{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# A Bayesian Test for Cointegration\n", "\n", "## R notebook implementation\n", "\n", "The code in this notebook is adapted from the original MATLAB implementation by Chris Bracegirdle for the paper [*Bayesian Conditional Cointegration*](http://icml.cc/2012/papers/570.pdf) presented at [*ICML 2012*](http://icml.cc/2012/)\n", "\n", "Contact me" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "The downloaded binary packages are in\n", "\t/var/folders/bc/dnbc_47x6j7036ft8dp3bckh0000gn/T//Rtmp9bibIM/downloaded_packages\n", "\n", "\n", "Bayesian Cointegration \n", "Implementation of a Bayesian test for cointegration\n", "\n", "Written by Chris Bracegirdle\n", "(c) Chris Bracegirdle 2015. All rights reserved." ] } ], "source": [ "install.packages(c(\"tseries\",\"pROC\"))\n", "options(repr.plot.width=4, repr.plot.height=4)\n", "\n", "cat(\"\n", "\n", "Bayesian Cointegration \n", "Implementation of a Bayesian test for cointegration\n", "\n", "Written by Chris Bracegirdle\n", "(c) Chris Bracegirdle 2015. All rights reserved.\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a rather contrived function to randomly generate two time series, x and y, after making a random decision as to whether they are cointegrated, and generating according to the corresponding generating function" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "GenerateData <- function(T) {\n", " cointegrated <- runif(1) > 0.5\n", " phi <- if(cointegrated) runif(1) * 2 - 1 else 1\n", "\n", " std_eta <- exp(rnorm(1))\n", " std_x <- exp(rnorm(1))\n", " intercept <- exp(rnorm(1, sd=5))\n", " slope <- exp(rnorm(1, mean=1, sd=5))\n", "\n", " epsilon <- double(length=T)\n", " x <- double(length=T)\n", " y <- double(length=T)\n", " epsilon[1] <- rnorm(1, sd=std_eta)\n", " x[1] <- rnorm(1, sd=std_x)\n", " y[1] <- intercept + slope * x[1] + epsilon[1]\n", " for (t in 2:T){\n", " epsilon[t] <- phi * epsilon[t-1] + rnorm(1, sd=std_eta)\n", " x[t] <- x[t-1] + rnorm(1, sd=std_x)\n", " y[t] <- intercept + slope * x[t] + epsilon[t]\n", " }\n", " return(list(\"cointegrated\" = cointegrated, \"x\" = x, \"y\" = y))\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And here's what some randomly-generated data look like. Give it a whirl!" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "$cointegrated = FALSE" ], "text/latex": [ "\\textbf{\\$cointegrated} = FALSE" ], "text/markdown": [ "**$cointegrated** = FALSE" ], "text/plain": [ "$cointegrated\n", "[1] FALSE\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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VZRuLBiOIHcXxUJXxzujNSd7V1mJpEx2t0mLrsY93J0l/nXn7An7kr0IFQNAyrz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FQc3/Sw3hBjEdhAesKujwTnW4Sl6glppO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\nLu+8ssz7/WeiLfVqXtktdjyPUakzTuJGh8DJyoqN7RMlvxW6a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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gendata = GenerateData(1000)\n", "par(cex.axis=0.7, cex.lab=0.7, cex.main=0.7, cex.sub=0.7)\n", "plot(gendata$x, type='l', col='blue', ylim=range(gendata$x, gendata$y), ylab='')\n", "par(new=T); plot(gendata$y, type='l', col='green', axes=F, ylab=''); par(new=F)\n", "gendata[names(gendata)=='cointegrated']" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "LinearRegression <- function(x,y) {\n", " slope <- cor(x, y) * (sd(y) / sd(x))\n", " intercept <- mean(y) - (slope * mean(x))\n", " std_eta = sd( y - intercept - slope * x)\n", " return(list(\"slope\"=slope, \"intercept\"=intercept, \"std_eta\"=std_eta))\n", "}" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
