{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Local level - Nile\n", "\n", "This notebook contains the example code from \"State Space Estimation of Time Series Models in Python: Statsmodels\" for the local level model of the Nile dataset." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# These are the basic import statements to get the required Python functionality\n", "%matplotlib inline\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Data\n", "\n", "For this example, we consider the annual flow volume of the Nile river between 1871 and 1970." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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tk3+ek/U9WKyK3wYHzoqSH/vHOQaGLPzwxmUIIUiPsRW2y3zM+UVvmLiFsVYj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\n8evULIoxktp9hq1bh55tm6pMjvfYZ/6xnWXxfrxXYm8C2V1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# This dataset is available in Statsmodels\n", "nile = sm.datasets.nile.load_pandas().data['volume']\n", "nile.index = pd.date_range('1871', '1970', freq='AS')\n", "\n", "# Plot the series to see what it looks like\n", "fig, ax = plt.subplots(figsize=(13, 3), dpi=300)\n", "ax.plot(nile.index, nile, label='Annual flow volume')\n", "ax.legend()\n", "ax.yaxis.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## State space model\n", "\n", "The local level model is:\n", "\n", "$$\n", "\\begin{align}\n", "y_t & = \\mu_t + \\varepsilon_t, \\qquad \\varepsilon_t \\sim N(0, \\sigma_\\varepsilon^2) \\\\\n", " \\mu_{t+1} & = \\mu_t + \\eta_t, \\qquad \\eta_t \\sim N(0, \\sigma_\\eta^2) \\\\\n", "\\end{align}\n", "$$\n", "\n", "This is already in state space form. Below we construct a custom class, `MLELocalLevel`, to estimate the local level model." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class MLELocalLevel(sm.tsa.statespace.MLEModel):\n", " start_params = [1.0, 1.0]\n", " param_names = ['obs.var', 'level.var']\n", "\n", " def __init__(self, endog):\n", " super(MLELocalLevel, self).__init__(endog, k_states=1)\n", "\n", " self['design', 0, 0] = 1.0\n", " self['transition', 0, 0] = 1.0\n", " self['selection', 0, 0] = 1.0\n", "\n", " self.initialize_approximate_diffuse()\n", " self.loglikelihood_burn = 1\n", "\n", " def transform_params(self, params):\n", " return params**2\n", "\n", " def untransform_params(self, params):\n", " return params**0.5\n", "\n", " def update(self, params, **kwargs):\n", " # Transform the parameters if they are not yet transformed\n", " params = super(MLELocalLevel, self).update(params, **kwargs)\n", "\n", " self['obs_cov', 0, 0] = params[0]\n", " self['state_cov', 0, 0] = params[1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Maximum likelihood estimation\n", "\n", "With this class, we can instantiate a new object with the Nile data and fit the model by maximum likelihood methods." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Statespace Model Results \n", "==============================================================================\n", "Dep. Variable: volume No. Observations: 100\n", "Model: MLELocalLevel Log Likelihood -632.538\n", "Date: Sat, 28 Jan 2017 AIC 1269.075\n", "Time: 10:26:43 BIC 1274.286\n", "Sample: 01-01-1871 HQIC 1271.184\n", " - 01-01-1970 \n", "Covariance Type: opg \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "obs.var 1.513e+04 2591.296 5.838 0.000 1e+04 2.02e+04\n", "level.var 1461.2648 843.355 1.733 0.083 -191.681 3114.211\n", "===================================================================================\n", "Ljung-Box (Q): 36.00 Jarque-Bera (JB): 0.05\n", "Prob(Q): 0.65 Prob(JB): 