Echo_State_Networks.ipynb

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    "### Overview\n",
    "In this notebook we study the formulation of the Reservoir Computing (RC) RNN. As an archetypal example, the RC implementation in time series for the Mackey-Glass chaotic system is recommended as a reference to this guide. This example can be found in the seminal paper: http://www.rctn.org/vs265/jaeger04-ESN.pdf; we encourage you to read this publication.\n",
    "\n",
    "In this notebook, for the implementation of the RC we will use the library \"pyESN\" which is available in https://github.com/cknd/pyESN. In the same directory, you can find the Mackey-Glass example that was discussed in the class. We encourage you to explore this library.\n",
    "\n",
    "We will employ the RC network to predict stock market prices. We will utilize time series data for the daily Amazon stock price (file: \"amazon.txt\"). You should study the Mackey-Glass example (mackey.ipynb) and then apply the RC for predicting the Amazon price.\n",
    "\n",
    "You can observe that the input is a vetor of ones, so there is not input function. In this case the prediction is not a response to the previous signal. Essentially, the network is learning the pattern of the history (training set) and trying to make predictions based on that. That approach works pretty well because RC prerforms well in pattern recognition and analysis tasks.\n",
    "\n",
    "We will predict 100 future time points by using the previous 1500 prices. As we discussed, RC is very sensitive to the hyper-parameter. So, you have to find the optimal set of hyper-parameter that gives the best predictions. For convenience, we are optimizing just two of the hyper-parameter, the spectrum radius  and a regularization term (noise). In particular, it adds noise in the hidden units to avoid the overfitting during the learning. The rest hyper-parameters are given.\n",
    "\n",
    "The goals of this notebook are for you to:\n",
    "1. learn the mechanics of RC\n",
    "2. confirm that RC training is fast\n",
    "3. learn how to use RC for forecasting\n",
    "4. acknowledge that RC is sensitive to hyper-parameters (no free lunch)\n",
    "5. learn how to optimize hyper-parameters of RC\n",
    "6. evaluate RC forecasting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
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   "source": [
    "import requests\n",
    "from IPython.core.display import HTML\n",
    "styles = requests.get(\"https://raw.githubusercontent.com/Harvard-IACS/2018-CS109A/master/content/styles/cs109.css\").text\n",
    "HTML(styles)"
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   "source": [
    "### Overview for the pyESN library for the RC implementation\n",
    "\n",
    "\n",
    "#### You call the RC as:\n",
    "esn = ESN(n_inputs = 1, <br>\n",
    " $\\quad$ $\\quad$     n_outputs = #, <br>\n",
    " $\\quad$ $\\quad$     n_reservoir = #,<br>\n",
    " $\\quad$ $\\quad$     sparsity= #,<br>\n",
    " $\\quad$ $\\quad$     random_state= #, <br>\n",
    " $\\quad$ $\\quad$     spectral_radius = #,<br>\n",
    " $\\quad$ $\\quad$     noise= #)\n",
    "<br> where # denotes the value that you choose.\n",
    "\n",
    "##### Brief explanation of the parameters:\n",
    "n_inputs: number of input dimensions <br>\n",
    "n_outputs: numberr of output dimensions <br>\n",
    "n_reservoir: number of reservoir neurons <br> \n",
    "random_state: seed for the random generator<br>\n",
    "sparsity: proportion of recurrent weights set to zero <br>\n",
    "spectral_radius: spectral radius of the recurrent weight matrix <br>\n",
    "noise: noise added to each neuron (regularization) <br>\n"
   ]
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  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "from matplotlib import pyplot as plt\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "# This is the library for the Reservoir Computing got it by: https://github.com/cknd/pyESN\n",