\n", "\t
$slope \n", "\t\t 3.07897265732507 \n", "\t$intercept
\n", "\t\t
-24.1198791434192
\n", "\t
$std_eta \n", "\t\t 21.3009305364026 \n", " \n" ], "text/latex": [ "\\begin{description}\n", "\\item[\\$slope] 3.07897265732507\n", "\\item[\\$intercept] -24.1198791434192\n", "\\item[\\$std\\_eta] 21.3009305364026\n", "\\end{description}\n" ], "text/markdown": [ "$slope\n", ": 3.07897265732507\n", "$intercept\n", ": -24.1198791434192\n", "$std_eta\n", ": 21.3009305364026\n", "\n", "\n" ], "text/plain": [ "$slope\n", "[1] 3.078973\n", "\n", "$intercept\n", "[1] -24.11988\n", "\n", "$std_eta\n", "[1] 21.30093\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "LinearRegression(gendata$x,gendata$y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is an implementation of logSumExp with support for a vector of indices (b)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "mylogsumexp <- function(a,b) {\n", " #LOGSUMEXP Compute log(sum(exp(a).*b)) valid for large a\n", " # example: mylogsumexp(c(-1000,-1001,-998),c(1,2,0.5))\n", " amax <- max(Re(a))\n", " if (amax == -Inf) {\n", " amax=0\n", " }\n", " return(amax + log(as.complex(sum(exp(a-amax)*b))))\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a key result from the paper: calculating the moments and area as derived in the paper" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "CalcLogAreaLog <- function(logf,logF) {\n", " lncdf <- pnorm(c(1, -1), mean = Re(exp(logf)), sd = Re(exp(0.5*logF)), log.p = TRUE)\n", " logarea <- Re(mylogsumexp(lncdf, c(1, -1))-log(2))\n", " return(logarea)\n", "}\n", "CalcMomentsLog <- function(logf,logF,logarea) {\n", " lnpdf <- dnorm(c(1,-1), mean = Re(exp(logf)), sd = Re(exp(0.5*logF)), log = TRUE)\n", " logmoment1 <- mylogsumexp(c(lnpdf[1]+logF-logarea, lnpdf[2]+logF-logarea, logf), c(-0.5, 0.5, 1))\n", " logmoment2 <- mylogsumexp(c(logF+logf+lnpdf[1]-logarea, logF+logf+lnpdf[2]-logarea, \n", " logF+lnpdf[1]-logarea, logF+lnpdf[2]-logarea, 2*logf, logF),\n", " c(-0.5, 0.5, \n", " -0.5, -0.5, 1, 1))\n", " return(list(\"moment1\"=Re(exp(logmoment1)), \"moment2\"=Re(exp(logmoment2))))\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now inference: filtering and the EM update routine." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [], "source": [ "Filtering <- function(V,std_eta) {\n", " T <- length(V)\n", " \n", " # DIRECT METHOD\n", " logft <- log(as.complex(sum(V[2:T]*V[1:T-1])))-log(sum(V[1:T-1]^2))\n", " logFt <- 2*log(std_eta) - log(sum(V[1:T-1]^2))\n", " stopifnot(!is.nan(logft)) #logft must be real\n", " stopifnot(!is.nan(logFt)) #logFt must be real\n", " stopifnot(is.double(logFt)) #logFt must be real\n", " logarea <- CalcLogAreaLog(logft,logFt)\n", " loglik <- -0.5*log(sum(V[1:T-1]^2))-0.5*(T-2)*log(2*pi*std_eta^2)+logarea\n", " -(sum(V[2:T]^2)-sum(V[2:T]*V[1:T-1])^2/sum(V[1:T-1]^2))/(2*std_eta^2)\n", "\n", " # calculate moments\n", " moments <- CalcMomentsLog(logft,logFt,logarea)\n", " \n", " return(list(\"loglik\"=loglik, \"moment1\"=moments$moment1, \"moment2\"=moments$moment2))\n", "}\n", "\n", "EMUpdate <- function(x,y,moment1,moment2) {\n", " T <- length(x)\n", " xt <- x[2:T]\n", " xtm1 <- x[1:T-1]\n", " yt <- y[2:T]\n", " ytm1 <- y[1:T-1]\n", " \n", " # find the