{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# US GDP vs. SPX: Holt-Winters time-series forecasting\n",
    "\n",
    "We examine the US gross domestic product's relationship to the \n",
    "US equity market (S&P500), in real terms. Forecasts for both are \n",
    "demonstrated using *Holt-Winters* time-series model. \n",
    "We derive the most likely range for real GDP growth, and \n",
    "identify excessive equity valuations aside from inflationary pressures.\n",
    "\n",
    "Our analysis would suggest the following\n",
    "***back of the envelope calculation***: say, SPX nominally has an annual gain of 6%\n",
    "and inflation stands at 2%, then the real SPX gain is 4%.\n",
    "Take half of that to arrive at real GDP growth: 2%.\n",
    "*Helpful because GDP numbers are announced after months of lag.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Dependencies:*\n",
    "\n",
    "- Repository: https://github.com/rsvp/fecon235\n",
    "- Python: matplotlib, pandas\n",
    "\n",
    "*CHANGE LOG*\n",
    "     \n",
    "    2017-04-09  Fix issue #2, update data and narrative, optimize HW parameters.\n",
    "                   Closing note on Didier Sornette research.\n",
    "    2015-02-20  Code review and revision.\n",
    "    2014-08-11  First version uses major revision yi_fred."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from fecon235.fecon235 import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " ::  Python 2.7.13\n",
      " ::  IPython 5.1.0\n",
      " ::  jupyter_core 4.2.1\n",
      " ::  notebook 4.1.0\n",
      " ::  matplotlib 1.5.1\n",
      " ::  numpy 1.11.0\n",
      " ::  pandas 0.19.2\n",
      " ::  pandas_datareader 0.2.1\n",
      " ::  Repository: fecon235 v5.17.0221 develop\n",
      " ::  Timestamp: 2017-04-12, 01:14:38 UTC\n",
      " ::  $pwd: /media/yaya/virt15h/virt/dbx/Dropbox/ipy/fecon235/nb\n"
     ]
    }
   ],
   "source": [
    "#  PREAMBLE-p6.15.1223 :: Settings and system details\n",
    "from __future__ import absolute_import, print_function\n",
    "system.specs()\n",
    "pwd = system.getpwd()   # present working directory as variable.\n",
    "print(\" ::  $pwd:\", pwd)\n",
    "#  If a module is modified, automatically reload it:\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "#       Use 0 to disable this feature.\n",
    "\n",
    "#  Notebook DISPLAY options:\n",
    "#      Represent pandas DataFrames as text; not HTML representation:\n",
    "import pandas as pd\n",
    "pd.set_option( 'display.notebook_repr_html', False )\n",
    "from IPython.display import HTML # useful for snippets\n",
    "#  e.g. HTML('<iframe src=http://en.mobile.wikipedia.org/?useformat=mobile width=700 height=350></iframe>')\n",
    "from IPython.display import Image \n",
    "#  e.g. Image(filename='holt-winters-equations.png', embed=True) # url= also works\n",
    "from IPython.display import YouTubeVideo\n",
    "#  e.g. YouTubeVideo('1j_HxD4iLn8', start='43', width=600, height=400)\n",
    "from IPython.core import page\n",
    "get_ipython().set_hook('show_in_pager', page.as_hook(page.display_page), 0)\n",
    "#  Or equivalently in config file: \"InteractiveShell.display_page = True\", \n",
    "#  which will display results in secondary notebook pager frame in a cell.\n",
    "\n",
    "#  Generate PLOTS inside notebook, \"inline\" generates static png:\n",
    "%matplotlib inline   \n",
    "#          \"notebook\" argument allows interactive zoom and resize."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Holt-Winters equations and code\n",
    "\n",
    "We adopt the Holt-Winters notation from Rob Hyndman's book, \n",
    "*Forecasting with Exponential Smoothing* (2008), ignoring the seasonal aspect of the H-W model.\n",
    "\n",
    "Our Python module `yi_timeseries.py` contains the core of model, see\n",
    "https://github.com/rsvp/fecon235/blob/master/lib/yi_timeseries.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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02Sy2g73D5s2boU8eACAUCocMHmJvZ8/j8QAA8+fN12BrpKWlQTnweLwxo8f4ePvA9Dk5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Bt4/PhxakoqkUg8f+G8WCRet27dpUuXcnNz79+7/+jRoz7nLNOmT6N0UPbu3fvu3bv4+PgT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\nzrpSGxsbgUDwKxeT56jduuTzHhLr9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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  Note that y represents the raw series in the equations.\n",
