polars.Series.ewm_mean_by

Series.ewm_mean_by(
    by: IntoExpr,
    *,
    half_life: str_ | timedelta,
) → Series

Compute time-based exponentially weighted moving average.

Given observations \(x_0, x_1, \ldots, x_{n-1}\) at times \(t_0, t_1, \ldots, t_{n-1}\), the EWMA is calculated as

\[ \begin{align}\begin{aligned}y_0 &= x_0\\\alpha_i &= 1 - \exp \left\{ \frac{ -\ln(2)(t_i-t_{i-1}) } { \tau } \right\}\\y_i &= \alpha_i x_i + (1 - \alpha_i) y_{i-1}; \quad i > 0\end{aligned}\end{align} \]

where \(\tau\) is the half_life.

Parameters:

by

Times to calculate average by. Should be DateTime, Date, UInt64, UInt32, Int64, or Int32 data type.

half_life

Unit over which observation decays to half its value.

Can be created either from a timedelta, or by using the following string language:

• 1ns (1 nanosecond)
• 1us (1 microsecond)
• 1ms (1 millisecond)
• 1s (1 second)
• 1m (1 minute)
• 1h (1 hour)
• 1d (1 day)
• 1w (1 week)
• 1i (1 index count)

Or combine them: “3d12h4m25s” # 3 days, 12 hours, 4 minutes, and 25 seconds

Note that half_life is treated as a constant duration - calendar durations such as months (or even days in the time-zone-aware case) are not supported, please express your duration in an approximately equivalent number of hours (e.g. ‘370h’ instead of ‘1mo’).

Returns:

Expr

Float16 if input is Float16, Float32 if input is Float32, otherwise Float64.

Examples

>>> from datetime import date, timedelta
>>> df = pl.DataFrame(
...     {
...         "values": [0, 1, 2, None, 4],
...         "times": [
...             date(2020, 1, 1),
...             date(2020, 1, 3),
...             date(2020, 1, 10),
...             date(2020, 1, 15),
...             date(2020, 1, 17),
...         ],
...     }
... ).sort("times")
>>> df["values"].ewm_mean_by(df["times"], half_life="4d")
shape: (5,)
Series: 'values' [f64]
[
    0.0
    0.292893
    1.492474
    null
    3.254508
]