{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Detrending auto-correlated data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here, we demonstrate spurious cross-correlations originating from auto-correlated time-series. We then show how taking correlations between detrended versions of these time series does not lead to falsely significant correlations. Our example revolves around two random walks, which one might intuitively believe to be independent. However, any two random walks (if long enough) are almost always correlated with extremely low p-values. This is due in part to random walks' autocorrelation, meaning that their position at any time is highly dependent on their position at the previous time step. Below, we show 1) how two random walks exhibit strong cross-correlations, as well as individual auto-correlations. We then show 2) how removing trends leads to non-significant correlations." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "1. Generate two random walks. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Intuititively, one would not think that two random walks should show a temporal correlation. But, due to auto-correlative effects, they often do." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import pylab as pl\n", "import scipy.stats as ss" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "# simulate two random walks using a series of random coinflips. the random walk is the cumulative sum of the number of heads (+1)\n", "# or tails (-1) flipped. \n", "np.random.seed(1)\n", "coinflip1_v = sign(1*(np.random.random(1000) > 0.5)-0.5)\n", "coinflip2_v = sign(1*(np.random.random(1000) > 0.5)-0.5)\n", "x1_v = cumsum(coinflip1_v)\n", "x2_v = cumsum(coinflip2_v)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Visualize the series of coinflips, and the resultant random walks" ] }, { "cell_type": "code", "collapsed": false, "input": [ "pl.figure(figsize=(24,2))\n", "pl.plot(coinflip1_v)\n", "pl.ylim([-1.5,1.5])\n", "pl.xlabel('Coinflip')\n", "pl.ylabel('Heads/Tails')\n", "pl.title('Coinflips #1');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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2o1o5Sxr0a1Rm8VAra402fSHbQjZlfdUEyRrRUjNX1ns5TzV60MZOa+To+R9J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JAAAg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\n8jRgqV5K53QNL08aazyPYkwkO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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "pl.figure(figsize=(24,2))\n", "pl.plot(coinflip2_v,'r')\n", "pl.ylim([-1.5,1.5])\n", "pl.xlabel('Coinflip')\n", "pl.ylabel('Heads/Tails')\n", "pl.title('Coinflips #2');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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wWVDFO6ywPt7VijTw06Fcdp5N4gI9tm+9iwr16Z3v9G2WrtHcfLPvmzFWSLmr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\ngnV8p6af5TptGqYN0R3xV1Zbd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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Visualize the random walks based on the coinflips. Position is based on the preceding total number of heads (+1) and tails (-1) coinflips. Do these look correlated?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "pl.figure()\n", "pl.plot(x1_v,label='Walk #1')\n", "pl.plot(x2_v,'r',label='Walk #2')\n", "pl.grid()\n", "pl.title('Random walks')\n", "pl.legend(loc=2)\n", "pl.xlabel('Coinflip')\n", "pl.ylabel('Position');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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B774DnntO2kejoRFF48Z2KYYQEqWEq0065O/vj99++w116tQBALRq1QoaO/U0nEWZ1T0X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\nu/4fCXPx367C+PAAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The cross-correlation though, may be surprising" ] }, { "cell_type": "code", "collapsed": false, "input": [ "xcorr_t = ss.pearsonr(x1_v,x2_v)\n", "print \"Random walk cross-correlation (rho): %1.2f\" % xcorr_t[0]\n", "print \"Random walk cross-correlation (pval): %1.4e\" % xcorr_t[1]" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Random walk cross-correlation (rho): 0.31\n", "Random walk cross-correlation (pval): 8.8596e-24\n" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This surprising cross-correlation is associated with the auto-correlative nature of the random walks. Below, we illustrate and measure this auto-correlation." ] }, { "cell_type": "code", "collapsed": false, "input": [ "pl.figure()\n", "pl.plot(x1_v[:-1],x1_v[1:],'o')\n", "pl.title('Walk #1')\n", "pl.xlabel('Position at Coinflip i')\n", "pl.ylabel('Position at Coinflip i+1')\n", "\n", "pl.figure()\n", "pl.plot(x2_v[:-1],x2_v[1:],'or')\n", "pl.title('Walk #2')\n", "pl.xlabel('Position at Coinflip i')\n", "pl.ylabel('Position at Coinflip i+1');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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7YmIiiYmJHhuTSMdl3aa6ulptqtubzMxMMjMzm/18y41p06ZN4/XXX+fqq692fYLNxoED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\nwoQJzse+dn6LFi1i9OjRXHf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KUgh3uz0qiotHjjjsTOqo/KM92xjgVahzvKUcXiPamgYTwv79+zlx4gSJiYls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\nPz8/fvzxx1aOyjFrici6p+B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VlcWXX35p957694+Ojub8+fPEx8fTr18/qqqqMBgM3Hjj\njTz00EMMHz6c+Ph4AHx8fHjvvfd4+OGHWb58ORUVFVxzzTWsXr2agIAAli9fzq233oq/vz+RkZGk\npaXxxhtv2N5TH4f2l6O/K1BXIY0dO5bz58+zZMmSOr3vHb1WCC3pdipEG5Cbm8vKlSvZunVra4ci\nvJiUjIRoA+obPQjRFDJCEEIIAcgIQQghRC1JCEIIIQBJCEIIIWpJQhBCCAFIQhBCCFFLEoIQQggA\n/j/eNS2BjLAQYwAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "print \"Random walk 1 auto-correlaton (rho): %1.2f\" % ss.pearsonr(x1_v[:-1],x1_v[1:])[0]\n", "print \"Random walk 2 auto-correlaton (rho): %1.2f\" % ss.pearsonr(x2_v[:-1],x2_v[1:])[0]" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Random walk 1 auto-correlaton (rho): 1.00\n", "Random walk 2 auto-correlaton (rho): 1.00\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "2. Detrending the random walks." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A common strategy for resolving the apparent cross-correlation between auto-correlated time-series, is to remove the trends within each time-series and instead study residual time-series. Below, we use ARIMA models (a common time-series tool) to detrend our random walks, since this is the tool we use in the manuscript. However, we note that if you knew all your time-series were random walks, a simpler method would be to just take the difference between neighboring time-points." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# this example calls R code. to run it, you'll need to install R, the rpy2 Python module, and the 'forecast' R package.\n", "import rpy2.robjects as R\n", "import rpy2.robjects.numpy2ri\n", "rpy2.robjects.numpy2ri.activate()\n", "R.r('library(forecast)');" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Loading required package: zoo\n", "\n", "Attaching package: \u2018zoo\u2019\n", "\n" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "The following objects are masked from \u2018package:base\u2019:\n", "\n", " as.Date, as.Date.numeric\n", "\n", "Loading required package: timeDate\n", "This is forecast 5.3 \n", "\n" ] } ], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "R.r.assign('x1_v',x1_v)\n", "R.r.assign('x2_v',x2_v)\n", "\n", "R.r('x1_arima<-auto.arima(x=x1_v,max.p=2,d=1,max.q=2,ic=\"bic\",approximation=FALSE)');\n", "R.r('x2_arima<-auto.arima(x=x2_v,max.p=2,d=1,max.q=2,ic=\"bic\",approximation=FALSE)');\n", "\n", "residual1_v = np.array(R.r('x1_arima$residuals'))\n", "residual2_v = np.array(R.r('x2_arima$residuals'))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The residual time-series resemble the series of coinflips that gave rise to the random walk. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "pl.figure(figsize=(24,2))\n", "pl.plot(residual1_v)\n", "pl.ylim([-1.5,1.5])\n", "pl.xlabel('Coinflip')\n", "pl.ylabel('Residual')\n", "pl.title('Residuals #1');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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3/v7uulZ7VL+/v3lv1UF96fG8zxHvU6f6fUpaNDS/Hn2oH68919+8ufszdgZo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YvniD89praPKLmR/chPVObNDZIWRMfICNFee/k0cN/eHGXZK0rkdZLKfQwNYZtD/Zf6gOyr7kvW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\nDtsIH3mE6JRTOk/oWlfC+O83v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"text": [ "" ] } ], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "pl.figure(figsize=(24,2))\n", "pl.plot(residual2_v,'r')\n", "pl.ylim([-1.5,1.5])\n", "pl.xlabel('Coinflip')\n", "pl.ylabel('Residual')\n", "pl.title('Residuals #2');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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IQsophg4t+jZ4cMnbhw71eaOnMxuNMidCWb/pTdWioqQTkux32qksrKINvv71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\nbhA5wct1mfo0S8+0OYc0J9HWCOg4c3vm4+DNuaw8XhprDiuX9PrnMpD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GDSr/DxrUGtMl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\ntW9PN63ynr+1+vf0rDQOEVsoy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Q133HEHffnLX6bR0VF4fcOGDXTeeefR7Nmz6frrr9+T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\nA1v5AAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The residual time-series should not be autocorrelated" ] }, { "cell_type": "code", "collapsed": false, "input": [ "print \"Residual 1 auto-correlaton (rho): %1.3f\" % ss.pearsonr(residual1_v[:-1],residual1_v[1:])[0]\n", "print \"Resdiual 2 auto-correlaton (rho): %1.3f\" % ss.pearsonr(residual2_v[:-1],residual2_v[1:])[0]" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Residual 1 auto-correlaton (rho): -0.058\n", "Resdiual 2 auto-correlaton (rho): -0.005\n" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "And, the cross-correlation of the random walks' residuals should not be correlated either. In our manuscript, we generally perform these kinds of cross-correlations (ones between residual time-series). " ] }, { "cell_type": "code", "collapsed": false, "input": [ "xcorr_t = ss.pearsonr(residual1_v,residual2_v)\n", "print \"Random walk cross-correlation (rho): %1.2f\" % xcorr_t[0]\n", "print \"Random walk cross-correlation (pval): %1.2f\" % xcorr_t[1]" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Random walk cross-correlation (rho): 0.02\n", "Random walk cross-correlation (pval): 0.61\n" ] } ], "prompt_number": 14 } ], "metadata": {} } ] }