polars.Expr.ewm_mean_by#

Expr.ewm_mean_by(
by: str | IntoExpr,
*,
half_life: str | timedelta,
check_sorted: bool = True,
) → Self[source]#

Calculate time-based exponentially weighted moving average.

Given observations \(x_1, x_2, \ldots, x_n\) at times \(t_1, t_2, \ldots, t_n\), the EWMA is calculated as

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

where \(\lambda\) equals \(\ln(2) / \text{half_life}\).

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’).

check_sorted

Check whether by column is sorted. Incorrectly setting this to False will lead to incorrect output.

Returns:
Expr

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.with_columns(
...     result=pl.col("values").ewm_mean_by("times", half_life="4d"),
... )
shape: (5, 3)
┌────────┬────────────┬──────────┐
│ values ┆ times      ┆ result   │
│ ---    ┆ ---        ┆ ---      │
│ i64    ┆ date       ┆ f64      │
╞════════╪════════════╪══════════╡
│ 0      ┆ 2020-01-01 ┆ 0.0      │
│ 1      ┆ 2020-01-03 ┆ 0.292893 │
│ 2      ┆ 2020-01-10 ┆ 1.492474 │
│ null   ┆ 2020-01-15 ┆ null     │
│ 4      ┆ 2020-01-17 ┆ 3.254508 │
└────────┴────────────┴──────────┘