LSMA (Least Squares Moving Average)

The Least Squares Moving Average (LSMA), also known as the Moving Linear Regression or End Point Moving Average, calculates the linear regression line for a specified period and returns the value at the current bar (or a projected point). Unlike traditional moving averages that simply average past prices, LSMA fits a straight line to the data to minimize the sum of squared errors, providing a better representation of the trend direction and strength.

Core Concepts

Linear Regression: Fits a line y = mx + b to the price data over the lookback period.
Trend Following: The slope of the regression line indicates the trend direction.
Reduced Lag: By projecting the line to the current bar (or future), LSMA reacts faster to price changes than SMA or EMA.
Projection: Can project the value into the future (positive offset) or past (negative offset).

Parameters

Parameter	Type	Default	Description
`period`	`int`	14	The number of bars to include in the regression calculation.
`offset`	`int`	0	The offset from the current bar. 0 = current bar, >0 = future projection, <0 = past value.

Formula

For a period n, we fit a line y = mx + b where x represents the time index (0 to n-1).

The slope m and intercept b are calculated as:

m = \frac{n \sum(xy) - \sum x \sum y}{n \sum(x^2) - (\sum x)^2} b = \frac{\sum y - m \sum x}{n}

The LSMA value is then calculated at the desired offset:

LSMA = b + m \times (n - 1 + \text{offset})

Note: In the implementation, we may adjust the coordinate system (e.g., x=0 as current bar) for computational efficiency, but the geometric result is identical.

C# Implementation

Standard Usage

using QuanTAlib;

// Create LSMA with period 14
var lsma = new Lsma(14);

// Update with new values
var result = lsma.Update(new TValue(DateTime.Now, 100.0));
Console.WriteLine($"LSMA: {result.Value}");

With Offset

// Create LSMA with period 14 and offset 1 (project 1 bar into future)
var lsma = new Lsma(14, offset: 1);

Span API (High Performance)

double[] input = { ... };
double[] output = new double[input.Length];

// Calculate LSMA in-place
Lsma.Calculate(input, output, period: 14);

Bar Correction

var lsma = new Lsma(14);

// Update for the current bar
lsma.Update(new TValue(time, 100.0));

// Correction for the same bar (e.g., market data update)
lsma.Update(new TValue(time, 101.0), isNew: false);

Interpretation

Trend Direction: If LSMA is moving up, the trend is bullish. If moving down, the trend is bearish.
Crossovers: Price crossing above LSMA can be a buy signal; crossing below can be a sell signal.
Support/Resistance: LSMA often acts as dynamic support or resistance in trending markets.
Slope: The steepness of the LSMA line indicates the strength of the trend.

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