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Model-selection-HMMR

Introduction

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.

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

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.

Let’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

selectedhmmr$plot(what = "smoothed")

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