    "#  We use Y as a generic label in dataframes.\n",
    "\n",
    "Image(filename='holt-winters-equations.png', embed=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Working with dataframes\n",
    "\n",
    "We now get **data** for real US GDP into a pandas DataFrame.\n",
    "Our Holt-Winters functions generally accept dataframes as arguments\n",
    "(but computation in the background is using numpy arrays,\n",
    "and we let the *fecon235* API abstract the messy details).\n",
    "The user interface is designed to easily get the job done."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#  Retrieve quarterly data for real US GDP as DataFrame:\n",
    "dfy = get( q4gdpusr )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That quarterly data comes from FRED (Federal Reserve Bank, St. Louis),\n",
    "seasonally adjusted and expressed in billions of 2009 dollars."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                  Y\n",
       "T                  \n",
       "2015-04-01  16374.2\n",
       "2015-07-01  16454.9\n",
       "2015-10-01  16490.7\n",
       "2016-01-01  16525.0\n",
       "2016-04-01  16583.1\n",
       "2016-07-01  16727.0\n",
       "2016-10-01  16813.3"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  So we are currently discussing a 17 trillion dollar economy...\n",
    "tail( dfy )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#  DEFINE start YEAR OF ANALYSIS:\n",
    "start = '1980'\n",
    "\n",
    "#  We can easily re-run the entire notebook from different start date."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Holt-Winters requires specification of two parameters,\n",
    "**alpha** and **beta**, which sometimes are guessed.\n",
    "Our default values have been found in practice to be \n",
    "good *a priori* choices (see Gelper 2007, ibid.):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.26 0.19  :: DEFAULT Holt-Winters alpha and beta\n"
     ]
    }
   ],
   "source": [
    "print(hw_alpha, hw_beta, \" :: DEFAULT Holt-Winters alpha and beta\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optimizing Holt-Winters parameters\n",
    "\n",
    "We developed an algorithm to optimize those parameters,\n",
    "conditional on specific data. See\n",
    "https://github.com/rsvp/fecon235/blob/master/lib/ys_opt_holt.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " !.  WARNING: __main__.py Optimizing Holt-Winters alphabetaloss may take TIME!\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[0.9388, 0.2245, 0.2126, 35.739584510104578]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  This optimization procedure may be computationally intensive\n",
    "#  depending on data size and the number of grids,\n",
    "#  so uncomment the next command to run it:\n",
    "\n",
    "ab = optimize_holt( dfy['1980':], grids=50 )\n",
    "\n",
    "ab"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first two elements in the *ab* list are alpha and beta respectively.\n",
    "The third element gives the median absolute loss as percent\n",
    "for an one-step ahead forecast given those parameters.\n",
    "The fourth element is the median absolute loss\n",
    "(which indicates we have used a L1 loss function\n",
    "for robust optimization).\n",
    "\n",
    "2017-04-09: For start='1980', median absolute loss of 0.21% is respectable. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#  Let's use the optimized values for alpha and beta\n",
    "#  to compute the Holt dataframe:\n",
    "\n",
    "holtdf = holt( dfy, alpha=ab[0], beta=ab[1] )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                  Y         Level      Growth\n",
      "count    148.000000    148.000000  148.000000\n",
      "mean   11470.863514  11470.784096   68.695330\n",
      "std     3238.250597   3238.355570   39.795440\n",
      "min     6382.900000   6384.321000  -87.758692\n",
      "25%     8749.000000   8749.651230   51.976210\n",
      "50%    11505.800000  11504.636809   72.513945\n",
      "75%    14592.850000  14598.388106   95.063670\n",
      "max    16813.300000  16812.880080  144.547727\n",
      "\n",
      " ::  Index on min:\n",
      "Y        1980-07-01\n",
      "Level    1980-07-01\n",
      "Growth   2009-01-01\n",
      "dtype: datetime64[ns]\n",
      "\n",
      " ::  Index on max:\n",
      "Y        2016-10-01\n",