0.98\n", "Heteroskedasticity (H): 0.61 Skew: -0.03\n", "Prob(H) (two-sided): 0.16 Kurtosis: 3.08\n", "===================================================================================\n", "\n", "Warnings:\n", "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n" ] } ], "source": [ "nile_model = MLELocalLevel(nile)\n", "nile_results = nile_model.fit()\n", "\n", "print(nile_results.summary())" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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bstAXfce9gSC1TX7GF6SzvrSeumY/RVnxlqp7CYYUlW4feemJ5NYl9rhlobTO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\nYc2azOXd2MElzCFBk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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nile_results.plot_diagnostics(figsize=(13, 5));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This model appears to achieve a reasonably good fit. At this point, we can perform forecasting and compute impulse responses. Note that those two operations are not very informative for a local level model. The model will forecast the data to remain at whatever level it was last at, and impulse responses last forever." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Ro3no0X9ite6/Q/fCc8/y9ltv8vlnnzH300947oV/86fbbmXup5+iFNxy2//x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\nUXSLc1HpDVBW46dGFlgT1JVNjSErJYZ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Construct the predictions / forecasts\n", "nile_forecast = nile_results.get_prediction(start='1960-01-01', end='1975-01-01')\n", "\n", "# Plot them\n", "fig, ax = plt.subplots(figsize=(13, 3), dpi=300)\n", "\n", "forecast = nile_forecast.predicted_mean\n", "ci = nile_forecast.conf_int(alpha=0.5)\n", "\n", "ax.fill_between(forecast.ix['1970-01-02':].index, 600, 1100, color='grey',\n", " alpha=0.15)\n", "lines, = ax.plot(forecast.index, forecast)\n", "ax.fill_between(forecast.index, ci['lower volume'], ci['upper volume'],\n", " alpha=0.2)\n", "\n", "p1 = plt.Rectangle((0, 0), 1, 1, fc=\"white\")\n", "p2 = plt.Rectangle((0, 0), 1, 1, fc=\"grey\", alpha=0.3)\n", "ax.legend([lines, p1, p2], [\"Predicted inflation\",\n", " \"In-sample one-step-ahead predictions\",\n", " \"Out-of-sample forecasts\"], loc='upper left')\n", "ax.yaxis.grid()" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 1.0\n", "1 1.0\n", "2 1.0\n", "3 1.0\n", "4 1.0\n", "5 1.0\n", "6 1.0\n", "7 1.0\n", "8 1.0\n", "9 1.0\n", "10 1.0\n", "Name: volume, dtype: float64\n" ] } ], "source": [ "# Construct the impulse responses\n", "nile_irfs = nile_results.impulse_responses(steps=10)\n", "\n", "print(nile_irfs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Local level in Statsmodels via UnobservedComponents\n", "\n", "The large class of unobserved components (or structural time series models) is implemented in Statsmodels in the `sm.tsa.UnobservedComponents` class.\n", "\n", "First, we'll check that fitting a local level model by maximum likelihood using `sm.tsa.UnobservedComponents` gives the same results as our `MLELocalLevel` class, above.\n", "\n", "Here, notice that the parameter estimates are very slightly different, but the loglikelihood is the same." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Unobserved Components Results \n", "==============================================================================\n", "Dep. Variable: volume No. Observations: 100\n", "Model: local level Log Likelihood -632.538\n", "Date: Sat, 28 Jan 2017 AIC 1269.076\n", "Time: 10:33:10 BIC 1274.286\n", "Sample: 01-01-1871 HQIC 1271.184\n", " - 01-01-1970 \n", "Covariance Type: opg \n", "====================================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------------\n", "sigma2.irregular 1.508e+04 2586.506 5.829 0.000 1e+04 2.01e+04\n", "sigma2.level 1478.8117 851.329 1.737 0.082 -189.762 3147.385\n", "===================================================================================\n", "Ljung-Box (Q): 35.98 Jarque-Bera (JB): 0.04\n", "Prob(Q): 0.65 Prob(JB): 0.98\n", "Heteroskedasticity (H): 0.61 Skew: -0.03\n", "Prob(H) (two-sided): 0.17 Kurtosis: 3.08\n", "===================================================================================\n", "\n", "Warnings:\n", "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n" ] } ], "source": [ "nile_model2 = sm.tsa.UnobservedComponents(nile, 'local level')\n", "nile_results2 = nile_model2.fit()\n", "\n", "print(nile_results2.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One of the features of the built-in `UnobservedComponents` class is the ability to plot the various components." ] }, { "cell_type": "code", "execution_count": 215, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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JY3lj+mw69OpHstlOssXu/uty03FKSed6ZQjwzmpNferRduh0Opb8tKFA57zv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UfLopqwMZbHV9R9R28XkTfWHaPlUU3IGMviGhEp1pXHT9cdo2VRHUOD0IVpC/Bbx237BHCrMWYj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\ncapQCptyICqkdV4NLigGsgXyxSLtzfUTb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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = nile_results2.plot_components(figsize=(13, 3.5))\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Metropolis-Hastings - Local level\n", "\n", "Here we show how to estimate the local level model via Metropolis-Hastings using PyMC. Recall that the local level model has two parameters: $(\\sigma_\\varepsilon^2, \\sigma_\\eta^2)$.\n", "\n", "For the associated prediction parameters $1 / \\sigma^2$, we specify a $\\Gamma(2, 4)$ prior." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [-----------------100%-----------------] 10000 of 10000 complete in 7.3 sec" ] } ], "source": [ "import pymc as mc\n", "\n", "# Priors\n", "prior_eps = mc.Gamma('eps', 0.5, 1)\n", "prior_eta = mc.Gamma('eta', 0.5, 1)\n", "\n", "# Create the model for likelihood evaluation\n", "model = sm.tsa.UnobservedComponents(nile, 'local level')\n", "\n", "# Create the \"data\" component (stochastic and observed)\n", "@mc.stochastic(dtype=sm.tsa.statespace.MLEModel, observed=True)\n", "def loglikelihood(value=model, eps=prior_eps, eta=prior_eta):\n", " return value.loglike([1 / eps, 1 / eta])\n", "\n", "# Create the PyMC model\n", "pymc_model = mc.Model((prior_eps, prior_eta, loglikelihood))\n", "\n", "# Create a PyMC sample and perform sampling\n", "sampler = mc.MCMC(pymc_model)\n", "sampler.sample(iter=10000, burn=1000, thin=10)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Plotting eps\n", "Plotting eta\n" ] }, { "data": { "image/png": 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lIt1CTtq+SONXV1e3X0lEOkwiidoSYIyZjSaWZM0A/qlZnQXAjcEctE8CO4MEbEsb1y6g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\njnmGGcc8k1v8oaEhhoaGcotvZtkUOkZN0gTgWuC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XDMxoufQHE/Q/OYkYTOD4g6H5zYGfjLN3eo7e60i3otYd0ERNKaX6w02itgU4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\nJo11RhGRMZfNZklP2TH4ghKLbDZLNpsNHUMEiO/U5wHg3Jr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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot traces\n", "mc.Matplot.plot(sampler)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recall that these parameters are *precisions*, and we need to invert them to get the implied variances. The values are very close to those estimated by maximum likelihood." ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean sigma_eps^2 = 15172.1835608\n", "Mean sigma_eta^2 = 1497.97199417\n" ] } ], "source": [ "print 'Mean sigma_eps^2 = ', (1 / sampler.trace('eps').gettrace()).mean()\n", "print 'Mean sigma_eta^2 = ', (1 / sampler.trace('eta').gettrace()).mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gibbs Sampling - Local level\n", "\n", "Here we show how to estimate the local level model via Gibbs Sampling. The key to doing this is noting that conditional on the states, the observation and transition equations provide a formula for $\\varepsilon_t$ and $\\eta_t$:\n", "\n", "$$\n", "\\begin{align}\n", "\\varepsilon_t & = y_t - \\mu_t \\\\\n", "\\eta_t & = \\mu_{t+1} - \\mu_t \\\\\n", "\\end{align}\n", "$$\n", "\n", "In order to apply Gibbs sampling, we select the conjugate inverse Gamma prior, specifically $IG(3, 3)$, for both variances." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\begin{align}\n", "p(x) & = \\frac{1}{\\Gamma(a)} x^{-a-1} e^{-1/x} \\\\\n", "& \\implies \\frac{1}{\\beta} \\frac{1}{\\Gamma(a)} (x / \\beta)^{-a-1} e^{-1/(x / \\beta)} \\\\\n", "& = \\beta^{-1} \\beta^{a+1} \\frac{1}{\\Gamma(a)} x^{-a-1} e^{-\\beta/x} \\\\\n", "& = \\frac{\\beta^\\alpha}{\\Gamma(a)} x^{-a-1} e^{-\\beta/x} \\\\\n", "\\end{align}\n", "$$" ] }, { "cell_type": "code", "execution_count": 201, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from scipy.stats import invgamma\n", "\n", "def draw_posterior_sigma2_eps(model, states):\n", " resid = model.endog[:, 0] - states[0]\n", " post_shape = len(resid)\n", " post_scale = np.sum(resid**2)\n", "\n", " return invgamma.rvs(post_shape, scale=post_scale)\n", "\n", "def draw_posterior_sigma2_eta(model, states):\n", " resid = states[0, 1:] - states[0, :-1]\n", " post_shape = len(resid)\n", " post_scale = np.sum(resid**2)\n", "\n", " return invgamma.rvs(post_shape, scale=post_scale)\n", "\n", "np.random.seed(17429)\n", "\n", "# Create the model for likelihood evaluation and the simulation smoother\n", "model = sm.tsa.UnobservedComponents(nile, 'local level')\n", "sim_smoother = model.simulation_smoother()\n", "\n", "# Create storage arrays for the traces\n", "n_iterations = 10000\n", "trace = np.zeros((n_iterations + 1, 2))\n", "trace_accepts = np.zeros(n_iterations)\n", "trace[0] = [15000., 1300.] # Initial values\n", "\n", "# Iterations\n", "for s in range(1, n_iterations + 1):\n", " # 1. Gibbs step: draw the states using the simulation smoother\n", " model.update(trace[s-1], transformed=True)\n", " sim_smoother.simulate()\n", " states = sim_smoother.simulated_state\n", "\n", " # 2-3. Gibbs steps: draw the variance parameters\n", " sigma2_eps = draw_posterior_sigma2_eps(model, states)\n", " sigma2_eta = draw_posterior_sigma2_eta(model, states)\n", " trace[s] = [sigma2_eps, sigma2_eta]\n", "\n", "# For analysis, burn the first 1000 observations, and only\n", "# take every tenth remaining observation\n", "burn = 1000\n", "thin = 10\n", "final_trace = trace[burn:][::thin]" ] }, { "cell_type": "code", "execution_count": 204, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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2vdWRlFLJEGn/njMmF+v8la2OkjI1noBbKjOheQ4K5LA6jFJKZT7ZvggVkTR5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DZ9sWM/9zOZlhLCiK75qJ+Vhu17Syvfb5abgckjOuGeD5aGfY4JEeGIDk24vdY95/X8mfG67tqk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\n1v1aUQE8OQL4ykjAk9faeYxOG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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.stats