---
title: "Least Squares Moving Average With Reference"
description: "The Least Squares Moving Average (LSMA) of a target in relation with a reference fits a least squares regression line of the ta..."
canonical: https://www.quantconnect.com/docs/v2/writing-algorithms/indicators/supported-indicators/least-squares-moving-average-with-reference
markdown: https://www.quantconnect.com/docs/v2/writing-algorithms/indicators/supported-indicators/least-squares-moving-average-with-reference.md
language: python
source: https://github.com/QuantConnect/Documentation/tree/master/03%20Writing%20Algorithms/28%20Indicators/01%20Supported%20Indicators/060%20Least%20Squares%20Moving%20Average%20With%20Reference
modified: 2026-11-03
index: https://www.quantconnect.com/llms.txt
---

# Least Squares Moving Average With Reference

[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 With Reference

> 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) of a target in relation with a reference fits a least squares regression line of the target close prices on the reference close prices over the given period, instead of on the time index used by `LeastSquaresMovingAverage`. It then returns the value the regression line takes for the most recent reference price, which is the price the target is expected to have given where the reference is trading. It is common practice to use the SPX index as the reference, so that the indicator describes the target price in terms of the overall market level. The indicator only updates when both assets have a price for a time step. When a bar is missing for one of the assets, the indicator value fills forward to improve the accuracy of the indicator.

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

## Using LSMA Indicator

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

```python
class LeastSquaresMovingAverageWithReferenceAlgorithm(QCAlgorithm):
    def initialize(self) -> None:
        self._symbol = self.add_equity("QQQ", Resolution.DAILY).symbol
        self._reference = self.add_equity("SPY", Resolution.DAILY).symbol
        self._lsma = self.lsma(self._symbol, self._reference, 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("LeastSquaresMovingAverageWithReference", "lsma", self._lsma.current.value)
            # Plot all attributes of self._lsma
            self.plot("LeastSquaresMovingAverageWithReference", "intercept", self._lsma.intercept.current.value)
            self.plot("LeastSquaresMovingAverageWithReference", "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 `LeastSquaresMovingAverageWithReference` 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 LeastSquaresMovingAverageWithReferenceAlgorithm(QCAlgorithm):
    def initialize(self) -> None:
        self._symbol = self.add_equity("QQQ", Resolution.DAILY).symbol
        self._reference = self.add_equity("SPY", Resolution.DAILY).symbol
        self._leastsquaresmovingaveragewithreference = LeastSquaresMovingAverageWithReference(self._symbol, self._reference, 20)

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

        if self._leastsquaresmovingaveragewithreference.is_ready:
            # The current value of self._leastsquaresmovingaveragewithreference is represented by self._leastsquaresmovingaveragewithreference.current.value
            self.plot("LeastSquaresMovingAverageWithReference", "leastsquaresmovingaveragewithreference", self._leastsquaresmovingaveragewithreference.current.value)
            # Plot all attributes of self._leastsquaresmovingaveragewithreference
            self.plot("LeastSquaresMovingAverageWithReference", "intercept", self._leastsquaresmovingaveragewithreference.intercept.current.value)
            self.plot("LeastSquaresMovingAverageWithReference", "slope", self._leastsquaresmovingaveragewithreference.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/LeastSquaresMovingAverageWithReference).

## Visualization

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

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

## Indicator History

To get the historical data of the `LeastSquaresMovingAverageWithReference` 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 LeastSquaresMovingAverageWithReferenceAlgorithm(QCAlgorithm):
    def initialize(self) -> None:
        self._symbol = self.add_equity("QQQ", Resolution.DAILY).symbol
        self._reference = self.add_equity("SPY", Resolution.DAILY).symbol
        self._lsma = self.lsma(self._symbol, self._reference, 20)

        indicator_history = self.indicator_history(self._lsma, [ self._symbol, self._reference ], 100, Resolution.MINUTE)
        timedelta_indicator_history = self.indicator_history(self._lsma, [ self._symbol, self._reference ], timedelta(days=10), Resolution.MINUTE)
        time_period_indicator_history = self.indicator_history(self._lsma, [ self._symbol, self._reference ], 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"]
```