      "Level    2016-10-01\n",
      "Growth   2000-04-01\n",
      "dtype: datetime64[ns]\n",
      "\n",
      " ::  Head:\n",
      "                 Y        Level     Growth\n",
      "T                                         \n",
      "1980-01-01  6524.9  6526.504564  39.445264\n",
      "1980-04-01  6392.6  6403.209009   2.909950\n",
      "1980-07-01  6382.9  6384.321000  -1.983692\n",
      " ::  Tail:\n",
      "                  Y         Level     Growth\n",
      "T                                           \n",
      "2016-04-01  16583.1  16584.138088  68.284753\n",
      "2016-07-01  16727.0  16722.435878  84.002680\n",
      "2016-10-01  16813.3  16812.880080  85.448801\n",
      "\n",
      " ::  Correlation matrix:\n",
      "               Y     Level    Growth\n",
      "Y       1.000000  0.999999  0.175057\n",
      "Level   0.999999  1.000000  0.174776\n",
      "Growth  0.175057  0.174776  1.000000\n"
     ]
    }
   ],
   "source": [
    "stats( holtdf[start:] )\n",
    "#  Summary stats from custom start point:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DNjLIGJNBtm93zT8PPpj8awDiYdNGGGNMmr37rpv3p3p1uPFGNxnc6NGJXwcQi91PwBhj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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xaa34598c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#  Y here is the raw series, i.e. real GDP in billions of dollars:\n",
    "plot( holtdf['Y'][start:] )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2.58, 2.59, 1.46, 4, 148, '1980-01-01', '2016-10-01']"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  Annualized geometric mean return of the raw series:\n",
    "georet( todf(holtdf['Y'][start:]), yearly=4 )\n",
    "\n",
    "#  Since 1980, real GDP growth is about 2.6%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#  Level can be thought of as the smoothed series:\n",
    "\n",
    "# plot( holtdf['Level'][start:] )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#  Growth is the fitted slope at each point,\n",
    "#  expressed in units of the original series:\n",
    "\n",
    "# plot( holtdf['Growth'][start:] )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But we are most interested in the *forecasted*\n",
    "annualized growth rate in percentage terms.\n",
    "The specialized function *holtpc* handles that need."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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WFbHW9/XXmzd74401OUfcRUGua1QJ33vzZrMcpk3Lrieb351gn30s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\neDyeRogP3h6Px9MI+f97XLnGQeXrcwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xaa40882c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pc = holtpc( dfy, yearly=4, alpha=ab[0], beta=ab[1] )\n",
    "plot( pc[start:] )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0329366789936247"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gdp_forecast = tailvalue( pc )\n",
    "gdp_forecast"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That *tailvalue* of pc gives us the **latest forecast\n",
    "for real GDP growth over the next year**.\n",
    "But to understand its precision,\n",
    "we examine the big picture.\n",
    "\n",
    "### Big GDP Trend for discerning precision"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " ::  regresstime slope = -0.0061459975175\n"
     ]
    },
    {
     "data": {
      "image/png": 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tkH9guxyor5lDPOmdqPxxKX9cqecHMDMDxrD8sNjzgcdb7YN+e/uDkie7+xW9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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xaa2aaf2c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#  Here is the BIG GDP TREND since the end of World War 2:\n",
    "\n",
    "trendpc = trend( pc )\n",
    "\n",
    "plot( trendpc )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                Y\n",
      "count  280.000000\n",
      "mean     2.943414\n",
      "std      0.497661\n",
      "min      2.086048\n",
      "25%      2.514731\n",
      "50%      2.943414\n",
      "75%      3.372098\n",
      "max      3.800781\n"
     ]
    }
   ],
   "source": [
    "stat( trendpc )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Projected annualized real GDP growth has decreased from 3.8% post-WW2 \n",
    "to 2.1% most recently over the long time scale.\n",
    "\n",
    "Using our *detrend* function we can visualize the local fluctuations\n",
