VAR: Estimation

Estimate VAR(1) models by efficiently sampling from the posterior distribution. This provides two graphical structures: (1) a network of undirected relations (the GGM, controlling for the lagged predictors) and (2) a network of directed relations (the lagged coefficients). Note that in the graphical modeling literature, this model is also known as a time series chain graphical model (Abegaz and Wit 2013) .

Usage

var_estimate(
  Y,
  rho_sd = sqrt(1/3),
  beta_sd = 1,
  iter = 5000,
  progress = TRUE,
  seed = NULL,
  ...
)

Arguments

Y

Matrix (or data frame) of dimensions n (observations) by p (variables).

rho_sd

Numeric. Scale of the prior distribution for the partial correlations, approximately the standard deviation of a beta distribution (defaults to sqrt(1/3) as this results to delta = 2, and a uniform distribution across the partial correlations).

beta_sd

Numeric. Standard deviation of the prior distribution for the regression coefficients (defaults to 1). The prior is by default centered at zero and follows a normal distribution (Equation 9, Sinay and Hsu 2014)

iter

Number of iterations (posterior samples; defaults to 5000).

progress

Logical. Should a progress bar be included (defaults to TRUE) ?

seed

An integer for the random seed (defaults to 1).

...

Currently ignored.

Value

An object of class var_estimate containing a lot of information that is used for printing and plotting the results. For users of BGGM, the following are the useful objects:

• beta_mu A matrix including the regression coefficients (posterior mean).

• pcor_mu Partial correlation matrix (posterior mean).

• fit A list including the posterior samples.

Details

Each time series in Y is standardized (mean = 0; standard deviation = 1).

Note

Regularization:

A Bayesian ridge regression can be fitted by decreasing beta_sd (e.g., beta_sd = 0.25). This could be advantageous for forecasting (out-of-sample prediction) in particular.

References

Abegaz F, Wit E (2013). “Sparse time series chain graphical models for reconstructing genetic networks.” Biostatistics, 14(3), 586–599. doi:10.1093/biostatistics/kxt005 .

Sinay MS, Hsu JS (2014). “Bayesian inference of a multivariate regression model.” Journal of Probability and Statistics, 2014.

Examples

# \donttest{
# data
Y <- subset(ifit, id == 1)[,-1]

# use alias (var_estimate also works)
fit <- var_estimate(Y, progress = FALSE)

fit
#> BGGM: Bayesian Gaussian Graphical Models 
#> --- 
#> Vector Autoregressive Model (VAR) 
#> --- 
#> Posterior Samples: 5000 
#> Observations (n): 94 
#> Nodes (p): 7 
#> --- 
#> Call: 
#> var_estimate(Y = Y, progress = FALSE)
#> --- 
#> Partial Correlations: 
#> 
#>               interested disinterested excited  upset strong stressed  steps
#> interested         0.000        -0.189   0.377 -0.208  0.326    0.286  0.077
#> disinterested     -0.189         0.000  -0.179 -0.045  0.109    0.159 -0.087
#> excited            0.377        -0.179   0.000 -0.125  0.493   -0.176 -0.002
#> upset             -0.208        -0.045  -0.125  0.000  0.111    0.362 -0.047
#> strong             0.326         0.109   0.493  0.111  0.000   -0.016  0.173
#> stressed           0.286         0.159  -0.176  0.362 -0.016    0.000 -0.014
#> steps              0.077        -0.087  -0.002 -0.047  0.173   -0.014  0.000
#> --- 
#> Coefficients: 
#> 
#>                  interested disinterested excited  upset strong stressed  steps
#> interested.l1         0.219        -0.012   0.176 -0.097  0.173    0.015  0.107
#> disinterested.l1     -0.052        -0.004   0.055 -0.021  0.051    0.088 -0.021
#> excited.l1           -0.081        -0.185   0.007  0.049 -0.080    0.086  0.101
#> upset.l1             -0.154         0.261  -0.096  0.431  0.055    0.320 -0.095
#> strong.l1             0.030         0.172   0.027  0.047  0.183   -0.067 -0.183
#> stressed.l1          -0.019        -0.010  -0.032 -0.043 -0.073    0.151  0.130
#> steps.l1             -0.155         0.181  -0.207  0.152 -0.091    0.206  0.041
#> --- 
#> Date: Fri Dec 13 11:54:05 2024 

# }