EWCov¶

Exponentially weighted covariance.

This is the bivariate counterpart of stats.EWVar. It tracks the covariance between two variables while giving more weight to recent observations, which is what you want when the relationship between the variables drifts over time (e.g. the co-movement of two asset returns during a changing market regime).

Internally it uses the identity \(Cov(x, y) = E\[xy\] - E\[x\]E\[y\]\), with each expectation estimated by an exponentially weighted mean (stats.EWMean). Using the same fading_factor on the diagonal recovers stats.EWVar exactly.

Parameters¶

• fading_factor

  Default → 0.5

  The closer fading_factor is to 1 the more the statistic will adapt to recent values.

Attributes¶

• name

Examples¶

from river import stats

x = [1, 3, 5, 4]
y = [2, 4, 3, 6]

ewcov = stats.EWCov(fading_factor=0.5)
for xi, yi in zip(x, y):
    ewcov.update(xi, yi)
    print(ewcov.get())

0.0
1.0
0.5
0.625

Methods¶

References¶

• Finch, T., 2009. Incremental calculation of weighted mean and variance. University of Cambridge, 4(11-5), pp.41-42.

• Exponential Moving Average on Streaming Data