In tomaskrehlik/frequencyConnectedness: Spectral Decomposition of Connectedness Measures

A package implementing frequency dependent connectedness due to Barunik, Krehlik (2018) as well as the traditional definitions of Diebold, Yilmaz (2009, 2012). See the papers for detailed description.

Installation

The stable version can be installed from CRAN by the standard means of using install.packages("frequencyConnectedness"). If there is any other development version, you can install it using the following instructions.

Be sure to have installed the devtools package that allows you to install packages from Github directly. To install the version from branch dev do

# install.packages("devtools")
library(devtools)
install_github("tomaskrehlik/frequencyConnectedness", tag = "dev") 

Usage

Currently the package works in close cooperation with the vars, urca, and BigVAR packages. In general, if you have any model that can produce the forecast error variance decomposition, it can be relatively easily made to work with this package. Let me know by filing an issue, if that is the case and I will try to incorporate it.

For the time being the following is available:

• Traditional estimation of VAR
• Fitting of the VECM model
• Using BigVAR to fit VAR models with various penalization schemes

For the illustration purposes we include some simulated data and volatilities data from the Ox-Man institute.

Let's walk through some basics. First load packages and get some data.

library(frequencyConnectedness)
data(exampleSim)
# Shorten the data, rolling estimation takes quite some time
exampleSim <- exampleSim[1:600,]

Then compute a system estimate on which the computation of connectedness is based:

# Compute the VAR(2) estimate with constant and save results
est <- VAR(exampleSim, p = 2, type = "const")
# Alternatively, you could use VECM
# est <- vec2var(ca.jo(exampleSim, ecdet = "trend", K = 2), r = 1)

Then use the estimate to compute the connectedness measures. First, the traditional overall measures that are not frequency dependent as in Diebold and Yilmaz, also with the possibility of nullifying the cross correlation elements. These commands print out the table and all the relevant measures.

# Compute traditional spillovers
spilloverDY09(est, n.ahead = 100, no.corr = F)
spilloverDY12(est, n.ahead = 100, no.corr = F)
spilloverDY09(est, n.ahead = 100, no.corr = T)
spilloverDY12(est, n.ahead = 100, no.corr = T)

If you save them, you can use the functions overall, to, from, net, pairwise to extract the spillovers in numeric form

sp <- spilloverDY12(est, n.ahead = 100, no.corr = T)
overall(sp)
to(sp)
from(sp)
net(sp)
pairwise(sp)

Next, we can decompose the measure on desired frequencies and get the frequency dependent measures.

# Get the frequency connectedness on partition (pi,pi/4), (pi/4,0), roughly
# corresponding to movements of 1 to 4 days and 4 to longer.
bounds <- c(pi+0.00001, pi/4, 0)
spilloverBK09(est, n.ahead = 100, no.corr = F, partition = bounds)
spilloverBK12(est, n.ahead = 100, no.corr = F, partition = bounds)

spilloverBK09(est, n.ahead = 100, no.corr = T, partition = bounds)
spilloverBK12(est, n.ahead = 100, no.corr = T, partition = bounds)

Note that the bounds should cover the range (1.001, 0)*pi, because the overall variance of the system is computed over these frequencies. (So if you wanted to remove the trend from computations, you could use (1.001, 0.01)*pi and the computation will ignore the variance created around the zero frequency.) Again, if you save the outputs from the spillover.... function, you can evaluate the overall, to, from, net, pairwise to get the relevant tables.

Moreover, if you want to aggregate the behaviour of some of the bands, you can do:

# Get the frequency connectedness on partition (pi,pi/4), (pi/4,0), roughly
# corresponding to movements of 1 to 4 days and 4 to longer.
bounds <- c(pi+0.00001, pi/4, pi/10, 0)

spilloverBK12(est, n.ahead = 100, no.corr = F, partition = bounds)
collapseBounds(spilloverBK12(est, n.ahead = 100, no.corr = F, partition = bounds), 1:2)

In many cases, one is interested in the dynamics of the connectedness. This can be achieved within the package by the following commands.

