README.md
In fchamroukhi/MRHLP: Multiple Regression Model with a Hidden Logistic Process ('MRHLP') for Joint Segmentation of Multivariate Time Series
Overview
MRHLP is an R package for flexible and user-friendly
probabilistic joint segmentation of multivariate time series (or
multivariate structured longitudinal data) with smooth and/or abrupt
regime changes by a mixture model-based multiple regression approach
with a hidden logistic process (Multiple Regression model with a Hidden
Logistic Process (MRHLP)). The model is fitted by the EM algorithm.
Installation
You can install the MRHLP package from GitHub
with:
# install.packages("devtools")
devtools::install_github("fchamroukhi/MRHLP")
To build vignettes for examples of usage, type the command below
instead:
# install.packages("devtools")
devtools::install_github("fchamroukhi/MRHLP",
build_opts = c("--no-resave-data", "--no-manual"),
build_vignettes = TRUE)
Use the following command to display vignettes:
browseVignettes("MRHLP")
Usage
library(MRHLP)
# Application to a toy data set
data("toydataset")
x <- toydataset$x
y <- toydataset[,c("y1", "y2", "y3")]
K <- 5 # Number of regimes (mixture components)
p <- 1 # Dimension of beta (order of the polynomial regressors)
q <- 1 # Dimension of w (order of the logistic regression: to be set to 1 for segmentation)
variance_type <- "heteroskedastic" # "heteroskedastic" or "homoskedastic" model
n_tries <- 1
max_iter <- 1500
threshold <- 1e-6
verbose <- TRUE
verbose_IRLS <- FALSE
mrhlp <- emMRHLP(X = x, Y = y, K, p, q, variance_type, n_tries,
max_iter, threshold, verbose, verbose_IRLS)
#> EM - MRHLP: Iteration: 1 | log-likelihood: -4807.6644322901
#> EM - MRHLP: Iteration: 2 | log-likelihood: -3314.25165556383
#> EM - MRHLP: Iteration: 3 | log-likelihood: -3216.8871750704
#> EM - MRHLP: Iteration: 4 | log-likelihood: -3126.33556053822
#> EM - MRHLP: Iteration: 5 | log-likelihood: -2959.59933830667
#> EM - MRHLP: Iteration: 6 | log-likelihood: -2895.65953485704
#> EM - MRHLP: Iteration: 7 | log-likelihood: -2892.93263500326
#> EM - MRHLP: Iteration: 8 | log-likelihood: -2889.34084959654
#> EM - MRHLP: Iteration: 9 | log-likelihood: -2884.56422084139
#> EM - MRHLP: Iteration: 10 | log-likelihood: -2878.29772085061
#> EM - MRHLP: Iteration: 11 | log-likelihood: -2870.61242183846
#> EM - MRHLP: Iteration: 12 | log-likelihood: -2862.86238149363
#> EM - MRHLP: Iteration: 13 | log-likelihood: -2856.85351443338
#> EM - MRHLP: Iteration: 14 | log-likelihood: -2851.74642203885
#> EM - MRHLP: Iteration: 15 | log-likelihood: -2850.00381259526
#> EM - MRHLP: Iteration: 16 | log-likelihood: -2849.86516522686
#> EM - MRHLP: Iteration: 17 | log-likelihood: -2849.7354103643
#> EM - MRHLP: Iteration: 18 | log-likelihood: -2849.56953544124
#> EM - MRHLP: Iteration: 19 | log-likelihood: -2849.40322468732
#> EM - MRHLP: Iteration: 20 | log-likelihood: -2849.40321381274
mrhlp$summary()
#> ----------------------
#> Fitted MRHLP model
#> ----------------------
#>
#> MRHLP model with K = 5 regimes
#>
#> log-likelihood nu AIC BIC ICL
#> -2849.403 68 -2917.403 -3070.651 -3069.896
#>
#> 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 0.11943184 0.6087582 -2.038486
#> X^1 -0.08556857 4.1038126 2.540536
#>
#> Covariance matrix:
#>
#> 1.19063336 0.12765794 0.05537134
#> 0.12765794 0.87144062 -0.05213162
