File:Gaussianprocess SnowboardTrend.svg

#This source code is public domain
#Author: Christian Schirm 
import numpy, scipy.spatial
import matplotlib.pyplot as plt

# Data source: https://www.google.de/trends/explore?date=all&q=Snowboard
x = numpy.array([ 2004.08,  2004.17,  2004.25,  2004.33,  2004.42,  2004.50,  2004.58,
        2004.67,  2004.75,  2004.83,  2004.92,  2005.00,  2005.08,  2005.17,  2005.25,
        2005.33,  2005.42,  2005.50,  2005.58,  2005.67,  2005.75,  2005.83,  2005.92,
        2006.00,  2006.08,  2006.17,  2006.25,  2006.33,  2006.42,  2006.50,  2006.58,
        2006.67,  2006.75,  2006.83,  2006.92,  2007.00,  2007.08,  2007.17,  2007.25,
        2007.33,  2007.42,  2007.50,  2007.58,  2007.67,  2007.75,  2007.83,  2007.92,
        2008.00,  2008.08,  2008.17,  2008.25,  2008.33,  2008.42,  2008.50,  2008.58,
        2008.67,  2008.75,  2008.83,  2008.92,  2009.00,  2009.08,  2009.17,  2009.25,
        2009.33,  2009.42,  2009.50,  2009.58,  2009.67,  2009.75,  2009.83,  2009.92,
        2010.00,  2010.08,  2010.17,  2010.25,  2010.33,  2010.42,  2010.50,  2010.58,
        2010.67,  2010.75,  2010.83,  2010.92,  2011.00,  2011.08,  2011.17,  2011.25,
        2011.33,  2011.42,  2011.50,  2011.58,  2011.67,  2011.75,  2011.83,  2011.92,
        2012.00,  2012.08,  2012.17,  2012.25,  2012.33,  2012.42,  2012.50,  2012.58,
        2012.67,  2012.75,  2012.83,  2012.92,  2013.00,  2013.08,  2013.17,  2013.25,
        2013.33,  2013.42,  2013.50,  2013.58,  2013.67,  2013.75,  2013.83,  2013.92,
        2014.00,  2014.08,  2014.17,  2014.25,  2014.33,  2014.42,  2014.50,  2014.58,
        2014.67,  2014.75,  2014.83,  2014.92,  2015.00,  2015.08,  2015.17,  2015.25,
        2015.33,  2015.42,  2015.50,  2015.58,  2015.67,  2015.75,  2015.83,  2015.92,
        2016.00,  2016.08,  2016.17,  2016.25,  2016.33,  2016.42,  2016.50,  2016.58])
y = numpy.array([ 100.,   75.,   44.,   24.,   18.,   17.,   19.,   26.,   37.,
         57.,   77.,   95.,   84.,   70.,   43.,   21.,   16.,   15.,
         18.,   24.,   33.,   50.,   70.,   94.,   78.,   80.,   43.,
         21.,   14.,   13.,   15.,   22.,   31.,   46.,   61.,   72.,
         60.,   49.,   28.,   15.,   11.,   11.,   13.,   17.,   23.,
         33.,   50.,   68.,   58.,   44.,   27.,   14.,   10.,   10.,
         12.,   16.,   22.,   31.,   46.,   66.,   61.,   44.,   26.,
         13.,   10.,   11.,   12.,   16.,   21.,   31.,   39.,   56.,
         56.,   65.,   28.,   13.,   10.,    9.,   10.,   13.,   17.,
         24.,   37.,   57.,   44.,   30.,   19.,   10.,    7.,    8.,
          9.,   11.,   14.,   20.,   29.,   37.,   36.,   30.,   15.,
         10.,   10.,    8.,    8.,    9.,   12.,   16.,   23.,   34.,
         34.,   26.,   15.,    7.,    5.,    5.,    6.,    7.,   10.,
         14.,   22.,   31.,   28.,   42.,   14.,    6.,    5.,    4.,
          5.,    7.,    8.,   11.,   18.,   25.,   27.,   21.,   11.,
          5.,    4.,    4.,    5.,    6.,    7.,   10.,   16.,   21.,
         27.,   18.,   10.,    6.,    4.,    4.,    4.])

x_known = x
y_known = numpy.log(y)
x_unknown = numpy.arange(2016.5,2023,1/12.)
def covFunc(d):
    return 0.8*numpy.exp(-numpy.abs(numpy.sin(numpy.pi*d))/0.5  -numpy.abs(d/25.)**2 - 2.5) + \
        (0.2-0.01)*numpy.exp(-(numpy.abs(numpy.sin(numpy.pi*d/4))/0.2)) + 0.01*numpy.exp(-numpy.abs(d/45.))

def covMat(x1, x2, covFunc, noise=0):
    cov = covFunc(scipy.spatial.distance_matrix(numpy.atleast_2d(x1).T, numpy.atleast_2d(x2).T))
    if noise: numpy.fill_diagonal(cov, numpy.diag(cov) + noise)
    return cov

Ckk = covMat(x_known, x_known, covFunc, noise=0.02)
Cuu = covMat(x_unknown, x_unknown, covFunc, noise=0.00)
CkkInv = numpy.linalg.inv(Ckk)
Cuk = covMat(x_unknown, x_known, covFunc, noise=0)
m = numpy.mean(y_known)
y_unknown = m + numpy.dot(numpy.dot(Cuk,CkkInv), y_known - m)
sigmaPrior = numpy.sqrt(numpy.mean(numpy.square(y_known)))
sigma = sigmaPrior*numpy.sqrt(numpy.diag(Cuu - numpy.dot(numpy.dot(Cuk,CkkInv),Cuk.T)))

fig = plt.figure(figsize=(6,3), dpi=100)
plt.plot(x,y,'-')
plt.plot(x_unknown,numpy.exp(y_unknown),'r-')
plt.fill_between(x_unknown, numpy.exp(y_unknown - sigma), numpy.exp(y_unknown + sigma), color = '0.85')
plt.xlim(2004,2022.5)
plt.xticks(numpy.arange(2004,2023,2))
plt.ylim(0,100)
plt.vlines([2016.5], 0, 100,'0.6','--')
plt.title('Google-Trend zum Suchbegriff "Snowboard"')
plt.ylabel('Suchanfragen pro Monat (%)')
plt.savefig('Gaussianprocess_SnowboardTrend.svg')