Hull Moving Average (HMA)
Calculate the Hull Moving Average (HMA) for a given price series.
The Hull Moving Average (HMA) reduces the lag typically associated with moving averages while improving smoothing, by combining a Weighted Moving Average (WMA) of half the window length, a WMA of the full window length, and a further WMA over the square root of the window length.
The formula is as follows:
\[\text{Raw HMA} = (2 \cdot \operatorname{WMA}(\text{Close},\; \text{Window} / 2)) - \operatorname{WMA}(\text{Close},\; \text{Window})\] \[\text{HMA} = \operatorname{WMA}(\text{Raw HMA},\; \sqrt{\text{Window}})\]Also known as: HMA, Hull MA.
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Calculate the Hull Moving Average (HMA) in Python
The Hull Moving Average (HMA) is available in the Technicals module of the open-source Finance Toolkit. Install it with:
pip install financetoolkit -U
Then call get_hull_moving_average as shown below.
from financetoolkit import Toolkit
toolkit = Toolkit(tickers=["AAPL", "MSFT"])
toolkit.technicals.get_hull_moving_average()
Which returns:
| Date | AAPL | MSFT | Benchmark |
|---|---|---|---|
| 2026-06-18 | 300.742 | 408.527 | 745.79 |
| 2026-06-22 | 300.078 | 401.871 | 744.779 |
| 2026-06-23 | 298.585 | 397.059 | 742.923 |
| 2026-06-24 | 297.358 | 392.639 | 741.423 |
| 2026-06-25 | 294.781 | 387.266 | 739.795 |
| 2026-06-26 | 293.098 | 384.145 | 739.184 |
| 2026-06-29 | 291.684 | 381.061 | 739.311 |
| 2026-06-30 | 291.599 | 378.891 | 740.005 |
| 2026-07-01 | 291.799 | 377.956 | 741.457 |
| 2026-07-02 | 292.727 | 377.967 | 741.959 |
Parameters
get_hull_moving_average accepts the following parameters:
- period (str, optional): The time period to consider for historical data. Can be “daily”, “weekly”, “quarterly”, or “yearly”. Defaults to “daily”.
- close_column (str, optional): The column name for closing prices in the historical data. Defaults to “Adj Close”.
- window (int, optional): Number of periods to consider for the HMA. The number of periods (time intervals) over which to calculate the HMA.
- rounding (int | None, optional): The number of decimals to round the results to. Defaults to 4.
- growth (bool, optional): Whether to calculate the growth of the HMA. Defaults to False.
- lag (int | list[int], optional): The lag to use for the growth calculation.
- standardize (bool, optional): Whether to standardize (Z-Score) the result. When combined with growth=True, standardizes the growth values instead of the raw values. Defaults to False. Defaults to 1.
Related Overlap Indicators
The Technicals module page introduces the module, and the sidebar lists all of its functions.