{"id":244988,"date":"2026-06-23T10:45:46","date_gmt":"2026-06-23T14:45:46","guid":{"rendered":"https:\/\/ibkrcampus.com\/campus\/?p=244988"},"modified":"2026-06-23T10:48:55","modified_gmt":"2026-06-23T14:48:55","slug":"r-var1-simulation","status":"publish","type":"post","link":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/quant-development\/r-var1-simulation\/","title":{"rendered":"R: VAR(1) Simulation"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><em>The article &#8220;R: VAR(1) Simulation&#8221; was originally published on <a href=\"https:\/\/shleeai.blogspot.com\/2026\/01\/r-var1-simulation.html\">SHLee AI Financial Model<\/a> blog.<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This post explains how to perform simulations of a VAR(1) model.<\/p>\n\n\n\n<h2 id=\"h-var-1-simulation\" class=\"wp-block-heading\">VAR(1) Simulation<\/h2>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"r\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#========================================================#\n# Quantitative Financial Econometrics &amp; Deep Learning,\n# R, Python, Excel by Sang-Heon Lee \n#\n# https:\/\/shleeai.blogspot.com\n#--------------------------------------------------------#\n# VAR(1) Simulation\n#========================================================#\ngraphics.off(); rm(list = ls())\n \nlibrary(vars)\nlibrary(MASS)\n \n#----------------------------------------\n# data\n#----------------------------------------\ndata(usmacro, package = \"bvarsv\")\nM &lt;- usmacro[,c(1,3)]\n \nthor &lt;- 36+1 # with last one observation, VAR(1)\nnlag &lt;- 1; nvar &lt;- 2; nsim &lt;- 5000\n \nnobs &lt;- nrow(M)\nnold &lt;- nobs # historical data in graph\n \n#----------------------------------------\n# VAR(1) estimation\n#----------------------------------------\nest &lt;- vars::VAR(M, p = nlag, type = \"const\", \n                      season = NULL)\nARsC &lt;- do.call(rbind, lapply(est$varresult, \n                              \\(x) x$coefficients))\na0   &lt;- ARsC[,ncol(ARsC)]     # constant term\na1   &lt;- ARsC[,-ncol(ARsC)]    # AR(1) coef. matrix\nsig  &lt;- summary(est)$covres   # covariance matrix\n \n#----------------------------------------\n# VAR(1) forecast and fanchart\n#----------------------------------------\nfcst &lt;- predict(est, n.ahead = thor, ci = 0.99)\n \nnWd = 5*2; nHt = 6\nx11(width=nWd, height=nHt); par(mai=rep(0.4,4))\nplot(fcst)\nx11(width=nWd, height=nHt); par(mai=rep(0.4,4))\nfanchart(fcst, cis=c(0.01,0.1,0.3,0.5,0.7,0.9,0.99))\n \n#----------------------------------------\n# VAR(1) simulation\n#----------------------------------------\nYsim &lt;- array(NA, dim = c(nsim, thor, nvar))\nfor (s in 1:nsim) {\n    y1 &lt;- matrix(0, nrow=thor, ncol=nvar)\n    y1[1,] &lt;- t(tail(M, nlag))\n    for (i in 2:thor) {\n        mvr &lt;- mvrnorm(1, c(0,0), sig)\n        y1[i,] &lt;- a0 + a1 %*% y1[i-1,] + mvr\n    }\n    Ysim[s, , ] &lt;- y1\n}\n#----------------------------------------\n# Percentiles\n#----------------------------------------\nperc = c(0.995, 0.50, 0.005)\nYpct &lt;- array(NA, dim = c(length(perc), thor, nvar))\nfor (h in 1:thor) { for (k in 1:nvar) {\n    Ypct[, h, k] &lt;- quantile(Ysim[, h, k], probs = perc, \n                             names = FALSE, type = 7)\n}}\n \n#----------------------------------------\n# Graph\n#----------------------------------------\ndraw.VAR1.sim &lt;- function(nth) {\n    xfcst &lt;- (nold):(nold+thor-1)\n    plot(1:nold, M[(nobs-nold+1):nobs,nth], \n         main = paste0(\"X\",nth), xlim = c(1,nold+thor), \n         ylim = c(-2, max(Ysim[,,nth],M[,nth])),\n         type=\"l\", lty=1, lwd=2, col=\"black\", \n         ylab = paste0(\"X\",nth), xlab=\"Date\")\n    \n    for (i in 1:nsim) {\n        col1 &lt;- rgb(0.53,0.81,0.92,alpha=0.1)      # sky blue\n        if(nth == 2) col1 &lt;- rgb(1,0.5,0.5,alpha=0.1)  # pink\n        lines(xfcst, Ysim[i,,nth], type=\"l\", \n              lty=1, lwd=0.5, col=col1)\n    }\n    lines(xfcst, Ypct[1,,nth], type=\"l\", lty=1, lwd=1, col=\"blue\")\n    lines(xfcst, Ypct[2,,nth], type=\"l\", lty=1, lwd=2, col=\"blue\")\n    lines(xfcst, Ypct[3,,nth], type=\"l\", lty=1, lwd=1, col=\"blue\")\n}\n \nx11(width=nWd, height=nHt)\npar(mfrow = c(2,1), mar = c(3,4,2,2), mgp = c(2,0.6,0))\ndraw.VAR1.sim(1)\ndraw.VAR1.sim(2)<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Visit <a href=\"https:\/\/shleeai.blogspot.com\/2026\/01\/r-var1-simulation.html\">SHLee AI Financial Model<\/a> blog for additional insights on this topic.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This post explains how to perform simulations of a VAR(1) model.<\/p>\n","protected":false},"author":662,"featured_media":181803,"comment_status":"open","ping_status":"closed","sticky":true,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[339,343,338,341,342],"tags":[806,5479,487],"contributors-categories":[13728],"class_list":["post-244988","post","type-post","status-publish","format-standard","has-post-thumbnail","category-data-science","category-programing-languages","category-ibkr-quant-news","category-quant-development","category-r-development","tag-data-science","tag-data-visualisation","tag-r","contributors-categories-sh-fintech-modeling"],"pp_statuses_selecting_workflow":false,"pp_workflow_action":"current","pp_status_selection":"publish","acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v26.9 (Yoast SEO v27.8) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>R: VAR(1) Simulation | IBKR 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