Find relationships between multiple time series

Visualizing Time Series Data in Python

Thomas Vincent

Head of Data Science, Getty Images

Correlations between two variables

  • In the field of Statistics, the correlation coefficient is a measure used to determine the strength or lack of relationship between two variables:
    • Pearson's coefficient can be used to compute the correlation coefficient between variables for which the relationship is thought to be linear
    • Kendall Tau or Spearman rank can be used to compute the correlation coefficient between variables for which the relationship is thought to be non-linear
Visualizing Time Series Data in Python

Compute correlations

from scipy.stats.stats import pearsonr
from scipy.stats.stats import spearmanr
from scipy.stats.stats import kendalltau
x = [1, 2, 4, 7]
y = [1, 3, 4, 8]
pearsonr(x, y)

SpearmanrResult(correlation=0.9843, pvalue=0.01569)

spearmanr(x, y)

SpearmanrResult(correlation=1.0, pvalue=0.0)

kendalltau(x, y)

KendalltauResult(correlation=1.0, pvalue=0.0415)
Visualizing Time Series Data in Python

What is a correlation matrix?

  • When computing the correlation coefficient between more than two variables, you obtain a correlation matrix
    • Range: [-1, 1]
    • 0: no relationship
    • 1: strong positive relationship
    • -1: strong negative relationship
Visualizing Time Series Data in Python

What is a correlation matrix?

  • A correlation matrix is always "symmetric"
  • The diagonal values will always be equal to 1
   x     y     z
x  1.00 -0.46  0.49
y -0.46  1.00 -0.61
z  0.49 -0.61  1.00
Visualizing Time Series Data in Python

Computing Correlation Matrices with Pandas

corr_p = meat[['beef', 'veal','turkey']].corr(method='pearson')
print(corr_p)

          beef     veal     turkey
beef      1.000   -0.829    0.738
veal     -0.829    1.000   -0.768
turkey    0.738   -0.768    1.000

corr_s = meat[['beef', 'veal','turkey']].corr(method='spearman')
print(corr_s)

          beef     veal     turkey
beef      1.000   -0.812    0.778
veal     -0.812    1.000   -0.829
turkey    0.778   -0.829    1.000
Visualizing Time Series Data in Python

Computing Correlation Matrices with Pandas

corr_mat = meat.corr(method='pearson')
Visualizing Time Series Data in Python

Heatmap

import seaborn as sns

sns.heatmap(corr_mat)
Visualizing Time Series Data in Python

Heatmap

A heatmap of the correlation matrix

Visualizing Time Series Data in Python

Clustermap

sns.clustermap(corr_mat)
Visualizing Time Series Data in Python

A clustermap of the correlation matrix

Visualizing Time Series Data in Python

Let's practice!

Visualizing Time Series Data in Python

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