This post explains how to use Spillover R package to calculate Diebold-Yilmaz spillover index. It measures a return or volatility spillover across asset classes and also a time series of rolling spillover index for taking time-varying spillovers into account.

Diebold-Yilmaz Spillover Index using R package

Diebold and Yilmaz (DY;2009,2012) introduce a volatility spillover measure based on VAR model's forecast error variance decompositions (FEVD).They said that It can be used to measure spillovers in returns or return volatilities across assets or similar categories. Fortunately, Spillover R package does this job in a simple manner.

Spillover Table and Rolling Spillover Index

DY spillover is calculated based on VAR(p) model's FEVD which uses Cholesky ordering or generalized FEVD and measures total, directional, net spillovers and so on.

Given a width of a rolling window such as 200-day, repeated VAR(p) estimations with successive rolling samples and calculations of a spillover produce a series of spillovers, in other words, dynamic spillover index.

R code : Spillover Table

We can calculate DY spillover table using O.spillover() and G.spillover() functions of Spillover R package. The following R code calculates the spillover table using Diebold and Yilmaz (2012) data set with estimated VAR(4) model.

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#========================================================# # Quantitative ALM, Financial Econometrics & Derivatives  # ML/DL using R, Python, Tensorflow by Sang-Heon Lee  # # https://shleeai.blogspot.com #--------------------------------------------------------# # Diebold-Yilmaz Spillover Index #========================================================#   graphics.off(); rm(list = ls())   library(Spillover)   #-------------------------------------------------- # Data : Diebold and Yilmaz (2012) #-------------------------------------------------- data(dy2012) df.data <- dy2012[,-1] date <- as.Date(dy2012$Date)   p.ar    <- 4  # VAR order n.ahead <- 10 # days   #-------------------------------------------------- # Spillover Table #--------------------------------------------------   # VAR(p) estimation VAR.est <- VAR(df.data, p=p.ar)    # based on Choleskdy FEVD O_table <- O.spillover(x=VAR.est, n.ahead=n.ahead,                        standardized = FALSE)   # based on Generalized FEVD G_table <- G.spillover(x=VAR.est, n.ahead=n.ahead,                        standardized = FALSE)   O_table G_table   Colored by Color Scripter

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The second spillover table is a replication of that of Diebold and Yilmaz (2012).

R code : Spillover Index

By using roll.spillover() function with the size of window being a 200-day, the rolling spillover index is calculated.

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#-------------------------------------------------- # Rolling Spillovers or Spillover Index #--------------------------------------------------   n.window <- 200   # data set for rolling spillover functions zoo.data <- zoo(df.data, date)   # Orthogonalized rolling spillover index O_index <- roll.spillover(data = zoo.data, width = n.window,                  n.ahead=n.ahead, p=p.ar)   # Generalized rolling spillover index G_index<- roll.spillover(data = zoo.data, width = n.window,                 n.ahead=n.ahead, index="generalized", p=p.ar)  # plot out <- cbind(O_index, G_index) head(out) x11(); plot(out, col=c(4,2), lwd = 2,             main="Diebold-Yilmaz Rolling Spillover index")   Colored by Color Scripter

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The second plot of dynamic spillover index is also a replication of that of Diebold and Yilmaz (2012).

Concluding Remarks

This post shows how to use Spillover R package to calculate Diebold-Yilmaz spillover table and dynamic rolling spillover index with only a few lines of code.

Reference

Diebold, F. X. and K. Yilmaz (2012), Better to give than to receive: Predictive directional measurement of volatility spillovers, International Journal of Forecasting 28-1, 57-66.