import gaussian_kde\n", "\n", "fig, axes = plt.subplots(2, 2, figsize=(13, 5), dpi=300)\n", "\n", "sigma2_eps_kde = gaussian_kde(final_trace[:, 0])\n", "sigma2_eta_kde = gaussian_kde(final_trace[:, 1])\n", "\n", "axes[0, 0].hist(final_trace[:, 0], bins=20, normed=True, alpha=1)\n", "X = np.linspace(np.min(final_trace[:, 0]), np.max(final_trace[:, 0]), 5000)\n", "line, = axes[0, 0].plot(X, sigma2_eps_kde(X))\n", "ylim = axes[0, 0].get_ylim()\n", "vline = axes[0, 0].vlines(final_trace[:, 0].mean(), ylim[0], ylim[1],\n", " linewidth=2)\n", "axes[0, 0].set(title=r'$\\sigma_\\varepsilon^2$')\n", "\n", "axes[0, 1].hist(final_trace[:, 1], bins=20, normed=True, alpha=1)\n", "X = np.linspace(np.min(final_trace[:, 1]), np.max(final_trace[:, 1]), 5000)\n", "axes[0, 1].plot(X, sigma2_eta_kde(X))\n", "ylim = axes[0, 1].get_ylim()\n", "vline = axes[0, 1].vlines(final_trace[:, 1].mean(), ylim[0], ylim[1],\n", " linewidth=2)\n", "axes[0, 1].set(title=r'$\\sigma_\\eta^2$')\n", "\n", "p1 = plt.Rectangle((0, 0), 1, 1, alpha=0.7)\n", "axes[0, 0].legend([p1, line, vline],\n", " [\"Histogram\", \"Gaussian KDE\", \"Sample mean\"],\n", " loc='upper left')\n", "\n", "axes[1, 0].plot(final_trace[:, 0], label=r'$\\sigma_\\varepsilon^2$')\n", "axes[1, 0].plot(final_trace[:, 1], label=r'$\\sigma_\\eta^2$')\n", "axes[1, 0].legend(loc='upper left')\n", "axes[1, 0].set(title=r'Trace plots')\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Expanded model: UnobservedComponents\n", "\n", "We'll try a more complicated model now by adding a stochastic cycle to the local level. We'll estimate the model via maximum likelihood." ] }, { "cell_type": "code", "execution_count": 205, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Unobserved Components Results \n", "==============================================================================\n", "Dep. Variable: volume No. Observations: 100\n", "Model: local level Log Likelihood -624.934\n", " + stochastic cycle AIC 1257.868\n", "Date: Sat, 28 Jan 2017 BIC 1268.289\n", "Time: 12:36:46 HQIC 1262.086\n", "Sample: 01-01-1871 \n", " - 01-01-1970 \n", "Covariance Type: opg \n", "====================================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------------\n", "sigma2.irregular 1.462e+04 2910.491 5.023 0.000 8915.930 2.03e+04\n", "sigma2.level 824.8473 496.110 1.663 0.096 -147.510 1797.205\n", "sigma2.cycle 224.9072 230.550 0.976 0.329 -226.963 676.777\n", "frequency.cycle 0.5236 0.037 14.092 0.000 0.451 0.596\n", "===================================================================================\n", "Ljung-Box (Q): 35.24 Jarque-Bera (JB): 0.65\n", "Prob(Q): 0.68 Prob(JB): 0.72\n", "Heteroskedasticity (H): 0.55 Skew: -0.00\n", "Prob(H) (two-sided): 0.09 Kurtosis: 2.60\n", "===================================================================================\n", "\n", "Warnings:\n", "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n" ] } ], "source": [ "nile_model3 = sm.tsa.UnobservedComponents(nile, 'local level', cycle=True, stochastic_cycle=True)\n", "nile_results3 = nile_model3.fit()\n", "\n", "print(nile_results3.