    "from pyESN import ESN \n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Read the data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Read your dataset from the file amazon.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Read dataset amazon.txt\n",
    "data = open(\"amazon.txt\").read().split()\n",
    "data = np.array(data).astype('float64')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class='exercise'><b> Part 1: Predictions with the RC  </b></div>\n",
    "Use the ESN from the pyESN library to employ an RC network. The task here is to predict two time points ahead by using the previous 1500 points and do that for 100 future points (check the figure below). So, in the end you will have a 100 time step prediction with prediction-window = 2. This will be your validation set.\n",
    "\n",
    "In this section you should use the following hyper-parameters:  \n",
    "- n_reservoir = 500\n",
    "- sparsity=0.2\n",
    "- random_state=23\n",
    "- spectral_radius=1.2\n",
    "- noise = 0.005\n",
    "\n",
    "<br> *Hint: Follow the mackey.ipynb example in pyESN*\n",
    "<img src=\"seq_prediction2.gif\">\n",
    "\n",
    "\n"
   ]
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  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_reservoir= 500\n",
    "sparsity=0.2\n",
    "rand_seed=23\n",
    "spectral_radius = 1.2\n",
    "noise = .0005\n",
    "\n",
    "\n",
    "esn = ESN(n_inputs = 1,\n",
    "      n_outputs = 1, \n",
    "      n_reservoir = n_reservoir,\n",
    "      sparsity=sparsity,\n",
    "      random_state=rand_seed,\n",
    "      spectral_radius = spectral_radius,\n",
    "      noise=noise)\n",
    "\n",
    "trainlen = 1500\n",
    "future = 10\n",
    "futureTotal=100\n",
    "pred_tot=np.zeros(futureTotal)\n",
    "\n",
    "for i in range(0,futureTotal,future):\n",
    "    pred_training = esn.fit(np.ones(trainlen),data[i:trainlen+i])\n",
    "    prediction = esn.predict(np.ones(future))\n",
    "    pred_tot[i:i+future] = prediction[:,0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot your prediction along with the ground truth (data) for the training and for the validation dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "from matplotlib import rc\n",
    "#rc('font',**{'family':'sans-serif','sans-serif':['Helvetica']})\n",
    "rc('text', usetex=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
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\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16,8))\n",
    "plt.plot(range(1000,trainlen+futureTotal),data[1000:trainlen+futureTotal],'b',label=\"Data\", alpha=0.3)\n",
    "#plt.plot(range(0,trainlen),pred_training,'.g',  alpha=0.3)\n",
    "plt.plot(range(trainlen,trainlen+futureTotal),pred_tot,'k',  alpha=0.8, label='Free Running ESN')\n",
    "\n",
    "lo,hi = plt.ylim()\n",
    "plt.plot([trainlen,trainlen],[lo+np.spacing(1),hi-np.spacing(1)],'k:', linewidth=4)\n",
    "\n",
    "plt.title(r'Ground Truth and Echo State Network Output', fontsize=25)\n",
    "plt.xlabel(r'Time (Days)', fontsize=20,labelpad=10)\n",
    "plt.ylabel(r'Price ($)', fontsize=20,labelpad=10)\n",
    "plt.legend(fontsize='xx-large', loc='best')\n",
    "sns.despine()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comment on the computational complexity of the training and evaluation of the RC. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The computational complexity for an RC is quite small comparing standard RNNs. The reason is that we essentially train only the the weights of the output layer, which is a linear layer, so the computational complexity is the same with a linear regression task. In particular, the training complexity is of the order O(N) where N is the number of hidden units located in the reservoir. This makes the training and the evaluation very fast."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class='exercise'><b> Part 2: Hyper-parameters optimization </b></div>\n",