# Get the rolling window estimates
params_est = list(p = 2, type = "const")
sp <- spilloverRollingDY09(exampleSim, n.ahead = 100, no.corr = F, "VAR", params_est = params_est, window = 100)
# alternatively for co-integration you could do
# coint_est <- function(data, r) {
#     return(vec2var(ca.jo(data, ecdet = "trend", K = 2), r = r))
# }
# params_est = list(r = 1)
# sp <- spilloverRollingDY09(exampleSim, n.ahead = 100, no.corr = F, "coint_est", params_est = params_est, window = 100)

In general, the spilloverRolling.... function takes the following arguments:

• data, as exampleSim
• the arguments for relevant spillover function, as n.ahead, no.corr, and alternatively partition in case of the BK variant.
• window, what window you should roll
• name of function used for estimates, in this case "VAR", and list of parameters for this function called params_est

Using this, one can plot the resulting spillover measures.

plotOverall(sp)
plotTo(sp)
plotFrom(sp)
plotNet(sp)
plotPairwise(sp)

It is generally not a good idea to print all the spillover tables as they are not informative.

To make your own rolling estimate, let's follow this example. First, we start with construction of unconditional estimate and then use the same function for the rolling estimate. We perform VAR-LASSO estimation on a big system of log-volatilities of financial indices with automatic selection of the LASSO penalty using cross-validation.

# Example of usage of BigVAR package on the volatilities data that are included
library(BigVAR)
data(volatilities)

big_var_est <- function(data) {
    Model1 = constructModel(as.matrix(data), p = 4, struct = "Basic", gran = c(50, 50), VARX = list(), verbose = F)
    Model1Results = cv.BigVAR(Model1)
}

# Perform the estimation
oo <- big_var_est(log(volatilities[apply(volatilities>0, 1, all),]))

spilloverDY12(oo, n.ahead = 100, no.corr = F)
spilloverBK12(oo, n.ahead = 100, no.corr = F, partition = bounds)

# Now use the same function to perform the rolling estimation.
# The original estimation call was:
# big_var_est(log(volatilities[apply(volatilities>0, 1, all),]))
# so our data are:
# log(volatilities[apply(volatilities>0, 1, all),]) (we only use 1:150) because it takes a lot of time to fit
# n.ahead, no.corr, and window are self explanatory.
# name of the function to use for estimation is the big_var_est.
sp <- spilloverRollingBK12(log(volatilities[apply(volatilities>0, 1, all),])[1:150, ], n.ahead = 100, no.corr = F, func_est = "big_var_est", params_est = list(), window = 100, partition = bounds)

plotOverall(sp)

# I only plot 5 of the To indicators as plotting all of them is not nice
plotTo(sp, which = 1:5)

# You can extract the to spillovers
head(to(sp)[[1]])

If you have more cores at your disposal as is usual in the computers nowadays, it is beneficial to use them through parallel package especially in case of rolling estimation. If you use two cores it usually almost doubles the speed. For example

library(parallel)
library(frequencyConnectedness)

exampleSim <- exampleSim[1:600,]
params_est = list(p = 2, type = "const")

# Export the relevant variables to the cluster so that it can use them
cl <- makeCluster(16)
clusterExport(cl, c("params_est", "exampleSim"))

sp <- spilloverRollingDY09(exampleSim, n.ahead = 100, no.corr = F, "VAR", params_est = params_est, window = 100, cluster=cl)

stopCluster(cl)

Replication of paper and tests

I will release later some codes that replicat papers that we wrote using this package and the methodology.

If you would be interested in having your script included, write me an e-mail, or create an issue.

Because the package might change in the future, there is a set of test to always preserve the integrity of the original functions. You can read what is tested in the testfile. Also provided that you have the testthat package installed, you can run the tests yourself.

library(frequencyConnectedness)
library(testthat)
test_package("frequencyConnectedness")

License

This package is free and open source software, licensed under GPL (>= 2).

tomaskrehlik/frequencyConnectedness documentation built on Feb. 28, 2023, 8:46 a.m.