coefficients\n", " a <- 2 * (T-1) * moment1 - (T-1) * moment2 - (T-1)\n", " b <- moment1 * sum(xt+xtm1) - moment2 * sum(xtm1) - sum(xt)\n", " c <- moment2 * sum(ytm1) - moment1 * sum(yt + ytm1) + sum(yt)\n", " d <- 2 * moment1 * sum(xt * xtm1) - moment2 * sum(xtm1 ^ 2) - sum(xt ^ 2)\n", " e <- moment2 * sum(xtm1 * ytm1) - moment1 * sum(xtm1 * yt + xt * ytm1) + sum(xt * yt)\n", " \n", " # solve simultaneous equations\n", " slope <- ((a * e) - (c * b)) / ((b ^ 2) - (a * d))\n", " intercept <- (-slope * d / b) - (e / b)\n", "\n", " # now find optimal sigma\n", " eps <- y - intercept - slope * x\n", " ept <- eps[2:T]\n", " eptm1 <- eps[1:T-1]\n", " std_eta <- sqrt( (sum(ept^2) - 2 * moment1 * sum( ept * eptm1) + moment2 * sum(eptm1 ^ 2)) / (T-1) )\n", "\n", " stopifnot(std_eta>0) #Standard deviation must be positive\n", " stopifnot(is.double(std_eta)) #Standard deviation must be real\n", " return(list(\"slope\"=slope,\"intercept\"=intercept,\"std_eta\"=std_eta))\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is the real meat of the routine, simple since the inference routines are given above." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "CointInference <- function(epsilon,std_eta,x,y) {\n", " filtering <- Filtering(epsilon,std_eta)\n", " update <- EMUpdate(x,y,filtering$moment1,filtering$moment2)\n", " #std_eta_with_old_regression <- sqrt( (sum(epsilon[1:]**2) \\\n", " # - 2 * sum(moment1 * epsilon[1:] * epsilon[:-1]) \\\n", " # + sum(moment2 * epsilon[:-1] ** 2)) / (x.size - 1) )\n", " return(list(\"loglik\"=filtering$loglik,\n", " \"slope\"=update$slope, \"intercept\"=update$intercept,\n", " \"std_eta\"=update$std_eta#,\"std_eta_with_old_regression\"=std_eta_with_old_regression\n", " #,\"moment1\"=filtering$moment1\n", " ))\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And finally, the function we'll expose to check for cointegration using the Bayesian method." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "BayesianLearningTest <- function(x,y) {\n", " T <- length(x)\n", " ols <- LinearRegression(x,y)\n", " slope <- ols$slope\n", " intercept <- ols$intercept\n", " std_eta_coint <- ols$std_eta\n", "\n", " # cointegrated case - learn slope, intercept, std by ML\n", " logliks <- c(-Inf)\n", " for (i in 1:1000){\n", " stopifnot(!is.nan(intercept)) #Intercept cannot be nan\n", " stopifnot(!is.nan(slope)) #Slope cannot be nan\n", " stopifnot(is.double(std_eta_coint)) #Standard deviation must be real\n", " stopifnot(std_eta_coint > 0) #Standard deviation must be greater then 0\n", "\n", " inference <- CointInference(y-intercept-slope*x,std_eta_coint,x,y)\n", " slope <- inference$slope\n", " intercept <- inference$intercept\n", " std_eta_coint <- inference$std_eta\n", " \n", " if (inference$loglik-tail(logliks, n=1)<0.00001) {\n", " break\n", " }\n", " logliks <- c(logliks,inference$loglik)\n", " }\n", " \n", " # non-cointegrated case - use above slope, intercept, use ML std\n", " epsilon <- y-intercept-slope*x\n", " std_eta_p1 <- sqrt(mean((epsilon[2:T]-epsilon[1:T-1])^2))\n", " loglik_p1 <- sum(dnorm(epsilon[2:T], mean = epsilon[1:T-1], sd = std_eta_p1, log = TRUE))\n", "\n", " bayes_factor <- exp(loglik_p1 - inference$loglik)\n", " cointegrated <- inference$loglik > loglik_p1\n", " \n", " return(loglik_p1 - inference$loglik)\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bringing it all together\n", "Here we'll test the routine. First, generate some data to use." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "$cointegrated = TRUE" ], "text/latex": [ "\\textbf{\\$cointegrated} = TRUE" ], "text/markdown": [ "**$cointegrated** = TRUE" ], "text/plain": [ "$cointegrated\n", "[1] TRUE\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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N0cjqn72QUbq+tj+e2eopuoEOBRX/gBp39VHh+zcVWEKb+W7m/LzsFG1dAZDG1F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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gendata = GenerateData(1000)\n", "par(cex.axis=0.7, cex.lab=0.7, cex.main=0.7, cex.sub=0.7)\n", "plot(gendata$x, type='l', col='blue', ylim=range(gendata$x, gendata$y), ylab='')\n", "par(new=T); plot(gendata$y, type='l', col='green', axes=F, ylab=''); par(new=F)\n", "gendata[names(gendata)=='cointegrated']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And let's try the Bayesian routine to see if the result matches the truth given above when generating" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
\n", "\t
$test_result \n", "\t\t TRUE \n", "\t$comparison
\n", "\t\t
'Congratulations! The result of the routine matches the ground truth'
\n", "
\n" ], "text/latex": [ "\\begin{description}\n", "\\item[\\$test\\_result] TRUE\n", "\\item[\\$comparison] 'Congratulations! The result of the routine matches the ground truth'\n", "\\end{description}\n" ], "text/markdown": [ "$test_result\n", ": TRUE\n", "$comparison\n", ": 'Congratulations! The result of the routine matches the ground truth'\n", "\n", "\n" ], "text/plain": [ "$test_result\n", "[1] TRUE\n", "\n", "$comparison\n", "[1] \"Congratulations! The result of the routine matches the ground truth\"\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "BF <- BayesianLearningTest(gendata$x,gendata$y)\n", "test_result <- BF<0\n", "if (test_result == gendata$cointegrated) {\n", " comparison <- \"Congratulations! The result of the routine matches the ground truth\"\n", "} else {\n", " comparison <- \"Unfortunately the routine disagreed with the ground truth\"\n", "}\n", "list(\"test_result\"=test_result, \"comparison\"=comparison)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Comparing with Dickey-Fuller\n", "\n", "For comparison purposes we now test for cointegration using the standard test." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Loading required package: tseries\n", "Warning message in adf.test(epsilon, k = 1):\n", "“p-value smaller than printed p-value”" ] }, { "data": { "text/html": [ "TRUE" ], "text/latex": [ "TRUE" ], "text/markdown": [ "TRUE" ], "text/plain": [ "[1] TRUE" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "require(tseries)\n", "ols <- LinearRegression(gendata$x,gendata$y)\n", "epsilon <- gendata$y-ols$intercept-ols$slope*gendata$x\n", "adf <- adf.test(epsilon, k=1)\n", "pvalue <- adf$p.value\n", "cointegrated_adf <- pvalue<0.05\n", "cointegrated_adf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ROC curve: Bayesian test versus Dickey Fuller\n", "\n", "Both the Bayesian learning test and the Dickey-Fuller test do the job and provide a test statistic which we compare against a threshold. To compare which test is better, we look at the ROC curve, and in particular, the AUC of the ROC. To do that, we repeatedly generate time series and perform both tests, then plot the resulting ROC curve." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1] \"Experiment 250 of 5000\"\n", "[1] \"Experiment 500 of 5000\"\n", "[1] \"Experiment 750 of 5000\"\n", "[1] \"Experiment 1000 of 5000\"\n", "[1] \"Experiment 1250 of 5000\"\n", "[1] \"Experiment 1500 of 5000\"\n", "[1] \"Experiment 1750 of 5000\"\n", "[1] \"Experiment 2000 of 5000\"\n", "[1] \"Experiment 2250 of 5000\"\n", "[1] \"Experiment 2500 of 5000\"\n", "[1] \"Experiment 2750 of 5000\"\n", "[1] \"Experiment 3000 of 5000\"\n", "[1] \"Experiment 3250 of 5000\"\n", "[1] \"Experiment 3500 of 5000\"\n", "[1] \"Experiment 3750 of 5000\"\n", "[1] \"Experiment 4000 of 5000\"\n", "[1] \"Experiment 4250 of 5000\"\n", "[1] \"Experiment 4500 of 5000\"\n", "[1] \"Experiment 4750 of 5000\"\n", "[1] \"Experiment 5000 of 5000\"\n" ] } ], "source": [ "T <- 20\n", "experiments <- 5000\n", "\n", "cointegratedActual <- logical(length=experiments)\n", "logBF <- double(length=experiments)\n", "pvalue <- double(length=experiments)\n", "\n", "for (expr in 1:experiments) {\n", " gendata <- GenerateData(T)\n", " cointegratedActual[expr] <- gendata$cointegrated\n", "\n", " #classical test\n", " ols <- LinearRegression(gendata$x,gendata$y)\n", " epsilon <- gendata$y-ols$intercept-ols$slope*gendata$x\n", " suppressWarnings(adf <- adf.test(epsilon, k=1))\n", " pvalue[expr] <- adf$p.value\n", "\n", " #bayesian test\n", " logBF[expr] <- BayesianLearningTest(gendata$x,gendata$y)\n", " if (expr %% (experiments/20) == 0) {\n", " print(paste(\"Experiment\",expr,\"of\",experiments))\n", " }\n", "}" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Loading required package: pROC\n", "Type 'citation(\"pROC\")' for a citation.\n", "\n", "Attaching package: ‘pROC’\n", "\n", "The following objects are masked from ‘package:stats’:\n", "\n", " cov, smooth, var\n", "\n" ] }, { "data": { "text/plain": [ "$adf\n", "\n", "Call:\n", "roc.default(response = cointegratedActual, predictor = -pvalue)\n", "\n", "Data: -pvalue in 2539 controls (cointegratedActual FALSE) < 2461 cases (cointegratedActual TRUE).\n", "Area under the curve: 0.7822\n", "\n", "$bayes\n", "\n", "Call:\n", "roc.default(response = cointegratedActual, predictor = -logBF)\n", "\n", "Data: -logBF in 2539 controls (cointegratedActual FALSE) < 2461 cases (cointegratedActual TRUE).\n", "Area under the curve: 0.8976\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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emJ4PWH+M6nIydNQOabNHGdLw4CG+GgF0G8TrYWtDvUAbHF8C50CJR08N5Mnj98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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "require(pROC)\n", "roc_adf <- roc(cointegratedActual, -pvalue)\n", "roc_bayes <- roc(cointegratedActual, -logBF)\n", "par(cex.axis=0.7, cex.lab=0.7, cex.main=0.7, cex.sub=0.7)\n", "plot.roc(roc_adf, col='blue')\n", "plot.roc(roc_bayes, add=TRUE, col='green')\n", "legend(\"bottomright\", legend=c(\"DF\", \"Bayes\"),\n", " col=c(\"blue\",'green'), lwd=2, text.width = 0.15, cex=0.7)\n", "list(\"adf\"=roc_adf, \"bayes\"=roc_bayes)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above curve shows the efficacy of the classification of the test between cointegrated and non-cointegrated. Perfect classification occurs in the top left of the chart.\n", "\n", "Contact me" ] } ], "metadata": { "kernelspec": { "display_name": "R", "language": "R", "name": "ir" }, "language_info": { "codemirror_mode": "r", "file_extension": ".r", "mimetype": "text/x-r-source", "name": "R", "pygments_lexer": "r", "version": "3.4.1" } }, "nbformat": 4, "nbformat_minor": 0 }