    "We are asking you to find the optimal values for spectral_radius, noise  that gives the best prediction of this time series. In other words, we are looking for the hyper-parameters set that returns the minimum mean-square-error MSE. As previously, for each set of (spectral_radius, noise) you have to predict two time points ahead by using the previous 1500 points and do that for 100 steps as you did in part 1. These are essentially your validation set. Then calculate the MSE loss for the validation set and show through visualization which set gives the lowest MSE.\n",
    "<br>\n",
    "\n",
    "Hints:\n",
    "- Build a function for the MSE\n",
    "- Perform a grid search for the hyper parameters spectral_radius and noise\n",
    "- Use the ranges: spectrum_radius = [0.5, 1.5] and noise=[0.0001, 0.01]\n",
    "- For each set of (spectral_radius, noise) train the RC and make predictions as in part 1; these predictions are the validation sets\n",
    "- For each validation set calculate the MSE and store it\n",
    "- Make a 2D color plot to show the MSE for the different values of spectral_radius and noise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Build a function for the MSE**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "def MSE(yhat, y):\n",
    "    return np.sqrt(np.mean((yhat.flatten() - y)**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Perform a grid search**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('rho = ', 0.5, ', noise = ', 0.0001, ', MSE = ', 20.367056799629353)\n",
      "('rho = ', 0.5, ', noise = ', 0.0003, ', MSE = ', 22.44956008062169)\n",
      "('rho = ', 0.5, ', noise = ', 0.0007, ', MSE = ', 24.574909979223666)\n",
      "('rho = ', 0.5, ', noise = ', 0.001, ', MSE = ', 25.862558649155638)\n",
      "('rho = ', 0.5, ', noise = ', 0.003, ', MSE = ', 29.882933676750657)\n",
      "('rho = ', 0.5, ', noise = ', 0.005, ', MSE = ', 32.63942614291128)\n",
      "('rho = ', 0.5, ', noise = ', 0.007, ', MSE = ', 36.441245548726)\n",
      "('rho = ', 0.5, ', noise = ', 0.01, ', MSE = ', 44.77637915282457)\n",
      "('rho = ', 0.7, ', noise = ', 0.0001, ', MSE = ', 19.560517902720054)\n",
      "('rho = ', 0.7, ', noise = ', 0.0003, ', MSE = ', 20.12742795009036)\n",
      "('rho = ', 0.7, ', noise = ', 0.0007, ', MSE = ', 20.81801427735713)\n",
      "('rho = ', 0.7, ', noise = ', 0.001, ', MSE = ', 21.26142619965559)\n",
      "('rho = ', 0.7, ', noise = ', 0.003, ', MSE = ', 23.270880660885513)\n",
      "('rho = ', 0.7, ', noise = ', 0.005, ', MSE = ', 26.061347331527354)\n",
      "('rho = ', 0.7, ', noise = ', 0.007, ', MSE = ', 30.298361979419834)\n",
      "('rho = ', 0.7, ', noise = ', 0.01, ', MSE = ', 39.17074955771047)\n",
      "('rho = ', 0.9, ', noise = ', 0.0001, ', MSE = ', 18.612970860501118)\n",
      "('rho = ', 0.9, ', noise = ', 0.0003, ', MSE = ', 18.681815816990774)\n",
      "('rho = ', 0.9, ', noise = ', 0.0007, ', MSE = ', 18.835785386862582)\n",
      "('rho = ', 0.9, ', noise = ', 0.001, ', MSE = ', 18.982346096338105)\n",
      "('rho = ', 0.9, ', noise = ', 0.003, ', MSE = ', 20.81632098844061)\n",
      "('rho = ', 0.9, ', noise = ', 0.005, ', MSE = ', 24.60968377490799)\n",
      "('rho = ', 0.9, ', noise = ', 0.007, ', MSE = ', 30.231007189936882)\n",
      "('rho = ', 0.9, ', noise = ', 0.01, ', MSE = ', 41.28587340583505)\n",
      "('rho = ', 1, ', noise = ', 0.0001, ', MSE = ', 18.23852181110818)\n",
      "('rho = ', 1, ', noise = ', 0.0003, ', MSE = ', 18.27010615150326)\n",
      "('rho = ', 1, ', noise = ', 0.0007, ', MSE = ', 18.36078059388596)\n",
      "('rho = ', 1, ', noise = ', 0.001, ', MSE = ', 18.47920006882226)\n",
      "('rho = ', 1, ', noise = ', 0.003, ', MSE = ', 20.613227951906246)\n",
      "('rho = ', 1, ', noise = ', 0.005, ', MSE = ', 25.153712109142973)\n",
      "('rho = ', 1, ', noise = ', 0.007, ', MSE = ', 31.700838835741898)\n",
      "('rho = ', 1, ', noise = ', 0.01, ', MSE = ', 44.23736750779224)\n",
