{"id":38397,"date":"2020-03-16T12:01:00","date_gmt":"2020-03-16T16:01:00","guid":{"rendered":"https:\/\/ibkrcampus.com\/?p=38397"},"modified":"2022-11-21T09:45:12","modified_gmt":"2022-11-21T14:45:12","slug":"vector-autoregression-trading-model","status":"publish","type":"post","link":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/vector-autoregression-trading-model\/","title":{"rendered":"A Vector Autoregression Trading Model"},"content":{"rendered":"\n<p><strong><em>Excerpt<\/em><\/strong><\/p>\n\n\n\n<p>The <strong>vector autoregression (VAR)<\/strong> framework is common in econometrics for modelling correlated variables with bi-directional relationships and feedback loops. If you google <em>\u201cvector autoregression\u201d<\/em> you\u2019ll find all sorts of academic papers related to modelling the effects of monetary and fiscal policy on various aspects of the economy. This is only of passing interest to traders.<\/p>\n\n\n\n<p>However, if we consider that the VAR framework finds application in the modelling of correlated time series, the implication being that correlation implies a level of forecasting utility, then perhaps we could model a group of related financial instruments and make predictions that we can translate into trading decisions?<\/p>\n\n\n\n<p>So we\u2019ll give that a try. But first, a brief overview of VAR models.<\/p>\n\n\n\n<p><strong>Overview of VAR models<\/strong><\/p>\n\n\n\n<p>The univariate autoregression (AR) is a model of a time series as a function of past values of itself:<\/p>\n\n\n\n<p style=\"background-color:#fcfcdb;font-size:14px\" class=\"has-background\"><em>Y<\/em><em>t<\/em>=<em>\u03b1<\/em>+<em>\u03b2<\/em>1<em>Y<\/em><em>t<\/em>\u22121+<em>\u03b2<\/em>2<em>Y<\/em><em>t<\/em>\u22122\n\n<\/p>\n\n\n\n<p>That\u2019s an AR(2) model because it uses two previous values in the time series <em>Y<\/em>\n\n to estimate the next value. The name of the game is figuring out how many previous values to use, and estimating the coefficients (the <em>\u03b2<\/em>\n\ns) and the intercept (<em>\u03b1<\/em>\n\n).<\/p>\n\n\n\n<p>A vector autoregression (VAR) is an extension of this idea. It models multiple time series that affect one another together, as a system. It specifically allows for bi-directional relationships such as feedback loops, where say an increase in variable <em>X<\/em>\n\n may predict an increase in variable <em>Y<\/em>\n\n, but equally an increase in variable <em>Y<\/em>\n\n may predict an increase in variable <em>X<\/em>\n\n.<\/p>\n\n\n\n<p>Here\u2019s a VAR(1) model of two time series, <em>Y<\/em>1\n\n and <em>Y<\/em>2\n\n:<\/p>\n\n\n\n<p style=\"background-color:#fcfcdb;font-size:14px\" class=\"has-background\"><em>Y<\/em>1,<em>t<\/em>=<em>\u03b1<\/em>1+<em>\u03b2<\/em>11,1<em>Y<\/em>1,<em>t<\/em>\u22121+<em>\u03b2<\/em>12,1<em>Y<\/em>2,<em>t<\/em>\u22121+<em>\u03f5<\/em>1,<em>t<\/em>\n\n<br><em>Y<\/em>2,<em>t<\/em>=<em>\u03b1<\/em>2+<em>\u03b2<\/em>21,1<em>Y<\/em>1,<em>t<\/em>\u22121+<em>\u03b2<\/em>22,1<em>Y<\/em>2,<em>t<\/em>\u22121+<em>\u03f5<\/em>2,<em>t<\/em>\n\n<\/p>\n\n\n\n<p>The model uses a single lag of each time series to predict the next values of both time series. It requires the estimation of four coefficients and two intercepts.<\/p>\n\n\n\n<p>Just looking at the single lag case, you get a sense that these models have lots of parameters. Which of course triggers all the usual alarm bells around overfitting. In fact, if we have <em>N<\/em>\n\n time series and <em>p<\/em>\n\n lags in a VAR model, we must estimate <em>N<\/em>+<em>N<\/em><em>p<\/em>2\n\n parameters!<\/p>\n\n\n\n<p><strong>How do you figure out the number of lags?<\/strong><\/p>\n\n\n\n<p>Standard practice in econometrics is to use an information criterion. It\u2019s questionable how useful that would be in modelling financial asset returns, and in my view it makes sense to stick with a single lag unless you have a compelling reason to do otherwise.<\/p>\n\n\n\n<p>If you must, lean towards the Bayesian information criterion (BIC), which introduces a penalty term for the number of parameters in the model (the Aikake information criterion does too, but the BIC\u2019s penalty is bigger).