Satationarity.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import stats\n",
    "from scipy.stats import skewnorm\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# An example of Wide Sense Stationary process that is not strictly stationary\n",
    "\n",
    "### Create `num_realisations` realisations of the process you believe will be WSS but not strictly stationary\n",
    "\n",
    "*Hint 1*: you can sample form the distribution you know is skewed (with differend skew at each time) and then normalise the distribution to have constant mean and variance. \n",
    "*Hint 2*: if you don't have any idea for a distribuition, check `scipy.stats.skewnorm`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1d7c8110550>]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_realisations = 10000\n",
    "ks = list(range(10)) # time indexes\n",
    "a = 0\n",
    "steps =  skewnorm.rvs(a, size=200)\n",
    "plt.plot(steps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Histograms at each timestamp\n",
    "Observe the empirical distribution of your proces over time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "ename": "IndexError",
     "evalue": "too many indices for array",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-31-c308866c9f36>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mk\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mks\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m     \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m     \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mhist\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msteps\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mk\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m50\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      4\u001b[0m     \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtitle\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"k: {k}, mean: {mean:.2f}, std: {std:.2f}\"\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mk\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mk\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmean\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msteps\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mk\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstd\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstd\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msteps\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mk\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m     \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mIndexError\u001b[0m: too many indices for array"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for k in ks:\n",
    "    plt.figure()\n",
    "    plt.hist(steps[k, :], 50)\n",
    "    plt.title(\"k: {k}, mean: {mean:.2f}, std: {std:.2f}\".format(k=k, mean=np.mean(steps[k, :]), std=np.std(steps[k,:])))\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Empirical distributions using boxplot\n",
    "Another way to look at the distributions is boxplot (right). It's sometimes more \n",
    "convenient than histogram. \n",
    "The orange horizontal lines in the middle are the medians, the boxes depicts the \n",
    "\"middle\" 50% of the distributions, the vertical lines cover most of the \n",
    "distribution and the dots depict \"unlikely\" points, outliers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.boxplot(steps.T, labels=ks)\n",
    "plt.title(\"Empirical distribution at each k\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'x' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-49-cd8c6a760a9c>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mfunction\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcos\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.14\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m440\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfunction\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'x' is not defined"
     ]
    }
   ],
   "source": [
    "function = math.cos(2*3.14*440*x)\n",
    "print(function)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The realizations\n",
    "If you look at just a few (for example 10) realizations of this process it's \n",
    "hard to judge if it a stationary (gaussian) noise, or if it is some more \n",
    "complicated distriburion. If you look at 500 realisations you can see some \n",
    "pattern emerge that changes over time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "ename": "IndexError",
     "evalue": "too many indices for array",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-28-0d6107337281>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mks\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msteps\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;36m10\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcolor\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'C0'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0malpha\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m0.7\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtitle\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"10 realizations of the process\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mks\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msteps\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;36m500\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcolor\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'C0'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0malpha\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m0.1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtitle\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"500 realizations of the process\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mIndexError\u001b[0m: too many indices for array"
     ]
    }
   ],
   "source": [
    "plt.plot(ks, steps[:,0:10], color='C0', alpha=0.7)\n",
    "plt.title(\"10 realizations of the process\")\n",
    "plt.show()\n",
    "plt.plot(ks, steps[:,0:500], color='C0', alpha=0.1)\n",
    "plt.title(\"500 realizations of the process\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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