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Model-selection-RHLP

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")

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