# 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")