Introduction

HMMR: Flexible and user-friendly probabilistic segmentation of time series (or structured longitudinal data) with regime changes by a regression model governed by a hidden Markov process, fitted by the EM (Baum-Welch) algorithm.

It was written in R Markdown, using the knitr package for production.

See help(package="samurais") for further details and references provided by citation("samurais").

Load data

data("univtoydataset")

Set up HMMR model parameters

K <- 5 # Number of regimes (states)
p <- 3 # Dimension of beta (order of the polynomial regressors)
variance_type <- "heteroskedastic" # "heteroskedastic" or "homoskedastic" model

Set up EM parameters

n_tries <- 1
max_iter <- 1500
threshold <- 1e-6
verbose <- TRUE

Estimation

hmmr <- emHMMR(univtoydataset$x, univtoydataset$y, K, p, variance_type, n_tries, 
               max_iter, threshold, verbose)
## EM: Iteration : 1 || log-likelihood : -1556.39696825748
## EM: Iteration : 2 || log-likelihood : -1022.479357477
## EM: Iteration : 3 || log-likelihood : -1019.51830707444
## EM: Iteration : 4 || log-likelihood : -1019.51780361393

Summary

hmmr$summary()
## ---------------------
## Fitted HMMR model
## ---------------------
## 
## HMMR model with K = 5 components:
## 
##  log-likelihood nu       AIC       BIC
##       -1019.518 49 -1068.518 -1178.946
## 
## 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    6.031872e-02   -5.326689    -2.65064    120.8611    3.858683
## X^1 -7.424715e+00  157.189455    43.13601   -474.9869   13.757278
## X^2  2.931651e+02 -643.706204   -92.68115    598.3724  -34.384733
## X^3 -1.823559e+03  855.171715    66.18499   -244.5174   20.632196
## 
## Variances:
## 
##  Sigma2(K = 1) Sigma2(K = 2) Sigma2(K = 3) Sigma2(K = 4) Sigma2(K = 5)
##       1.220624      1.111487      1.080043     0.9779724      1.028399

Plots

Predicted time series and predicted regime probabilities

hmmr$plot(what = "predicted")

Filtered time series and filtering regime probabilities

hmmr$plot(what = "filtered")

Fitted regressors

hmmr$plot(what = "regressors")

Smoothed time series and segmentation

hmmr$plot(what = "smoothed")

Log-likelihood

hmmr$plot(what = "loglikelihood")

A-quick-tour-of-HMMR