model selected via the "BIC" has K = 5 regimes
## and the order of the polynomial regression is p = 0.
## BIC = -1136.39152222095
## AIC = -1059.76780111041
```

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:

```
selectedhmmr$summary()
## ---------------------
## Fitted HMMR model
## ---------------------
##
## HMMR model with K = 5 components:
##
## log-likelihood nu AIC BIC
## -1025.768 34 -1059.768 -1136.392
##
## 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 0.1694566 7.063444 4.036769 -2.134901 3.49582
##
## Variances:
##
## Sigma2(K = 1) Sigma2(K = 2) Sigma2(K = 3) Sigma2(K = 4) Sigma2(K = 5)
## 1.268478 1.126648 1.086297 1.011927 1.046276
```