#> 0.05537134 -0.05213162 0.87885166
#> ------------------
#> Regime 2 (k = 2):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 6.924025 4.9368460 10.288339
#> X^1 1.118034 0.4726707 -1.409218
#>
#> Covariance matrix:
#>
#> 1.0690431 -0.18293369 0.12602459
#> -0.1829337 1.05280632 0.01390041
#> 0.1260246 0.01390041 0.75995058
#> ------------------
#> Regime 3 (k = 3):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 3.6535241 6.3654379 8.488318
#> X^1 0.6233579 -0.8866887 -1.126692
#>
#> Covariance matrix:
#>
#> 1.02591553 -0.05445227 -0.02019896
#> -0.05445227 1.18941700 0.01565240
#> -0.02019896 0.01565240 1.00257195
#> ------------------
#> Regime 4 (k = 4):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 -1.439637 -4.463014 2.952470
#> X^1 0.703211 3.649717 -4.187703
#>
#> Covariance matrix:
#>
#> 0.88000190 -0.03249118 -0.03411075
#> -0.03249118 1.12087583 -0.07881351
#> -0.03411075 -0.07881351 0.86060127
#> ------------------
#> Regime 5 (k = 5):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 3.4982408 2.5357751 7.652113
#> X^1 0.0574791 -0.7286824 -3.005802
#>
#> Covariance matrix:
#>
#> 1.13330209 0.25869951 0.03163467
#> 0.25869951 1.21230741 0.04746018
#> 0.03163467 0.04746018 0.80241715
mrhlp$plot()
# Application to a real data set (human activity recogntion data)
data("realdataset")
x <- realdataset$x
y <- realdataset[,c("y1", "y2", "y3")]
K <- 5 # Number of regimes (mixture components)
p <- 3 # Dimension of beta (order of the polynomial regressors)
q <- 1 # Dimension of w (order of the logistic regression: to be set to 1 for segmentation)
variance_type <- "heteroskedastic" # "heteroskedastic" or "homoskedastic" model
n_tries <- 1
max_iter <- 1500
threshold <- 1e-6
verbose <- TRUE
verbose_IRLS <- FALSE
mrhlp <- emMRHLP(X = x, Y = y, K, p, q, variance_type, n_tries,
max_iter, threshold, verbose, verbose_IRLS)
#> EM - MRHLP: Iteration: 1 | log-likelihood: -792.888668727036
#> EM - MRHLP: Iteration: 2 | log-likelihood: 6016.45835957306
#> EM - MRHLP: Iteration: 3 | log-likelihood: 6362.81791662824
#> EM - MRHLP: Iteration: 4 | log-likelihood: 6615.72233403002
#> EM - MRHLP: Iteration: 5 | log-likelihood: 6768.32107943849
#> EM - MRHLP: Iteration: 6 | log-likelihood: 6840.97339565987
#> EM - MRHLP: Iteration: 7 | log-likelihood: 6860.97262839295
#> EM - MRHLP: Iteration: 8 | log-likelihood: 6912.25605673784
#> EM - MRHLP: Iteration: 9 | log-likelihood: 6945.96718258737
#> EM - MRHLP: Iteration: 10 | log-likelihood: 6951.28584396645
#> EM - MRHLP: Iteration: 11 | log-likelihood: 6952.37644678517
#> EM - MRHLP: Iteration: 12 | log-likelihood: 6954.80510338749
#> EM - MRHLP: Iteration: 13 | log-likelihood: 6958.99033092484
#> EM - MRHLP: Iteration: 14 | log-likelihood: 6964.81099837456
#> EM - MRHLP: Iteration: 15 | log-likelihood: 6999.90358068156
#> EM - MRHLP: Iteration: 16 | log-likelihood: 7065.39327246318
#> EM - MRHLP: Iteration: 17 | log-likelihood: 7166.23398344994
#> EM - MRHLP: Iteration: 18 | log-likelihood: 7442.73330846285
#> EM - MRHLP: Iteration: 19 | log-likelihood: 7522.65416438396
#> EM - MRHLP: Iteration: 20 | log-likelihood: 7524.41524338024
#> EM - MRHLP: Iteration: 21 | log-likelihood: 7524.57590110924
#> EM - MRHLP: Iteration: 22 | log-likelihood: 7524.73808801417
#> EM - MRHLP: Iteration: 23 | log-likelihood: 7524.88684996651
