Model-selection-MHMMR
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 MHMMR model for the following multivariate time series Y:
data("multivtoydataset")
x <- multivtoydataset$x
y <- multivtoydataset[, c("y1", "y2", "y3")]
matplot(x, y, type = "l", xlab = "x", ylab = "Y")
Model selection with BIC
selectedmhmmr <- selectMHMMR(X = x, Y = y, Kmin = 2, Kmax = 6, pmin = 0, pmax = 3)
## The MHMMR model selected via the "BIC" has K = 5 regimes
## and the order of the polynomial regression is p = 0.
## BIC = -3118.9815385353
## AIC = -2963.48045745801The selected model has K = 5 regimes and the order of the polynomial regression is p = 0. According to the way Y has been generated, these parameters are what we expected.
Let’s summarize the selected model:
selectedmhmmr$summary()
## ----------------------
## Fitted MHMMR model
## ----------------------
##
## MHMMR model with K = 5 regimes
##
## log-likelihood nu AIC BIC
## -2894.48 69 -2963.48 -3118.982
##
## Clustering table:
## 1 2 3 4 5
## 100 120 200 100 150
##
##
## ------------------
## Regime 1 (K = 1):
##
## Regression coefficients:
##
## Beta(d = 1) Beta(d = 2) Beta(d = 3)
## 1 0.1131005 0.9124035 -1.850509
##
## Covariance matrix:
##
## 1.19065699 0.12700417 0.05496662
## 0.12700417 0.90280499 -0.03272115
## 0.05496662 -0.03272115 0.89087804
## ------------------
## Regime 2 (K = 2):
##
## Regression coefficients:
##
## Beta(d = 1) Beta(d = 2) Beta(d = 3)
## 1 7.190603 5.049411 9.952148
##
## Covariance matrix:
##
## 1.0728107 -0.18105877 0.12234096
## -0.1810588 1.05365247 0.01237708
## 0.1223410 0.01237708 0.76556432
## ------------------
## Regime 3 (K = 3):
##
## Regression coefficients:
##
## Beta(d = 1) Beta(d = 2) Beta(d = 3)
## 1 3.951395 5.942001 7.950474
##
## Covariance matrix:
##
## 1.02908516 -0.05875508 -0.02499614
## -0.05875508 1.19504114 0.02287346
## -0.02499614 0.02287346 1.01258737
## ------------------
## Regime 4 (K = 4):
##
## Regression coefficients:
##
## Beta(d = 1) Beta(d = 2) Beta(d = 3)
## 1 -0.9461282 -1.901665 0.0135667
##
## Covariance matrix:
##
## 0.88093255 -0.02771294 -0.03959332
## -0.02771294 1.14568525 -0.10726848
## -0.03959332 -0.10726848 0.89326063
## ------------------
## Regime 5 (K = 5):
##
## Regression coefficients:
##
## Beta(d = 1) Beta(d = 2) Beta(d = 3)
## 1 3.549319 1.888239 4.981038
##
## Covariance matrix:
##
## 1.1333259 0.25852405 0.03091090
## 0.2585241 1.21454178 0.05663565
## 0.0309109 0.05663565 0.84027581