# staircase.Stairs.cov¶

Stairs.cov(other, lower=-inf, upper=inf, lag=0, clip='pre')

Calculates either covariance, autocovariance or cross-covariance.

The calculation is between two step functions described by self and other. If lag is None or 0 then covariance is calculated, otherwise cross-covariance is calculated. Autocovariance is a special case of cross-covariance when other is equal to self.

Parameters: other (Stairs) – the stairs instance with which to compute the covariance lower (int, float or pandas.Timestamp) – lower bound of the domain on which to perform the calculation upper (int, float or pandas.Timestamp) – upper bound of the domain on which to perform the calculation lag (int, float, pandas.Timedelta) – a pandas.Timedelta is only valid when using dates. If using dates and delta is an int or float, then it is interpreted as a number of hours. clip ({'pre', 'post'}, default 'pre') – only relevant when lag is non-zero. Determines if the domain is applied before or after other is translated. If ‘pre’ then the domain over which the calculation is performed is the overlap of the original domain and the translated domain. The covariance (or cross-covariance) between self and other float

Examples

>>> fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(12,5), sharey=True, sharex=True)
>>> for ax, title, stair_instance in zip(axes, ("s1", "s2"), (s1, s2)):
...     stair_instance.plot(ax, label=title)
...     ax.set_title(title)

>>> s1.cov(s2)
0.1404958677685951

>>> s2.cov(s1)
0.1404958677685951

>>> s1.cov(s2, lower=0, upper=6)
0.125

>>> # autocovariance with lag 1
>>> s1.cov(s1, lower=1, upper=5, lag=1)
-0.3333333333333333

>>> # cross-covariance with lag 1
>>> s1.cov(s2, lower=1, upper=4.5, lag=1)
0.15999999999999998

>>> # cross-covariance with lag 1
>>> s1.cov(s2, lower=1, upper=4.5, lag=1, clip='post')
0.163265306122449