---
title: "Least Squares Moving Average"
description: "The Least Squares Moving Average (LSMA) first calculates a least squares regression line over the preceding time periods, and t..."
canonical: https://www.quantconnect.com/docs/v2/writing-algorithms/indicators/supported-indicators/least-squares-moving-average
markdown: https://www.quantconnect.com/docs/v2/writing-algorithms/indicators/supported-indicators/least-squares-moving-average.md
language: python
source: https://github.com/QuantConnect/Documentation/tree/master/03%20Writing%20Algorithms/28%20Indicators/01%20Supported%20Indicators/059%20Least%20Squares%20Moving%20Average
modified: 2026-10-31
index: https://www.quantconnect.com/llms.txt
---

# Least Squares Moving Average

[Documentation](https://www.quantconnect.com/docs/v2.md) > [Writing Algorithms](https://www.quantconnect.com/docs/v2/writing-algorithms.md) > Indicators > [Supported Indicators](https://www.quantconnect.com/docs/v2/writing-algorithms/indicators/supported-indicators.md) > Least Squares Moving Average

> Code examples are shown in Python. Append `?lang=csharp` to this URL for the C# version of this page.

## Introduction

The Least Squares Moving Average (LSMA) first calculates a least squares regression line over the preceding time periods, and then projects it forward to the current period. In essence, it calculates what the value would be if the regression line continued. [source](https://rtmath.net/assets/docs/finanalysis/html/b3fab79c-f4b2-40fb-8709-fdba43cdb363.htm)

To view the implementation of this indicator, see the [LEAN GitHub repository](https://github.com/QuantConnect/Lean/tree/master/Indicators/LeastSquaresMovingAverage.cs).

## Using LSMA Indicator

To create an automatic indicator for `LeastSquaresMovingAverage`, call the `lsma` helper method from the `QCAlgorithm` class. The `lsma` method creates a `LeastSquaresMovingAverage` object, hooks it up for automatic updates, and returns it so you can used it in your algorithm. In most cases, you should call the helper method in the `initialize` method.

```python
class LeastSquaresMovingAverageAlgorithm(QCAlgorithm):
    def initialize(self) -> None:
        self._symbol = self.add_equity("SPY", Resolution.DAILY).symbol
        self._lsma = self.lsma(self._symbol, 20)

    def on_data(self, slice: Slice) -> None:

        if self._lsma.is_ready:
            # The current value of self._lsma is represented by self._lsma.current.value
            self.plot("LeastSquaresMovingAverage", "lsma", self._lsma.current.value)
            # Plot all attributes of self._lsma
            self.plot("LeastSquaresMovingAverage", "intercept", self._lsma.intercept.current.value)
            self.plot("LeastSquaresMovingAverage", "slope", self._lsma.slope.current.value)
```

For more information about this method, see the [QCAlgorithm class](https://www.lean.io/docs/v2/lean-engine/class-reference/py/QuantConnect/Algorithm/QCAlgorithm/#QuantConnect.Algorithm.QCAlgorithm.lsma).

You can manually create a `LeastSquaresMovingAverage` indicator, so it doesn't automatically update. Manual indicators let you update their values with any data you choose.

Updating your indicator manually enables you to control when the indicator is updated and what data you use to update it. To manually update the indicator, call the `update` method. The indicator will only be ready after you prime it with enough data.

```python
class LeastSquaresMovingAverageAlgorithm(QCAlgorithm):
    def initialize(self) -> None:
        self._symbol = self.add_equity("SPY", Resolution.DAILY).symbol
        self._leastsquaresmovingaverage = LeastSquaresMovingAverage(20)

    def on_data(self, slice: Slice) -> None:
        bar = slice.bars.get(self._symbol)
        if bar:
            self._leastsquaresmovingaverage.update(bar.end_time, bar.close)

        if self._leastsquaresmovingaverage.is_ready:
            # The current value of self._leastsquaresmovingaverage is represented by self._leastsquaresmovingaverage.current.value
            self.plot("LeastSquaresMovingAverage", "leastsquaresmovingaverage", self._leastsquaresmovingaverage.current.value)
            # Plot all attributes of self._leastsquaresmovingaverage
            self.plot("LeastSquaresMovingAverage", "intercept", self._leastsquaresmovingaverage.intercept.current.value)
            self.plot("LeastSquaresMovingAverage", "slope", self._leastsquaresmovingaverage.slope.current.value)
```

For more information about this indicator, see its [reference](https://www.lean.io/docs/v2/lean-engine/class-reference/py/QuantConnect/Indicators/LeastSquaresMovingAverage).

## Visualization

The following plot shows values for some of the `LeastSquaresMovingAverage` indicator properties:

![LeastSquaresMovingAverage line plot.](https://cdn.quantconnect.com/docs/i/writing-algorithms/indicators/supported-indicators/least-squares-moving-average.png)

## Indicator History

To get the historical data of the `LeastSquaresMovingAverage` indicator, call the `self.indicator_history` method. This method resets your indicator, makes a [history request](https://www.quantconnect.com/docs/v2/writing-algorithms/historical-data/history-requests.md), and updates the indicator with the historical data. Just like with regular history requests, the `indicator_history` method supports time periods based on a trailing number of bars, a trailing period of time, or a defined period of time. If you don't provide a `resolution` argument, it defaults to match the resolution of the security subscription.

```python
class LeastSquaresMovingAverageAlgorithm(QCAlgorithm):
    def initialize(self) -> None:
        self._symbol = self.add_equity("SPY", Resolution.DAILY).symbol
        self._lsma = self.lsma(self._symbol, 20)

        indicator_history = self.indicator_history(self._lsma, self._symbol, 100, Resolution.MINUTE)
        timedelta_indicator_history = self.indicator_history(self._lsma, self._symbol, timedelta(days=10), Resolution.MINUTE)
        time_period_indicator_history = self.indicator_history(self._lsma, self._symbol, datetime(2024, 7, 1), datetime(2024, 7, 5), Resolution.MINUTE)

        # Access all attributes of indicator_history
        indicator_history_df = indicator_history.data_frame
        intercept = indicator_history_df["intercept"]
        slope = indicator_history_df["slope"]
```