      "('rho = ', 1.1, ', noise = ', 0.0001, ', MSE = ', 17.981571756431556)\n",
      "('rho = ', 1.1, ', noise = ', 0.0003, ', MSE = ', 18.009398312163942)\n",
      "('rho = ', 1.1, ', noise = ', 0.0007, ', MSE = ', 18.09054736889828)\n",
      "('rho = ', 1.1, ', noise = ', 0.001, ', MSE = ', 18.218795249276663)\n",
      "('rho = ', 1.1, ', noise = ', 0.003, ', MSE = ', 20.82610561349463)\n",
      "('rho = ', 1.1, ', noise = ', 0.005, ', MSE = ', 26.272452530336505)\n",
      "('rho = ', 1.1, ', noise = ', 0.007, ', MSE = ', 33.91532767431614)\n",
      "('rho = ', 1.1, ', noise = ', 0.01, ', MSE = ', 48.22002405965967)\n",
      "('rho = ', 1.3, ', noise = ', 0.0001, ', MSE = ', 17.72839068197909)\n",
      "('rho = ', 1.3, ', noise = ', 0.0003, ', MSE = ', 17.799908079894703)\n",
      "('rho = ', 1.3, ', noise = ', 0.0007, ', MSE = ', 17.92917208443474)\n",
      "('rho = ', 1.3, ', noise = ', 0.001, ', MSE = ', 18.143905288756557)\n",
      "('rho = ', 1.3, ', noise = ', 0.003, ', MSE = ', 22.20343747458126)\n",
      "('rho = ', 1.3, ', noise = ', 0.005, ', MSE = ', 30.05977704513729)\n",
      "('rho = ', 1.3, ', noise = ', 0.007, ', MSE = ', 40.56654468067572)\n",
      "('rho = ', 1.3, ', noise = ', 0.01, ', MSE = ', 59.43231026660687)\n",
      "('rho = ', 1.5, ', noise = ', 0.0001, ', MSE = ', 17.627409489404897)\n",
      "('rho = ', 1.5, ', noise = ', 0.0003, ', MSE = ', 17.835052829116567)\n",
      "('rho = ', 1.5, ', noise = ', 0.0007, ', MSE = ', 18.100099619981393)\n",
      "('rho = ', 1.5, ', noise = ', 0.001, ', MSE = ', 18.481406587483956)\n",
      "('rho = ', 1.5, ', noise = ', 0.003, ', MSE = ', 24.887601182697498)\n",
      "('rho = ', 1.5, ', noise = ', 0.005, ', MSE = ', 36.34166374510305)\n",
      "('rho = ', 1.5, ', noise = ', 0.007, ', MSE = ', 50.99612645577753)\n",
      "('rho = ', 1.5, ', noise = ', 0.01, ', MSE = ', 75.94229622771246)\n"
     ]
    }
   ],
   "source": [
    "n_reservoir= 500\n",
    "sparsity   = 0.2\n",
    "rand_seed  = 23\n",
    "radius_set = [0.9,  1,  1.1]\n",
    "noise_set = [ 0.001, 0.004, 0.006]\n",
    "\n",
    "radius_set = [0.5, 0.7, 0.9,  1,  1.1,1.3,1.5]\n",
    "noise_set = [ 0.0001, 0.0003,0.0007, 0.001, 0.003, 0.005, 0.007,0.01]\n",
    "\n",
    "\n",
    "\n",
    "radius_set_size  = len(radius_set)\n",
    "noise_set_size = len(noise_set)\n",
    "\n",
    "trainlen = 1500\n",
    "future = 2\n",
    "futureTotal= 100\n",
    "\n",
    "loss = np.zeros([radius_set_size, noise_set_size])\n",
    "\n",
    "for l in range(radius_set_size):\n",
    "    rho = radius_set[l]\n",
    "    for j in range(noise_set_size):\n",
    "        noise = noise_set[j]\n",
    "\n",
    "        pred_tot=np.zeros(futureTotal)\n",
    "\n",
    "        esn = ESN(n_inputs = 1,\n",
    "          n_outputs = 1, \n",
    "          n_reservoir = n_reservoir,\n",
    "          sparsity=sparsity,\n",
    "          random_state=rand_seed,\n",
    "          spectral_radius = rho,\n",
    "          noise=noise)\n",
    "\n",
    "        for i in range(0,futureTotal,future):\n",
    "            pred_training = esn.fit(np.ones(trainlen),data[i:trainlen+i])\n",
    "            prediction = esn.predict(np.ones(future))\n",
    "            pred_tot[i:i+future] = prediction[:,0]\n",
    "        \n",
    "        loss[l, j] = MSE(pred_tot, data[trainlen:trainlen+futureTotal])        \n",
    "        print('rho = ', radius_set[l], ', noise = ', noise_set[j], ', MSE = ', loss[l][j] )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make a 2D plot to show the MSE for the different values of spectral_radius and noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16,8))\n",
    "im = plt.imshow(loss.T, vmin=abs(loss).min(), vmax=abs(loss).max(), origin='lower',cmap='PuRd')\n",
    "plt.xticks(np.linspace(0,radius_set_size-1,radius_set_size), radius_set);\n",
    "plt.yticks(np.linspace(0,noise_set_size-1, noise_set_size), noise_set);\n",
    "plt.xlabel(r'$\\rho$', fontsize=16); plt.ylabel('noise', fontsize=16); \n",