#> EM - MRHLP: Iteration: 24 | log-likelihood: 7524.9753964817
#> EM - MRHLP: Iteration: 25 | log-likelihood: 7524.97701548847
mrhlp$summary()
#> ----------------------
#> Fitted MRHLP model
#> ----------------------
#>
#> MRHLP model with K = 5 regimes
#>
#> log-likelihood nu AIC BIC ICL
#> 7524.977 98 7426.977 7146.696 7147.535
#>
#> Clustering table:
#> 1 2 3 4 5
#> 413 344 588 423 485
#>
#>
#> ------------------
#> Regime 1 (k = 1):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 1.64847721 2.33823068 9.40173242
#> X^1 -0.31396583 0.38235782 -0.10031616
#> X^2 0.23954454 -0.30105177 0.07812145
#> X^3 -0.04725267 0.06166899 -0.01586579
#>
#> Covariance matrix:
#>
#> 0.0200740364 -0.004238036 0.0004011388
#> -0.0042380363 0.006082904 -0.0012973026
#> 0.0004011388 -0.001297303 0.0013201963
#> ------------------
#> Regime 2 (k = 2):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 -106.0250571 -31.4671946 -107.9697464
#> X^1 45.2035210 21.2126134 72.0220177
#> X^2 -5.7330338 -4.1285514 -13.9857795
#> X^3 0.2343552 0.2485377 0.8374817
#>
#> Covariance matrix:
#>
#> 0.11899225 -0.03866052 -0.06693441
#> -0.03866052 0.17730401 0.04036629
#> -0.06693441 0.04036629 0.11983979
#> ------------------
#> Regime 3 (k = 3):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 9.0042249443 -1.247752962 -2.492119515
#> X^1 0.2191555621 0.418071041 0.310449523
#> X^2 -0.0242080660 -0.043802827 -0.039012607
#> X^3 0.0008494208 0.001474635 0.001427627
#>
#> Covariance matrix:
#>
#> 4.103351e-04 -0.0001330363 5.289199e-05
#> -1.330363e-04 0.0006297205 2.027763e-04
#> 5.289199e-05 0.0002027763 1.374405e-03
#> ------------------
#> Regime 4 (k = 4):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 -1029.9071752 334.4975068 466.0981076
#> X^1 199.9531885 -68.7252041 -105.6436899
#> X^2 -12.6550086 4.6489685 7.6555642
#> X^3 0.2626998 -0.1032161 -0.1777453
#>
#> Covariance matrix:
#>
#> 0.058674116 -0.017661572 0.002139975
#> -0.017661572 0.047588713 0.007867532
#> 0.002139975 0.007867532 0.067150809
#> ------------------
#> Regime 5 (k = 5):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 27.247199195 -14.393798357 19.741283724
#> X^1 -3.530625667 2.282492947 -1.511225702
#> X^2 0.161234880 -0.101613670 0.073003292
#> X^3 -0.002446104 0.001490288 -0.001171127
#>
#> Covariance matrix:
#>
#> 6.900384e-03 -0.001176838 2.966199e-05
#> -1.176838e-03 0.003596238 -2.395420e-04
#> 2.966199e-05 -0.000239542 5.573451e-04
mrhlp$plot()
Model selection
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 following parameters:
- K: The number of regimes;
- p: The order of the polynomial regression.
Let’s select a MRHLP model for the following multivariate time series
Y:
data("toydataset")
x <- toydataset$x
y <- toydataset[, c("y1", "y2", "y3")]
matplot(x, y, type = "l", xlab = "x", ylab = "Y", lty = 1)
selectedmrhlp <- selectMRHLP(X = x, Y = y, Kmin = 2, Kmax = 6, pmin = 0, pmax = 3)
#> Warning in emMRHLP(X = X1, Y = Y1, K, p): EM log-likelihood is decreasing
#> from -3105.78591044952to -3105.78627830471!
#> The MRHLP model selected via the "BIC" has K = 5 regimes
#> and the order of the polynomial regression is p = 0.
#> BIC = -3033.20042397111
#> AIC = -2913.75756459291
selectedmrhlp$plot(what = "estimatedsignal")
fchamroukhi/MRHLP documentation built on Sept. 23, 2019, 4:17 a.m.
