Introduction

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.

Data

Let’s select a RHLP model for the following time series \(Y\):

data("univtoydataset")
x <- univtoydataset$x
y <- univtoydataset$y
plot(x, y, type = "l", xlab = "x", ylab = "Y")

Model selection with BIC

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.

Let’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

selectedrhlp$plot(what = "estimatedsignal")

Model-selection-RHLP

Introduction

Data

Model selection with BIC