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the cycle component helps smooth out the level." ] }, { "cell_type": "code", "execution_count": 208, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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69HqRMQ7XOS9q1uDUanfOo2qxOTC5xhzfOFZbCPAw6vEwOgNSD6MOD6Meg06Q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\nI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2tPqILQBbBagtBWT48U+ebuo3z7saNMlOr05Hyuv2AtVw+t4cIN3cqwm3DOMVyosudo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fi+bqyot6W0imo/CVIy6XEHDNPctlofB73IcV0dnm2VaeSU5KqDHmKWCiTsIlwC+MMWPALhHZ\nDpwhIruBamPMfc5+PwZeiSqh08brEZbWh+ftCCRYpWZVc4R9vaNlHUI7Q8BrR9Hms5tac3WAkXiq\nYoKuZAJ9zRcFqKnKz2AsWVaRAOfDPNDZEPDajmNzVYB4Ms1oPMlYMs1YIk0smSKeTM/Yqu1xC36P\ni4DXcQP0ugl4XBU9n2uuURXwclyzh4ODMfqKHLXV73XRUhWYV27xijKegNdRRLuHSZfvDJaKolBz\nQhcB92X9b3eWJZzf45dPiIi8B3gPwJIluSeZr3SCPjdLG0Lzyg1iMrxuq9h1Do5xaKi8LDjZ+DzW\njVitB9BWoPmh+cbtEpY1zs1AX5MhIrTVB9nWWR5uufNtHuhssa5xRweEMcZYpTSZZiyRIpE2uEUc\ni82Rj8cluMT51vapInC7hEW1QZoifrqHxwqeQsTncdFc5ac25J03A3KKMhVBn1VEd3WPqCKaB46p\nhIrIHeCEpDya/zTG/CH/VTqCMea7wHfBpmgp5LHKnUxAG+0sHEFEWFATIOR3s693tOwaBI/bKjM6\naGCphPmhIrCkYX5a4PweN601ATpKnG4qEvDM23mg+UBEDltLmYdTNuYDPo+LhbVBmqv8dA/H6RkZ\ny+v7z+sRmiJ+6sM+VT4VZRwhn0cV0TxxTCXUGPOiWZS7H2jL+r/YWbbf+T1+uTIJYb+dBxTyaSDj\nyagOeA+75xZ6jtR0cblgWUN4XiozUxH2e2iu9tM5UJ7W60W1QSL++fusNUT8jMZTJQuCMp/nTivK\nTPG4XYcDFPaMjNEzHJ+1p4nf66I64KUqYNPrKIoyOaqI5odCtTQ3AT8TkWuxgYmOAx4wxqREZFBE\nzsIGJnob8I0C1aGiCXhdtNRoAIDp4ve4WdEYoWMgSt9IaaMI6rzdqWmuCjAyVn7zQ5uq/NSF516u\nu5myuC5IKm2Kng7J73WxrCGk3h6KMkPcLqG5KkBj2E/faJyRsRSJ9JFUHBN5nojYQZ/qgJfqoEcH\nTBVlhoR8HpY1hMvau6vcyTVFy6uwSmQTcLOIPGaMdTkNQwAAGmdJREFUudAYs0lEfgVsBpLA+53I\nuADv40iKllvRoERH4XELLdUB6nQOxoxxuYTFdSGq/AkODJYmimAk4KGtLjiv5hPOhnKbH1oT9LJA\nXUAB6865pD7Ezu6RogUq8nqEZQ1hfW4UJQdcLnFyWR69POmkCskopSIQ8Xv0eVOUHAn7j1hEVRGd\nOVIpKTpPP/1089BDDx17wxLQPTzGgRznUblc1hLTGParJSAPpNOG7uExuobGitYwNFf7aalWRWa6\njIwly6Lhrgl6aasP6qDPOJKpNDu7Rwqel9LtElY0hTVVgKIoilKRDI8l2V3E/sxxLZGyfmeKyMPG\nmNOPtZ0Og5UQEagKeFhUF2RNSxXNVQFVQPOEyyU0VwdYs6CK2gJH2XS5YGljSBXQGZKZH1pKakOq\ngE6Gx+1iaUMIj7tw10YEljWGyvplqiiKoihTEfF7WNYYRrsSM0NnnxcZl8sG0skEAFCls7B43S7a\n6kM0RJJ09Mfy7l4Y9NnydT7N7GiuCjCWSJckEI5VQENFP24l4fe4WdZQmLxoIrC0IaRB1xRFUZSK\nJ6OIFtMiWuno2z8P+D0uapxQ+IYjQQAMNmcb2CS31UEvYZ9brS4lIOTzsKo5Qt9InIODsbzMRawL\ne1lYo2lzcqWtPoTPE6NrsHgRc+vCXhbXqQI6HWx+4vy/WBfXBanSwGuKoijKHCHi97CyKcKe3pGS\nxCWpNFQJzQNVAa92piqEurCP2pCXobEkA6MJBmOJGVt4gj4X9WGbQ03JDy3VAQIeN/v6Rgs+gtgQ\n8bGwNljYg8wxIn4Pi+uC7OuN5qW81toAtSF9fhRFUZS5RdDnZlVThH190bLLAlBuqBKqzDtE5LBL\ntDHmmAppwOsi7Le50yJ+D261fBaEmpAXn6ewI4iNVT5aa1QBnQ21IR+JlOHgwOyDsPm9LlqqA4c9\nRxRFURRlruFxu1jeGObgQIxDQ+WZF70cUCVUmddMpJAORhOICBGfh7DfrWHsi0jQ57auLD2jeZ+/\n21Tl1zQsOdJU5cfrFrqH4zO6P5p6SlEURZlvLKgJEPS5ae8bzXtchbmAKqGK4pCtkCqlw+t2sbIp\nTHtfNC8Bi0SgucpPs0Yvzgu1IR+1IR+xRIqekTj9o/FJX64uFzRF/DRGNPWUoiiKMv+oCXoJeCPs\n7RklVuCUZ5WGKqGKopQdIkJbfYiAd2zW7p8+j4u6sJf6kE+t2QUg4HWzqDZIa3WA/miC3pEj1lER\nO/+6pcqv115RFEWZ1/g91strf39+BtfnCqqEKopStjRV+Qn53AzGEkTjKaKJ1JQuLSJ21LEu7CPi\n1+atGLhcQn3YR33YWkcHoglqQ15NW6QoiqIoDi6XHVyP+OP0RxOMjCXnfSoX7aUpilLWZIJCZYgl\nUkTjKUad71giZa2eIR91Ia9a3kpIwOsm4FXlU1EURVEmoi7soy7sI502jMSTDI8lGY4lJ3XVFbGp\nIANeN0Gfm5DPjd8zN/o5qoQqilJRZBSdOue/MUaD3SiKoiiKUjG4XHIkxWMNxJPpwwqpiA3UGPTa\nz1yNqaBKqKIoFY0qoIqiKIqiVDI+j4t6j29e5aCfG/ZcRVEURVEURVEUpSJQJVRRFEVRFEVRFEUp\nGqqEKoqiKIqiKIqiKEVDTIXEBxaRQ8CeUtdDyZlGoLvUlVCUcahcKuWKyqZSjqhcKuWIymV5sNQY\n03SsjSpGCVXmBiLykDHm9FLXQ1GyUblUyhWVTaUcUblUyhGVy8pC3XEVRVEURVEURVGUoqFKqKIo\niqIoiqIoilI0VAlVis13S10BRZkAlUulXFHZVMoRlUulHFG5rCB0TqiiKIqiKIqiKIpSNNQSqiiK\noiiKoiiKohQNVUKVnBGRH4pIl4g8mbXsFBG5T0QeE5GHROQMZ7lXRH4kIk+IyFMicmXWPreJyOMi\nsklEvi0i7lKcjzI3mEQuTxaRex35+6OIVGetu1JEtovI0yJyYdZylUslb8xELkXkxSLysLP8YRE5\nP2sflUslb8y0vXTWLxGRYRH5SNYylUslb8ziPX6Ss26Tsz7gLFe5LENUCVXywfXAReOWfQX4nDHm\nFOAzzn+A1wF+Y8x64DTgX0RkmbPuUmPMycCJQJOzraLMlut5plx+H/iEI3+/Az4KICJrgTcA65x9\nvpX1klK5VPLJ9UxTLrH57l7uLH87cEPWPiqXSj65nunLZYZrgVvHLVO5VPLJ9Uz/Pe4BfgK