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Matrix Functions

Functions whose output is a matrix

correlation​

PearsonsCorrelation computes correlations defined by the formula:

cor(X, Y) = sum[(xi - E(X))(yi - E(Y))] / [(n - 1)s(X)s(Y)]

where E(X) and E(Y) are means of X and Y and s(X), s(Y) are standard deviations.

Syntax​

correlation(list)

The list parameter is a list of variables which can be one of:

  • Timeseries
  • Reference to a Timeseries
  • String id of a Timeseries

Example​

Con = TimeSeries("2021-10-01", "BUSINESS", [8.12,1.19,2.82,4.1,-6.31,6.87,1.16,-0.63,1.25,0.93])
Man = TimeSeries("2021-10-01", "BUSINESS", [8.98,4.23,0.71,2.47,-8.29,7.34,-0.39,-2.18,3.86,-0.84])
Tech = TimeSeries("2021-10-01", "BUSINESS", [8.97,5.32,3.31,6,-7.75,7.51,3.38,-2.33,1.01,3.06])
Health = TimeSeries("2021-10-01", "BUSINESS", [5.25,3.23,0.48,-3.13,-3.37,6.84,-2.19,-0.61,-0.94,4.73])

lts = [Con, Man, Tech, Health]

print correlation(lts)

Output​

        Con         Man         Tech        Health
Con     1           0.926711    0.940898    0.627738
Man     0.926711    1           0.903867    0.660247
Tech    0.940898    0.903867    1           0.624856
Health  0.627738    0.660247    0.624856    1


covariance​

Unbiased covariances are given by the formula cov(X, Y) = sum [(xi - E(X))(yi - E(Y))] / (n - 1)

where E(X) is the mean of X and E(Y) is the mean of the Y values.

Non-bias-corrected estimates use n in place of n - 1. Whether or not covariances are bias-corrected is determined by the optional parameter, biasCorrected which defaults to true.

Syntax​

covariance(list)
covariance(list, biasCorrected)

The list parameter is a list of variables which can be one of:

  • Timeseries
  • Reference to a Timeseries
  • String id of a Timeseries

The biasCorrected parameter is a boolean.

Example​

Con = TimeSeries("2021-10-01", "BUSINESS", [8.12,1.19,2.82,4.1,-6.31,6.87,1.16,-0.63,1.25,0.93])
Man = TimeSeries("2021-10-01", "BUSINESS", [8.98,4.23,0.71,2.47,-8.29,7.34,-0.39,-2.18,3.86,-0.84])
Tech = TimeSeries("2021-10-01", "BUSINESS", [8.97,5.32,3.31,6,-7.75,7.51,3.38,-2.33,1.01,3.06])
Health = TimeSeries("2021-10-01", "BUSINESS", [5.25,3.23,0.48,-3.13,-3.37,6.84,-2.19,-0.61,-0.94,4.73])

lts = [Con, Man, Tech, Health]

mc = covariance(lts)
print mc
mc = covariance(lts, false)
print mc

Output​

        Con         Man         Tech        Health
Con     16.141200   18.532833   18.617622   9.361344
Man     18.532833   24.777610   22.158876   12.199110
Tech    18.617622   22.158876   24.256440   11.423153
Health  9.361344    12.199110   11.423153   13.777943

        Con         Man         Tech        Health
Con     14.527080   16.679550   16.755860   8.425210
Man     16.679550   22.299849   19.942988   10.979199
Tech    16.755860   19.942988   21.830796   10.280838
Health  8.425210    10.979199   10.280838   12.400149