    "around the BIG GDP TREND."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " ::  regresstime slope = -0.0061459975175\n"
     ]
    },
    {
     "data": {
      "image/png": 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c359Cebn1+9pyeXka//gH0NubQkWFvL93L9DTY739/n6gpSWFujpZrqwEmpqy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\n0mKuv7o3R2gAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa73d762c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "detpc = detrend( pc )\n",
    "plot( detpc )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                  Y\n",
      "count  2.800000e+02\n",
      "mean  -6.875453e-16\n",
      "std    1.655007e+00\n",
      "min   -4.929548e+00\n",
      "25%   -8.177042e-01\n",
      "50%    1.973708e-01\n",
      "75%    1.115531e+00\n",
      "max    3.720233e+00\n"
     ]
    }
   ],
   "source": [
    "stat( detpc )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Standard deviation = 1.66 for the variation around the BIG GDP TREND. \n",
    "So at 2\\*std, we are roughly looking at +/- 3.3 percentage points around the long-term trend. \n",
    "\n",
    "2017-04-10:  We can see from *detpc* that the United States has recovered \n",
    "from the Great Recession to mean GDP growth. \"Doing just OK, ah, on average...\" \n",
    "\n",
    "A band of two standard deviations from +2.1 gives us a ***forward estimated range of \n",
    "(horrible) -1.2% to (great) +5.4% for real GDP growth.***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Real GDP forecast using Holt-Winters\n",
    "\n",
    "By fitting Level and Growth, Holt-Winters essentially uses \n",
    "the slope to make point forecasts forward in time.\n",
    "We show an alternate, more direct, way to arrive at our forecast."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "       Forecast\n",
       "0  16813.300000\n",
       "1  16898.328881\n",
       "2  16983.777683\n",
       "3  17069.226484\n",
       "4  17154.675286"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  Forecast real GDP, four quarters ahead:\n",
    "foregdp = holtforecast( holtdf, h=4 )\n",
    "foregdp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Forecast    2.030388\n",
       "dtype: float64"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  Forecast real GDP rate of GROWTH, four quarters ahead:\n",
    "100 * ((foregdp.iloc[4] / foregdp.iloc[0]) - 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We thus have computed the **Holt-Winters forecast for real GDP rate for the year ahead:**\n",
    "2.03% (as of 2017-04-10)\n",
    "\n",
    "This should concur with our *holtpc* method above, i.e. *gdp_forecast*. \n",
    "\n",
    "Note that foregdp.iloc[0] is the last actual data point, rather than the last Level."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#  We can plot the point forecasts 12 quarters ahead (i.e. 3 years):\n",
    "\n",
    "# plotholt( holtdf, 12 )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Real GDP vs. real SPX (S&P 500)\n",
    "\n",
    "This section covers the measured economy of goods and services, \n",
    "versus the market valuation of equity shares."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " ::  S&P 500 prepend successfully goes back to 1957.\n"
     ]
    }
   ],
   "source": [
    "#  SPX is a daily series, but we can directly retrieve its monthly version:\n",
    "spx = get( m4spx )\n",
    "\n",
    "#  ... to match the monthly periodicity of our custom deflator:\n",
    "defl = get( m4defl )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#  Now we synthesize a quarterly real SPX version by resampling:\n",
    "spdefl = todf( spx * defl )\n",
    "spq = quarterly( spdefl )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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sxylX6mroD1fVA4ETgIEiciRm/OMpqGsm3j82Z469Zp9zjq08TcXy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\n0mVYgObJpAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa739d36c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#  Real SPX resampled quarterly in current dollars:\n",
    "plot( spq )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5.36, 6.23, 13.2, 4, 149, '1980-01-01', '2017-01-01']"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  Geometric mean return for real SPX:\n",
    "georet( spq[start:], yearly=4 )\n",
    "\n",
    "#  cf. volatility for real GDP = 1.5% \n",