81xiz\nDjgXSDj7qFyWIaqEKjljjLkL6B2/GMiMTtUAHVnLw05jEQTiwKBTzqCzjQfwOdsqyqyYRC5XA3c5\nv/8CvMb5fQnwC2PMmDFmF7AdOMMpR+VSyRszkUtjzKPGmEzbuQkIiojfWadyqeSNGbaXiMgrgV1Y\nucwuR+VSyRszlMsLgI3GmMedfXuMMSnnt8plGaJKqFIo/h34qojsA74GZNxubwRGgAPAXuBrxpjD\nDYyI3A50AUPOtoqSTzZhFU6wI6Ftzu9FwL6s7dqdZYDKpVJwJpPLbF4DPGKMGcssULlUCsyEciki\nEeDjwOcm2knlUikwk7WXqwEjIreLyCMi8rHsnVQuyw9VQpVC8a/Ah40xbcCHgR84y88AUsBCYDlw\nhYisyOxkjLkQaAX8wPkoSn55J/A+EXkYqMJa4o+JyqVSYKaUSxFZB3wZ+Jfs5SqXSoGZTC6vAq4z\nxgxPtJPKpVJgJpNLD3A28Gbn+1Ui8sLMTiqX5YcqoUqheDvwW+f3r3FcG4E3AbcZYxLGmC7gHuD0\n7B2NMTHgDxwZ6VKUvGCM2WKMucAYcxrwc2CHs2o/R1ufFjvLsvdVuVQKwhRyiYgsxs57epsxZscE\n+6pcKgVhCrk8E/iKiOzGej19UkQ+MG5flUulIEwhl+3AXcaYbmPMKHALcOq4fVUuywhVQpVC0QG8\nwPl9PrDN+b3X+Y+IhIGzgC0iEhGRVme5B3gpsKWoNVbmPCLS7Hy7gE8B33ZW3QS8QUT8IrIcOA54\nQOVSKQaTyaWI1AI3Y4Nw3JO1vcqlUnAmk0tjzDnGmGXGmGXAfwNfNMZ8U+VSKQZTvMdvB9aLSMiR\nvxcAm1UuyxdVQpUJEZHLROTuaW77c+BeYI2ItIvI5cC7gf8nIo8DXwT2i0gf1n9/mYiMAQ8C/2eM\n2QiEgZtEZCPwGNZv/9sTHK5oiMgyETFOo1UxiMibReTPpa5HqZlELt8oIluxL6AO4P8AjDGbgF8B\nm4HbgPcD5wBbKTO5nApHXleVuh6ViojcKiJvL/Axpi2XwAeAVcBnxKa7eszpgIWB3SKyEyuXbcCz\nso7xKhHZ56TPeJaIrHH2HRKRDxXy/LLqMO126Fjbisg5IvL0NMs66t3lXIMVU+0zU+RIapI5k+Zh\nhnI5GWX3Hlcqmxm+x/uwEZsfxMrfI8aYm1G5LFvEGA0QVSwc15UQsNwYM+IsexfwFmPMudPYfwPw\nE2PM9/NQl03AUudvEBvGOun8/yL2wX6XMebsPBzrHKzLxJrMeedQ1lXAKmPMW6bY5ifAC7ENz0Hg\nK7O5Zk7qmF2A1xiTnHrr0lAJdSwlInIu9plZXMx9S4WIGOA4Y8z2PJe7gTy1PfORQjynzvvkXcaY\nOyZYtwP4D2PMH5z/PwAGjTEfzsexC00uciwil5Gnd1dWmbuZ5ForiqIos0MtocXHDfxbqSthjFln\njIkYYyLAP4APZP4bY76Y58MtBXZPRwHNk9XxS8AyY0w18Arg8yJyWh7KzTtimVfPYaVZlpXKQWXr\nMEs5OnXG+P+KoiiKUlLmVee3TPgq8BFnrs8zEJHnisiDIjLgfD/XWf4FrHvgNx03oG86y48Xkb+I\nSK+IPC0il+azsiLyNRHpE5FdInJx1vIaEfmBiBwQkf0i8vmJXJMc14nvA89x6v05ETlXRNqzttkt\nIh93XCVGRMTj/N/vuI89LSIvFJGLgE8Cr3fKenyiOhtjNmWlMTDOZ+Uk5+cSkU+JyB4R6RKRH4tI\nzbjN3ikiHc65fiRr3zNE5CERGRSRThG5NmvdWSLyTxHpF5HHHataZt0GEfmCiNwDjAIfFZGHxtXr\nwyJyk/P7pSLyqHOcfY41OEMmV1a/c02eM4E72oQylVWX/xKRe5xr/WcRaXTWBUTkJyLS45zHgyLS\nMsl1/ISI7HDK2Cwir8pad5lT/nUi0oONrIiIvFNEnnLk63YRWTpJ2Rm36LeLyF4R6RaR/8xa7xeR\n/3buUYfz2y92zvGtwELn2gyLyMIJyn+JU+chR+Y+Mm79FY5sHBCRd2Qtr3Hk5ZAjP58SZ0DB+X+a\n8/vNTv3XOf8vF5HfO7+vEpFfOeUMicgmETkqUNdUiMhHnXp1iMg7x63bINbTIvs+ZMvFtNoOmbzt\nmVSuJihjOvLxTaesLZIV0dA5jy+JyAPOM/AHEal31mVk43IR2Qvc6Sx/hXMt+539T3CWr3TO91Tn\n/0Ln/p07/pqNk9t+EdnpnPNlYp/DLsly3ZUZPqfOPtN6Bpxt3+rIVU+2/DvrrhL7rPpFZBg72Pm4\nc83vBM7Lun+rp5INsVznnN+giDwhIic66/xi3wl7xbZ53xaR4CT1HS9vRkTeKyLbnOv5vyIiExw/\nc60ed+r7ennmO2NSeZqgHkZEVjn3ejjrMyrW4pqRizuda9stIj8V5x0tIjcAS4A/Ovt9TMZN1XDK\nvsmRre0i8u5x92bWz7iiKMqcxRijnyJ9gN3Ai7BRYz/vLHsXsMH5XQ/0AW/Fhpp+o/O/wVm/AesS\nlCkvjM1t+A5n+2cB3cBaZ/2bsIl7j1Wvo8p1ll2GddF9N7ZD869YF92MC/fvgO84dWgGHgD+ZZLy\nLwPuzvp/LtA+7rpk5jUFgTXOeS101i8DVjq/r8K6BR7rnL6FVfAM8AgQmWS7dwLbgRVAxLk3N2Qd\n12BdicPAeuAQ8CJn/b3AW53fEeAs5/cioAd4CXag58XO/6as670XWOfctxps3qrjsur1IPCGrOu1\n3inrJKATeOW4Onomut5MT6Z2YPNrBZ3/1zjr/gX4I9aF3A2cBlRPch1fh0274wJej80F25pVnyTw\nQacOQWxkuu3ACc6yTwH/nKTszDl+z9n3ZGAMOMFZfzVwH1YOm4B/Av81kaxNUv4B4Bzndx1wata+\nSad8r3M/R4E6Z/2PsVH2qpw6bgUuz1p3hfP7u841/tesdR/OkueYU7Yba8W/b5rtyUWOLJyIlc+f\nOddp1STtRbZcTNl2HKuN4BhyNUv5+LBznV8PDAD1Wcfen3Wev8FpA7Jk48fOuiBWlkewz50X+BhW\n1nzOPu/Gzv0NYQNZfG2i88yq1zuce/N57HP7v9gQ/xdgn9vILJ/TmTwDa4Fh4PnOsa916pZpi64i\nq13MloNJ7t9UsnEh8DBQC4hTv8y9ug4bxKseK/d/BL40zXbfAH9yyl2CbUsvmmLb7Pqfy9HvjGPJ\n06RlZS3/KfBz5/cqrLz4sW3IXcB/Z227O3OtJ7qfzvbfAgLAKc65nZ/rM64f/ehHP3P5o5bQ0vAZ\n4IMi0jRu+UuBbcaYG4wxSWPMz7ETr18+STkvw7q5/p+z/aPYDtrrAIwxPzPGnJRDPfcYY75njEkB\nP8LmV2oRaw17CfDvxpgRY1OtXAe8IYdj/Y8xZp8xJorNI+oH1oqI1xiz20yQmmAqjDHvw3aSzsEq\nlmOTbPpm4FpjzE5jc55diY2Smu3W9znnPJ/AToB/o7M8AawSkUZjzLAx5j5n+VuAW4wxtxhj0saY\nvwAPYa