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Overview
MRHLP is an R package for flexible and user-friendly probabilistic joint segmentation of multivariate time series (or multivariate structured longitudinal data) with smooth and/or abrupt regime changes by a mixture model-based multiple regression approach with a hidden logistic process (Multiple Regression model with a Hidden Logistic Process (MRHLP)). The model is fitted by the EM algorithm.
Installation
You can install the MRHLP package from GitHub with:
# install.packages("devtools")
devtools::install_github("fchamroukhi/MRHLP")
To build vignettes for examples of usage, type the command below instead:
# install.packages("devtools")
devtools::install_github("fchamroukhi/MRHLP",
build_opts = c("--no-resave-data", "--no-manual"),
build_vignettes = TRUE)
Use the following command to display vignettes:
browseVignettes("MRHLP")
Usage
library(MRHLP)
# Application to a toy data set
data("toydataset")
x <- toydataset$x
y <- toydataset[,c("y1", "y2", "y3")]
K <- 5 # Number of regimes (mixture components)
p <- 1 # Dimension of beta (order of the polynomial regressors)
q <- 1 # Dimension of w (order of the logistic regression: to be set to 1 for segmentation)
variance_type <- "heteroskedastic" # "heteroskedastic" or "homoskedastic" model
n_tries <- 1
max_iter <- 1500
threshold <- 1e-6
verbose <- TRUE
verbose_IRLS <- FALSE
mrhlp <- emMRHLP(X = x, Y = y, K, p, q, variance_type, n_tries,
max_iter, threshold, verbose, verbose_IRLS)
#> EM - MRHLP: Iteration: 1 | log-likelihood: -4807.6644322901
#> EM - MRHLP: Iteration: 2 | log-likelihood: -3314.25165556383
#> EM - MRHLP: Iteration: 3 | log-likelihood: -3216.8871750704
#> EM - MRHLP: Iteration: 4 | log-likelihood: -3126.33556053822
#> EM - MRHLP: Iteration: 5 | log-likelihood: -2959.59933830667
#> EM - MRHLP: Iteration: 6 | log-likelihood: -2895.65953485704
#> EM - MRHLP: Iteration: 7 | log-likelihood: -2892.93263500326
#> EM - MRHLP: Iteration: 8 | log-likelihood: -2889.34084959654
#> EM - MRHLP: Iteration: 9 | log-likelihood: -2884.56422084139
#> EM - MRHLP: Iteration: 10 | log-likelihood: -2878.29772085061
#> EM - MRHLP: Iteration: 11 | log-likelihood: -2870.61242183846
#> EM - MRHLP: Iteration: 12 | log-likelihood: -2862.86238149363
#> EM - MRHLP: Iteration: 13 | log-likelihood: -2856.85351443338
#> EM - MRHLP: Iteration: 14 | log-likelihood: -2851.74642203885
#> EM - MRHLP: Iteration: 15 | log-likelihood: -2850.00381259526
#> EM - MRHLP: Iteration: 16 | log-likelihood: -2849.86516522686
#> EM - MRHLP: Iteration: 17 | log-likelihood: -2849.7354103643
#> EM - MRHLP: Iteration: 18 | log-likelihood: -2849.56953544124
#> EM - MRHLP: Iteration: 19 | log-likelihood: -2849.40322468732
#> EM - MRHLP: Iteration: 20 | log-likelihood: -2849.40321381274
mrhlp$summary()
#> ----------------------
#> Fitted MRHLP model
#> ----------------------
#>
#> MRHLP model with K = 5 regimes
#>
#> log-likelihood nu AIC BIC ICL
#> -2849.403 68 -2917.403 -3070.651 -3069.896
#>
#> 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 0.11943184 0.6087582 -2.038486
#> X^1 -0.08556857 4.1038126 2.540536
#>
#> Covariance matrix:
#>
#> 1.19063336 0.12765794 0.05537134
#> 0.12765794 0.87144062 -0.05213162
#> 0.05537134 -0.05213162 0.87885166
#> ------------------
