EwaCovariance¶

Exponentially weighted covariance matrix.

A recency-weighted estimate of the covariance: each new observation is blended into the estimate with weight fading_factor, so the influence of past observations decays geometrically. This is the streaming analogue of the RiskMetrics covariance and the matrix counterpart of stats.EWVar / stats.EWCov (the diagonal is exactly stats.EWVar and each off-diagonal is exactly stats.EWCov).

When to use it. Reach for this over EmpiricalCovariance when the relationships between your variables change over time. The textbook example is asset returns, whose volatilities and correlations move with the market regime: a plain empirical covariance weights a return from years ago the same as yesterday's, whereas an exponentially weighted one forgets the distant past so the risk estimate tracks current conditions. Larger fading_factor reacts faster (shorter memory); smaller is smoother.

Parameters¶

• fading_factor

  Type → float

  Default → 0.5

  The closer fading_factor is to 1 the more weight recent observations carry. The effective memory is roughly 1 / fading_factor observations.

Attributes¶

• matrix

Examples¶

We estimate the covariance of daily returns (in percent) for a few stocks from the datasets.SP500Stocks dataset.

from river import covariance, datasets

tickers = ["AAPL", "JPM", "XOM"]
cov = covariance.EwaCovariance(fading_factor=0.02)
for x, _ in datasets.SP500Stocks():
    cov.update({t: x[t] for t in tickers})
cov

       AAPL    JPM     XOM
AAPL   1.944   0.766   0.760
 JPM   0.766   1.492   0.934
 XOM   0.760   0.934   1.705

There is also an update_many method to process mini-batches. It accepts any narwhals-compatible dataframe and yields the same result as feeding the rows one by one.

import pandas as pd
returns = pd.DataFrame(x for x, _ in datasets.SP500Stocks())[tickers]
cov = covariance.EwaCovariance(fading_factor=0.02)
cov.update_many(returns)
cov

       AAPL    JPM     XOM
AAPL   1.944   0.766   0.760
 JPM   0.766   1.492   0.934
 XOM   0.760   0.934   1.705

Individual entries are accessible by key:

cov["AAPL", "JPM"]

0.766...

Methods¶

References¶

• RiskMetrics Technical Document (J.P. Morgan, 1996)