9ZhuuNtdgmjTEDWGXmjQAichxwPLazhzFmgzHmCaesjVil+AVMj+nI1P8ZY7Y61/5X2E5U\n5vwasB24lDHmYWPM4EQHMcb82hjT4dTxl9hoyGdkbdJhjPmGU4co8F5s5/UpY+fIfRE4ZSpLEPY+\nRI0xjwOPY5VRsPfwamNMlzHmEDaB+luneX0y57lWRKqNMX3GmEfGrbva2JRCt2AVgTVirf5vAK40\nxgwZY3YD/y/ruH/nyD06B9vxzPx/gbM+w92OrKSAG7LO61hcir13Txrr6n7V9E956rZjGsyorZqG\nfHRhO/0JZ/3TzjEy3JB1np8GLpWjPS+ucp7RKFYpudkY8xdjTAL4GlY5fa5Tl+9hlb/7sW3aUVbF\ncexyrlEK+CV2oOxqY8yYMebP2Px0q5xyZ/qczuQZeC3wJ2PMXcZ6eXwaSE9Rdi4ksG3n8dhBx6eM\nMQccq+V7sAMovcaYIafOM2n3rzHG9Btj9gJ/40hbMyOmIU9TIiIfx57fO53ytjvyMua0IdcyzTZW\nRNqA5wEfN8bEjDGPYb1/3pa12WyfcUVRlDmLKqElwBjzJHZE+BPjVi0E9oxbtgdrWZuIpcCZjmtT\nv4j0YzvkC/JU1YOZH8bmXAJr8VuKtTAcyDrud7CWqNmyL+tY27G5x64CukTkFzKBG+WxcBSnu7E5\nH/91ks3GX/M9WKtEttvpvnHrM3W5HGt12SLWHfFlzvKlwOvG3ZezsR3eicoEa8XKKLdvAn6fueYi\ncqaI/E2s2+AAtvPaONW5T3F+mXPIlqmDWb9HsfcYbGfpduAXYt09vyIi3okOIiJvExt9M3O+J46r\n4/jzXQp8PWv7XqzVZTJZn6qeE93DmcjLa7ADBHtE5O/iuEo69JijA8lkjtuIfQbGHzdT/78D54gN\nC+/GKvfPExugpgZr+Z/svAIyvbmNC3mmbE6XXNuOGbVV05CP/caY7Ch54+/h+PP0Mrl8HVU3Y0za\nWZ9dt+85dfiGOeK6PxGdWb+jTnnjl0Wcc5zpczqTZ+Coe+0o4z1TlD1rjDF3At/EWny7ROS7IlKN\ntRCGgIez6nybs3y6TPYMz4hpyNNU+16MjcvwSmfQAhFpcd4z+0VkEPjJdMvD3puMUp7hWG3sdJ9x\nRVGUOYsqoaXjs1i3sOwXVQdHItZmWIJ1RQPr/pPNPuDvxpjarE/EGDOZwpUv9mEti41Zx602xqzL\nocyjzs1YK+7Z2OthgC9PtN008TDJnFCeec2XYN3csjuabePWdzh13GaMeSNW+f4ycKPYeYj7sJab\n7PsSNsZck32K4+rxF6BJRE7BKqM/y1r3M6xVtM0YU4MNLS6TlHOs88ucw/4Jtj0Kxyr1OWPMWqwV\n6WUcPboPgGO5+R42nUSDMaYWeDKrjhPVcx/WfTv7GgWNMf88Vr0mYKJ72DHJcZ+BMeZBY8wl2Pv4\ne6zCeCy6sRaj8cfd75S5HdvZ/CA2efYgtiP6HqxVJB9WrAM8UzazGcEqDRmyFcyZth3jr+O05Wqa\n8rEoMz8wq6yOrP/jzzOBvQcT1e+oujnltmXqJiIRbG7DHwBXiTO/NA/M9DmdyTNw1L0WkRDWS2G2\nTCUbGGP+x9hE8GuxA20fxV7vKLAuq741xga3KxrTlKfJ9l2D9eq51BiTPXDxRew9Wm9sQLu3MHX7\nlU0HUC8iVVnLptXGKoqizGdUCS0RTif1l0B2zrZbgNUi8iaxwXlej+0E/MlZ34mdu5jhT872bxUR\nr/N5tjhBOApY9wPAn7F5QKvFBvdZKSLTdRGdErE57c4XET92Lk2UI65nndg8oxPKrog0i8gbxCYn\ndovIhVil7q+THO7nwIdFZLnTOf0i8Mtx1q9Pi01+vA47P+yXzrHeIiJNjkLR72ybxo6iv1xELnTq\nEBAbWGPSVB+O2+CvsYGr6rFKaYYq7Eh7TETOwFpKMxxyjjlZHrxjydSkiMh5IrLecXscxHb8J1Ke\nwthO2iFnv3dgLRNT8W3gSjkSrKdGRKbrCjqenwOfEpEmsUGVPoO9B2DlpUGeGWwK57g+sYGDapx7\nMMg03Bwdt7pfAV8QkSqnY/wfWccFaw39AEdcbzeM+39MROR6Ebl+ktW/Ai4TkbWOUvLZcesfA17t\nyO4qrOU+w0zbjvFtz0zkajry0Qx8yKnH67DzEG/JWv+WrPO8GrjRuQcT8SvgpWKDmXmBK7CDZhnl\n7uvAQ8aYdwE3k798cTN9TmfyDNwIvExEzhYRH/Ya5PL+nlQ2HDk407l2I9g2OO20c98DrpMjyeIX\nOW1svhkvb9nMpr3Bseb+AfhPx0Mmmyqsq/2AiCzCKt3Tqo+jzP4T+JLT1p+EvZ4/mWh7RVEUxaJK\naGm5GvtCBcAY04O1Nl2BdbX6GPAyY0xmxP/rwGvFRlL8H8f95wLsnJwOrKXly9j5lJmonIUKy/82\nwIcN8NGH7SS1TrnH9PED12BH3g9iO6hXOut+7Xz3iMgjE+xrsK637U69voadu3rTJMf6Idbt9C5s\nHr8Y1nqVzd+xc8j+ig1ikkmqfhGwSWw0yq9jAwlFnU7JJdhIvoewFo+Pcuzn7WfYwFW/HqcEvw+4\nWkSGsArWYUud47L7BeAexzXtrKMuxrFlaioWYO/rIPCUcx1uGL+RMWYzdj7kvdjO2nrgnqkKNsb8\nDiurv3Dc354ELp5qnyn4PHbO7UbgCWwgqs87x9mCVVJ3OtdnIjfdtwK7nXq8F+uWOh0+iO2k7wTu\nxt6/H2at/zu2c3vXJP+nQxuTXEtjzK1Yi96dWPm8c9wm12HnLHZirT8/zdp3yrZjAsa3PdOWq2nK\nx/3Acdhn/gvAa51jZLgBuN6pZ4CjB+/GH+9prCXrG055LwdeboyJi8gl2Oc2Y/H9D+BUEZnuPZ+K\nGT2nM3kGjDGbgPdjZewAtm1rn2jbaTKpbADVWGWzD+tW2oMdHAP4OFbW7nPqfAc2kFy+uQr4kXOt\njoraPJv2xuFUbF2vk6wouc66zznrB7ADE78dt++XsANd/TIuerbDG7HBijqwQfs+a6aZU1REbhWR\nT05nW0VRlLlEJtKpoiiKUkY4Fq/HgZMcK+2cREQuw0ZqPXuS9RuwkV+/X8x6KYqiKIpSOHRivKIo\nShlijIlj3VIVRVEURVHmFOqOqyiKoiiKoiiKohQNdcdVFEVRFEVRFEVRioZaQhVFURRFURRFUZSi\noUqooiiKoiiKoiiKUjRUCVUURVEURVEURVGKhiqhiqIoiqIoiqIoStFQJVRRFEVRFEVRFEUpGqqE\nKoqiKIqiKIqiKEXj/wdoiFFfsASevQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = nile_results3.plot_components(figsize=(13, 6))\n", "fig.tight_layout()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.6" } }, "nbformat": 4, "nbformat_minor": 0 }