    "#      in contrast to equities = 13.2%"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**In real terms, the geometric mean return of SPX is double that of GDP.** \n",
    "\n",
    "Next, we examine their correlation.\n",
    "For start='1980' ***their correlation is around +0.9 which is fairly strong.***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " ::  FIRST variable:\n",
      "count      148.000000\n",
      "mean     11470.863514\n",
      "std       3238.250597\n",
      "min       6382.900000\n",
      "25%       8749.000000\n",
      "50%      11505.800000\n",
      "75%      14592.850000\n",
      "max      16813.300000\n",
      "Name: Y, dtype: float64\n",
      "\n",
      " ::  SECOND variable:\n",
      "count     149.000000\n",
      "mean     1118.668173\n",
      "std       587.281565\n",
      "min       260.527933\n",
      "25%       579.892749\n",
      "50%      1170.186413\n",
      "75%      1554.175713\n",
      "max      2308.843477\n",
      "Name: Y, dtype: float64\n",
      "\n",
      " ::  CORRELATION\n",
      "0.904455183426\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      Y   R-squared:                       0.818\n",
      "Model:                            OLS   Adj. R-squared:                  0.817\n",
      "Method:                 Least Squares   F-statistic:                     656.4\n",
      "Date:                Tue, 11 Apr 2017   Prob (F-statistic):           6.92e-56\n",
      "Time:                        18:16:41   Log-Likelihood:                -1279.7\n",
      "No. Observations:                 148   AIC:                             2563.\n",
      "Df Residuals:                     146   BIC:                             2569.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept   5871.9994    246.453     23.826      0.000      5384.922  6359.077\n",
      "X              5.0412      0.197     25.620      0.000         4.652     5.430\n",
      "==============================================================================\n",
      "Omnibus:                        3.518   Durbin-Watson:                   0.063\n",
      "Prob(Omnibus):                  0.172   Jarque-Bera (JB):                4.093\n",
      "Skew:                          -0.020   Prob(JB):                        0.129\n",
      "Kurtosis:                       3.814   Cond. No.                     2.71e+03\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 2.71e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "stat2( dfy['Y'][start:], spq['Y'][start:] )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The linear regression shows approximately that $dG / dS = 5.0$\n",
    "\n",
    "Therefore using mean values g and s: $ (dG/g) / (s/dS) = 5.0 * (s/g) $\n",
    "\n",
    "The right-hand side can be roughly interpreted as the ratio between percentage changes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.48761288617013465"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  2017-04-09, for start='1980':  5.0 * (s/g) = \n",
    "\n",
    "gsratio = 5.0 * div(spq[start:].mean(), dfy[start:].mean())\n",
    "gsratio = gsratio.values[0]\n",
    "gsratio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus **1% rise (100 bp) in real SPX would suggest additional 49 bp in real US GDP growth** \n",
    "(we note that regression $R^2 = 0.82$, so this seems reasonable). \n",
    "\n",
    "SPX is generally regarded as a leading economic indicator. \n",
    "(The regression fit improves if *start* is moved farther back.)\n",
    "\n",
    "***Back of the envelope calculation***: say, SPX nominally has an annual gain of 6%\n",
    "and inflation stands at 2%, then the real SPX gain is 4%.\n",
    "Take half of that to arrive at real GDP growth: 2%.\n",
    "*Helpful because GDP numbers are announced after months of lag.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Real SPX forecast using Holt-Winters\n",
    "\n",
    "Given that the log returns of SPX approximately follow an AR(1) process with unit root,\n",
    "we will resort to using our default values for alpha and beta \n",
    "which are ideal for smoothing a time-series with such characteristics.\n",
    "\n",
    "Accordingly, we shall look at projected (not actual) annual rates of return, \n",