#> Regime 2 (k = 2):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 6.924025 4.9368460 10.288339
#> X^1 1.118034 0.4726707 -1.409218
#>
#> Covariance matrix:
#>
#> 1.0690431 -0.18293369 0.12602459
#> -0.1829337 1.05280632 0.01390041
#> 0.1260246 0.01390041 0.75995058
#> ------------------
#> Regime 3 (k = 3):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 3.6535241 6.3654379 8.488318
#> X^1 0.6233579 -0.8866887 -1.126692
#>
#> Covariance matrix:
#>
#> 1.02591553 -0.05445227 -0.02019896
#> -0.05445227 1.18941700 0.01565240
#> -0.02019896 0.01565240 1.00257195
#> ------------------
#> Regime 4 (k = 4):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 -1.439637 -4.463014 2.952470
#> X^1 0.703211 3.649717 -4.187703
#>
#> Covariance matrix:
#>
#> 0.88000190 -0.03249118 -0.03411075
#> -0.03249118 1.12087583 -0.07881351
#> -0.03411075 -0.07881351 0.86060127
#> ------------------
#> Regime 5 (k = 5):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 3.4982408 2.5357751 7.652113
#> X^1 0.0574791 -0.7286824 -3.005802
#>
#> Covariance matrix:
#>
#> 1.13330209 0.25869951 0.03163467
#> 0.25869951 1.21230741 0.04746018
#> 0.03163467 0.04746018 0.80241715
mrhlp$plot()
# Application to a real data set (human activity recogntion data)
data("realdataset")
x <- realdataset$x
y <- realdataset[,c("y1", "y2", "y3")]
K <- 5 # Number of regimes (mixture components)
p <- 3 # Dimension of beta (order of the polynomial regressors)
q <- 1 # Dimension of w (order of the logistic regression: to be set to 1 for segmentation)
variance_type <- "heteroskedastic" # "heteroskedastic" or "homoskedastic" model
n_tries <- 1
max_iter <- 1500
threshold <- 1e-6
verbose <- TRUE
verbose_IRLS <- FALSE
mrhlp <- emMRHLP(X = x, Y = y, K, p, q, variance_type, n_tries,
max_iter, threshold, verbose, verbose_IRLS)
#> EM - MRHLP: Iteration: 1 | log-likelihood: -792.888668727036
#> EM - MRHLP: Iteration: 2 | log-likelihood: 6016.45835957306
#> EM - MRHLP: Iteration: 3 | log-likelihood: 6362.81791662824
#> EM - MRHLP: Iteration: 4 | log-likelihood: 6615.72233403002
#> EM - MRHLP: Iteration: 5 | log-likelihood: 6768.32107943849
#> EM - MRHLP: Iteration: 6 | log-likelihood: 6840.97339565987
#> EM - MRHLP: Iteration: 7 | log-likelihood: 6860.97262839295
#> EM - MRHLP: Iteration: 8 | log-likelihood: 6912.25605673784
#> EM - MRHLP: Iteration: 9 | log-likelihood: 6945.96718258737
#> EM - MRHLP: Iteration: 10 | log-likelihood: 6951.28584396645
#> EM - MRHLP: Iteration: 11 | log-likelihood: 6952.37644678517
#> EM - MRHLP: Iteration: 12 | log-likelihood: 6954.80510338749
#> EM - MRHLP: Iteration: 13 | log-likelihood: 6958.99033092484
#> EM - MRHLP: Iteration: 14 | log-likelihood: 6964.81099837456
#> EM - MRHLP: Iteration: 15 | log-likelihood: 6999.90358068156
#> EM - MRHLP: Iteration: 16 | log-likelihood: 7065.39327246318
#> EM - MRHLP: Iteration: 17 | log-likelihood: 7166.23398344994
#> EM - MRHLP: Iteration: 18 | log-likelihood: 7442.73330846285
#> EM - MRHLP: Iteration: 19 | log-likelihood: 7522.65416438396
#> EM - MRHLP: Iteration: 20 | log-likelihood: 7524.41524338024
#> EM - MRHLP: Iteration: 21 | log-likelihood: 7524.57590110924
#> EM - MRHLP: Iteration: 22 | log-likelihood: 7524.73808801417
#> EM - MRHLP: Iteration: 23 | log-likelihood: 7524.88684996651
#> EM - MRHLP: Iteration: 24 | log-likelihood: 7524.9753964817
