README.md

In b-brune/tvRRR: Time-varying reduced-rank regression using state-space models

tvRRR

Time-varying reduced rank regression using state-space models

WORK IN PROGRESS

The tvRRR package implements time-varying reduced rank regression as proposed in A state-space approach to time-varying reduced-rank regression (Work in progress, Brune, Bura and Scherrer).

Installation

The development version can be installed from GitHub with:

if (!require(devtools)) {
  install.packages("devtools")
}
devtools::install_github("b-brune/tvRRR")

Model

We fit a reduced-rank regression with time-varying coefficient matrices. We implement two types of time-variation, called model (A) and model (B):

(A)  yt = αtβ′xt + Γut + εt

(B)  yt = αβt′xt + Γut + εt

Model fitting is carried out using a Gaussian linear state-space model and the Kalman filter.

Example application

The function dataset() draws data from models (A) and (B) with different specifications of the time-variation in the parameter matrix.

library(tvRRR)

set.seed(712)
dat <- dataset("VARbreak", p = 5, d = 2, q = 5, t = 100, model = "A")
X <- dat$X; y <- dat$y

The main function of the dataset is tvRRR(). It automatically selects the rank of the model using BIC (in case it is unknown) and fits the tvRRR model.

fit <- tvRRR(X = X, y = y, select_rank = TRUE, d_max = 5, silent = TRUE, 
             model = "A")

fit
#> Time-varying reduced rank regression model of type A with latent rank d = 2 
#> 
#> Convergence information: 
#> 
#> Model selected based on BIC
#> 
#> Tried d = 1 to d = 5
#> Rank selected: d = 2 with BIC 558.277561
#> 
#> Model diagnostics / Convergence information 
#> 
#> Algorithm stopped after 29 iterations. 
#>  Relative likelihood difference: 0.000378
#>  Difference in Omega: 0.000968
#>  Difference in beta: 0.00052
#>  Difference in Sigma: 0.000436 
#> 
#> Estimated state covariance matrix: 
#> 
#>              [,1]         [,2]
#> [1,]  0.047435252 -0.003688764
#> [2,] -0.003688764  0.086516325

tvRRR() returns a list of the filtered time-varying parameters (one-step-ahead, filtered and smoothed), as well as the fitted parameters and some information on the data log-likelihood and convergence.

For more information on the model fitting algorithm see the paper, the accompanying vignette, and the function’s documentation.

Contributions

We are grateful for any contribution to the further development of the R package. If you experience any problems using the package or have suggestions for new features, please open an issue in the issue tracker.

Author

Barbara Brune ( b-brune ) - TU Wien, Vienna, Austria

b-brune/tvRRR documentation built on Dec. 19, 2021, 6:37 a.m.