    "rather than generating point forecasts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HY4/VO4HsgTCNjVrvue1N1aZLF9i0qZ5t2ypz/CD+eoYwhD33mp0yJdhdhF86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\n5Yky6vpGiMkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa72dbe8c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#       holtpc should be familiar from our GDP analysis.\n",
    "pcspq = holtpc( spq, yearly=4, alpha=hw_alpha, beta=hw_beta )\n",
    "plot( pcspq )\n",
    "\n",
    "#  Note we use all data since 1957."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.36048159499744"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spx_forecast = tailvalue( pcspq )\n",
    "spx_forecast"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Real SPX returns are very volatile, especially on the downside.\n",
    "\n",
    "2017-04-10: SPX is trading near all-time highs,\n",
    "and **Holt-Winters is forecasting +4.4% annualized over the next year**.\n",
    "Worth noting that the *real* rate is being projected, \n",
    "thus if inflation stands at 2%, the *nominal* rate of return will be +6.4%.\n",
    "\n",
    "\n",
    "### SPX over the long haul, bubbles and crashes\n",
    "\n",
    "So let's now look at the long-term trend in projected SPX rate of returns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " ::  regresstime slope = 0.0185216267691\n"
     ]
    },
    {
     "data": {
      "image/png": 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JP/8ZpgKeOhX+8Ad1zYikTWx98ma2MXB3sZq8md0NXOjuT0bLjwCnuPszRbZV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\nLyKSY0ryIiI5piQvIpJjSvIiIjn2/6MotaWrOcZPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa72b770c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trend_pcspq = trend( pcspq )\n",
    "plot( trend_pcspq )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are several major episodes of less than -20% forecasted on smoothed real SPX, but \n",
    "over the long-term US equities are showing increasingly better returns against inflation.\n",
    "\n",
    "(Curiously, in contrast, the long-term trend for real GDP growth was *downwards*.)\n",
    "\n",
    "To help identify local **BUBBLES**, i.e. excessive equity valuations \n",
    "apart from inflationary effects, we detrend the series as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " ::  regresstime slope = 0.0185216267691\n"
     ]
    },
    {
     "data": {
      "image/png": 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M+iHGhdK8uWmqQSYUmjjRHjCJNTZbtbKbK+hKTJn051mzTIro37/xsd12s1f+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\nTDp2hYjMEZGZInJEMdfxeDzVQ7LOPnd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      "text/plain": [
       "<matplotlib.figure.Figure at 0xa72a4e4c>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "det_pcspq = detrend( pcspq )\n",
    "plot( det_pcspq )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the plot above, we have filtered out both inflation and the underlying \n",
    "real rate of return on equities, leaving us with a picture of *extreme* valuations \n",
    "in the short-term.\n",
    "\n",
    "**The shift from overvaluation to collapse is very swift, \n",
    "and occurs historically on a regular but unpredictable basis.** \n",
    "***Instability is the norm.***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Further research\n",
    "\n",
    "*What are the arrival times of collapses in equity valuations?\n",
    "Are there signals which can be identified as precursors to such collapses?*\n",
    "\n",
    "There are structural similarities to the prediction of earthquakes\n",
    "where threshold tremors can be regarded as precursors.\n",
    "\n",
    "[Didier Sornette](https://scholar.google.com/citations?user=HGsSmMAAAAAJ&hl=en)\n",
    "has discovered log-periodic times, inspired by geophysics and self-organizing\n",
    "systems. A separate notebook will be dedicated to his findings regarding\n",
    "criticality: bubbles and anti-bubbles in financial markets."
   ]
  }
 ],
 "metadata": {
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   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
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   "codemirror_mode": {
    "name": "ipython",
    "version": 2
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   "file_extension": ".py",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
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 },
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}