#> EM - MRHLP: Iteration: 25 | log-likelihood: 7524.97701548847
mrhlp$summary()
#> ----------------------
#> Fitted MRHLP model
#> ----------------------
#>
#> MRHLP model with K = 5 regimes
#>
#> log-likelihood nu AIC BIC ICL
#> 7524.977 98 7426.977 7146.696 7147.535
#>
#> Clustering table:
#> 1 2 3 4 5
#> 413 344 588 423 485
#>
#>
#> ------------------
#> Regime 1 (k = 1):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 1.64847721 2.33823068 9.40173242
#> X^1 -0.31396583 0.38235782 -0.10031616
#> X^2 0.23954454 -0.30105177 0.07812145
#> X^3 -0.04725267 0.06166899 -0.01586579
#>
#> Covariance matrix:
#>
#> 0.0200740364 -0.004238036 0.0004011388
#> -0.0042380363 0.006082904 -0.0012973026
#> 0.0004011388 -0.001297303 0.0013201963
#> ------------------
#> Regime 2 (k = 2):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 -106.0250571 -31.4671946 -107.9697464
#> X^1 45.2035210 21.2126134 72.0220177
#> X^2 -5.7330338 -4.1285514 -13.9857795
#> X^3 0.2343552 0.2485377 0.8374817
#>
#> Covariance matrix:
#>
#> 0.11899225 -0.03866052 -0.06693441
#> -0.03866052 0.17730401 0.04036629
#> -0.06693441 0.04036629 0.11983979
#> ------------------
#> Regime 3 (k = 3):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 9.0042249443 -1.247752962 -2.492119515
#> X^1 0.2191555621 0.418071041 0.310449523
#> X^2 -0.0242080660 -0.043802827 -0.039012607
#> X^3 0.0008494208 0.001474635 0.001427627
#>
#> Covariance matrix:
#>
#> 4.103351e-04 -0.0001330363 5.289199e-05
#> -1.330363e-04 0.0006297205 2.027763e-04
#> 5.289199e-05 0.0002027763 1.374405e-03
#> ------------------
#> Regime 4 (k = 4):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 -1029.9071752 334.4975068 466.0981076
#> X^1 199.9531885 -68.7252041 -105.6436899
#> X^2 -12.6550086 4.6489685 7.6555642
#> X^3 0.2626998 -0.1032161 -0.1777453
#>
#> Covariance matrix:
#>
#> 0.058674116 -0.017661572 0.002139975
#> -0.017661572 0.047588713 0.007867532
#> 0.002139975 0.007867532 0.067150809
#> ------------------
#> Regime 5 (k = 5):
#>
#> Regression coefficients:
#>
#> Beta(d = 1) Beta(d = 2) Beta(d = 3)
#> 1 27.247199195 -14.393798357 19.741283724
#> X^1 -3.530625667 2.282492947 -1.511225702
#> X^2 0.161234880 -0.101613670 0.073003292
#> X^3 -0.002446104 0.001490288 -0.001171127
#>
#> Covariance matrix:
#>
#> 6.900384e-03 -0.001176838 2.966199e-05
#> -1.176838e-03 0.003596238 -2.395420e-04
#> 2.966199e-05 -0.000239542 5.573451e-04
mrhlp$plot()
Model selection
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 following parameters:
- K: The number of regimes;
- p: The order of the polynomial regression.
Let’s select a MRHLP model for the following multivariate time series Y:
data("toydataset")
x <- toydataset$x
y <- toydataset[, c("y1", "y2", "y3")]
matplot(x, y, type = "l", xlab = "x", ylab = "Y", lty = 1)
selectedmrhlp <- selectMRHLP(X = x, Y = y, Kmin = 2, Kmax = 6, pmin = 0, pmax = 3)
#> Warning in emMRHLP(X = X1, Y = Y1, K, p): EM log-likelihood is decreasing
#> from -3105.78591044952to -3105.78627830471!
#> The MRHLP model selected via the "BIC" has K = 5 regimes
#> and the order of the polynomial regression is p = 0.
#> BIC = -3033.20042397111
#> AIC = -2913.75756459291
selectedmrhlp$plot(what = "estimatedsignal")
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