    "\n",
    "# im.set_interpolation('bilinear')\n",
    "cb = plt.colorbar(im); "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is the optimal set? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('The optimal set is:\\nspectrum radius = ', 1.5, '\\nnoise = ', 0.0001, '\\nMSE = ', 17.627409489404897)\n"
     ]
    }
   ],
   "source": [
    "minLoss = np.min(loss)\n",
    "index_min = np.where(loss == minLoss)\n",
    "index_min\n",
    "rho_opt = radius_set[int(index_min[0])]\n",
    "noise_opt = noise_set[int(index_min[1])]\n",
    "print('The optimal set is:\\nspectrum radius = ',\n",
    "      rho_opt,'\\nnoise = ',noise_opt,'\\nMSE = ',minLoss)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class='exercise'><b> Explore the RC ability in long predictions </b></div>\n",
    "\n",
    "In the previous section you made predictions for two time points ahead by using the previous 1500 points and for 100 future points in total. In this section we are asking to explore if the prediction window (we used 2 in part 1 and part 2) affects the predictability. Using the optimal hyper parameters you found in part 2, perform the analysis for windows: 1, 2, 5, and 10. Does the MSE in the validation set depends on this window? \n",
    "<br>\n",
    "\n",
    "**Hints:**\n",
    "\n",
    "- Use the optimal set of hyper parameters that you found on part 2\n",
    "- For this set repeat the calculation of the part 1 for different prediction windows and for the optimal window. In particular, instead of predicting two time points ahead you have to predict for 1, 2, 5, 10.\n",
    "- For each prediction calculate the MSE in the validation set\n",
    "- Plot the MSE as a function of the prediction window\n",
    "- Comment  on your results (always!) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_reservoir= 500\n",
    "sparsity=0.2\n",
    "rand_seed=23\n",
    "spectral_radius = 1.1\n",
    "noise = .0001\n",
    "\n",
    "# let k_set be an array with the prediction-window values\n",
    "k_set = [1,2,5,10]\n",
    "\n",
    "k_size = len(k_set)\n",
    "loss_k = np.zeros(k_size)\n",
    "\n",
    "for l in range(k_size):\n",
    "    future = k_set[l]\n",
    "\n",
    "    trainlen = 1500    \n",
    "    futureTotal=100\n",
    "    \n",
    "    pred_tot=np.zeros(futureTotal)\n",
    "\n",
    "    esn = ESN(n_inputs = 1,\n",
    "          n_outputs = 1, \n",
    "          n_reservoir = n_reservoir,\n",
    "          sparsity=sparsity,\n",
    "          random_state=rand_seed,\n",
    "          spectral_radius = spectral_radius,\n",
    "          noise=noise)\n",
    "\n",
    "\n",
    "    for i in range(0,futureTotal,future):\n",
    "        pred_training = esn.fit(np.ones(trainlen),data[i:trainlen+i])\n",
    "        prediction = esn.predict(np.ones(future))\n",
    "        pred_tot[i:i+future] = prediction[:,0]\n",
    "        \n",
    "    loss_k[l] = MSE(pred_tot, data[trainlen:trainlen+futureTotal])   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the MSE as a function of the prediction window"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(14,8))\n",
    "plt.plot(k_set, loss_k,'-ok', alpha=0.6)\n",
    "plt.title('MSE as a Function of Window Length', fontsize=20)\n",
    "plt.xlabel('Window Length', fontsize=18)\n",
    "plt.ylabel('MSE', fontsize=18)\n",
    "sns.despine()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How does the predictability depend on the length of the prediction? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the future predictions the error propagates in time and thus it increases in time. This is the reason that as longer is a prediction as more difficult to make it. We can see this behavior in the plot above, where the MSE is an increasing monotonically function of the prediction-window, hence longer predictions mean larger MSE."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.15"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}