<\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p>In this example, our group of stocks appeared in the <a rel=\"noreferrer noopener\" href=\"https:\/\/robotwealth.com\/the-graphical-lasso-and-its-financial-applications\/\" target=\"_blank\">network model of stock relationships<\/a> that we built using the Graphical Lasso. This is only a single input into the universe selection model that we trade with, but it will do fine for demonstrating this VAR model. We\u2019ll take the stocks in the little purple cluster consisting of residential construction stocks:<\/p>\n\n\n\n<p style=\"background-color:#fcfcdb;font-size:11px\" class=\"has-background\">\n# Extract basket prices<br>\ntickers <- c('KBH', 'LEN', 'PHM', 'DHI', 'TOL', 'MTH', 'MDC')\n<\/p>\n\n\n\n<p>This group is a fairly arbitrary choice \u2013 the basket is small enough that we can explore VAR models efficiently but other than that there\u2019s nothing particularly special about it. Other than the fact that the Graphical Lasso identified relationships among the group\u2019s stocks.<\/p>\n\n\n\n<p>You can get historical prices and volumes for these tickers via <code>tidyquant::tq_get<\/code>, which wraps <code>quantmod::getSymbols<\/code>:<\/p>\n\n\n\n<p style=\"background-color:#fcfcdb;font-size:11px\" class=\"has-background\">\n### VAR MODEL STRATEGY ###<br><br>\n \nlibrary(tidyquant)<br>\nlibrary(tidyverse)<br>\n <br><br>\n# Load basket prices<br>\ntickers <- c('KBH', 'LEN', 'PHM', 'DHI', 'TOL', 'MTH', 'MDC')<br>\nbasket_prices <- tq_get(tickers, get='stock.prices', from='2000-01-01', to = '2020-01-01') %>%<br>\n  rename(ticker = symbol)<br><br>\n \nbasket_prices %>%<br>\n  ggplot(aes(x = date, y = adjusted)) +<br>\n    geom_line(aes(color = ticker))\n<\/p>\n\n\n\n<p>Plotting the price series:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"700\" height=\"400\" data-src=\"\/campus\/wp-content\/uploads\/sites\/2\/2020\/03\/robot-wealth.png\" alt=\"\" class=\"wp-image-38420 lazyload\" data-srcset=\"https:\/\/ibkrcampus.com\/campus\/wp-content\/uploads\/sites\/2\/2020\/03\/robot-wealth.png 700w, https:\/\/ibkrcampus.com\/campus\/wp-content\/uploads\/sites\/2\/2020\/03\/robot-wealth-300x171.png 300w\" data-sizes=\"(max-width: 700px) 100vw, 700px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 700px; aspect-ratio: 700\/400;\" \/><\/figure>\n\n\n\n<p style=\"background-color:#e3e0b6\" class=\"has-background\">Visit Robot Wealth website to download the code and read the full article:<br><a href=\"https:\/\/robotwealth.com\/a-vector-autoregression-trading-model\/\">https:\/\/robotwealth.com\/a-vector-autoregression-trading-model\/<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Kris Longmore demonstrates vector autoregression (VAR) framework and how it is applied in cases such as econometrics for modelling. Read-to-use R code available<\/p>\n","protected":false},"author":271,"featured_media":38395,"comment_status":"closed","ping_status":"open","sticky":true,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[339,343,338,350,341,344,342],"tags":[5479,4922,6860,487,6861,6859],"contributors-categories":[13676],"class_list":{"0":"post-38397","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-data-science","8":"category-programing-languages","9":"category-ibkr-quant-news","10":"category-quant-asia-pacific","11":"category-quant-development","12":"category-quant-regions","13":"category-r-development","14":"tag-data-visualisation","15":"tag-econometrics","16":"tag-glasso-htmlwidgets","17":"tag-r","18":"tag-rstats-rstudio","19":"tag-vector-autoregression","20":"contributors-categories-robot-wealth"},"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 v27.5) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>A Vector Autoregression Trading Model | IBKR Quant<\/title>\n<meta name=\"description\" content=\"Kris Longmore demonstrates vector autoregression framework and how it is applied in econometrics for modelling. 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