Time Series Graphical Lasso (tsGLASSO)

Introduction

Graphical modeling of high-dimensional time series

The tsGLASSO command estimates sparse inverse spectral density matrix for high-dimensional time series using Graphical Lasso (GLasso). It is related to graphical model selection. For details, see Dallakyan et. al 2021, Tugnait 2018, and Jung et. al 2015

Usage

First, we generate data from the VAR process using simulateVAR function. Then esimate sparse inverse spectral density matrix.

source("simulateVAR.R")
source("tsGLASSO.R")
K = 6
size = 128
burn = 100
halfWindowLength = 6
A_exp = matrix(c(0, 0.5, 0.5,
                 0, 0, 0.3,
                 0, 0.25, 0.5), 3, 3, byrow = TRUE)



sigma_u = matrix(c(18, 0, 6,
                   0, 1, 0,
                   6, 0 ,3), 3 ,3)

sigma = matrix(0, 6, 6)
sigma[1:3,1:3] = sigma_u
sigma[4:6, 4:6] = sigma_u / 1.5

A_6 = matrix(0, 6, 6)
A_6[1:3, 1:3] = A_exp
A_6[4:6, 4:6] = A_exp / 1.5
A_6[6,2]= 0.5
A_6[1,4] = 0.2
A = A_6
## simulate data from VAR process
set.seed(1234)
dta = simulateVAR(coefMatr = A, intercept = rep(0,K), size=size, 
                  burn = burn, Sigma = sigma, error.dist="normal")$simData
## run time series graphical lasso
TS = glasso_TimeSeries(dta, lambda = 2.5, halfWindowLength , 
                            rho = 100, alpha = 1.5, MAX_ITER = 100, 
                            thresh=TRUE, thr = 1e-5, rho.flex = TRUE, 
                            smooth = TRUE)
## Sparse inverse spectral density matrix
TS$Z
## Estimated sepctral density
TS$est_S
## Check the objective value
plot(TS$history.objval, type = 'l', main = "Objective value")

adallak/TSGlasso

Time Series Graphical Lasso (tsGLASSO)

Introduction

Usage