Least Squares Moving Average (LSMA)

The endpoint of a rolling linear regression — a statistics-based average that fits a trend line to each window of bars.

What it is

The Least Squares Moving Average (LSMA), also called the linear regression moving average or endpoint moving average, is built from a genuine statistical procedure rather than a weighting scheme. For every bar, it fits a straight line through the last N prices using ordinary least squares — the method that minimizes the sum of squared vertical distances between the prices and the line — and plots the value of that fitted line at the current (most recent) bar. Repeating this on every bar produces a smooth curve that tracks trends with less lag than an SMA of the same length, because a fitted line's endpoint leans toward where the recent trend is heading within the window. It is important to be precise about what the plotted history means: each historical LSMA point is the endpoint of the regression as it stood on that bar, which is what you would have seen live — but the full regression line drawn across a window (as in a regression channel) refits and changes shape as new bars arrive. LSMA is a description of past prices, not a prediction. Educational material only, not financial advice; trading involves risk of loss.

How it works

For each bar, take the last N closes and index them by time (1, 2, …, N). Ordinary least squares finds the slope and intercept of the line y = a + b·x that minimizes the squared errors against those closes; the LSMA value is that line evaluated at x = N, the newest bar. Equivalently, the LSMA is a weighted moving average with fixed linear weights that go negative for the oldest bars — which is why it can respond faster than price-averaging alone would allow, and also why it can overshoot. In Pine Script this is exactly ta.linreg(source, length, 0): the third argument is the offset, where 0 means 'evaluate the fitted line at the current bar'. A crucial honesty point: the LSMA plotted on historical bars is trustworthy (each point used only data available at that time), but a regression channel or full regression line drawn over a window is refit on every new bar — the line you see over last month's data is not the line you would have seen live during last month. The endpoint series does not repaint; the drawn line object does. Backtests must use the endpoint series, never conditions on the redrawn line.

How traders read it

• Slope as trend estimate: the LSMA's direction reflects the sign of the fitted regression slope over the window — a statistically grounded read of recent drift, though still computed entirely from past bars.
• Distance from price: price stretching far above or below the LSMA describes deviation from the recent linear fit; it is context about extension, not a mean-reversion guarantee.
• Crossovers: price crossing the LSMA, or a short LSMA crossing a long one, is read by some traders as a momentum-shift observation — lagging descriptions, not instructions to act.
• Curvature at turns: because the endpoint leans in the direction of the window's trend, the LSMA turns faster than an SMA but can hook and overshoot when a strong trend breaks suddenly.
• Distinguish the two objects: the LSMA line (endpoint per bar, non-repainting) versus a drawn regression channel (refit every bar, repaints by design) — only the first is safe to test conditions against.

Common settings

Common lengths are 25 (a widespread platform default), with 14 for faster reads and 50–100 for slower ones, applied to the close. The offset parameter is normally 0 (evaluate at the current bar); positive offsets shift the evaluation point back in time, and negative offsets — projecting the fitted line into the future — should be avoided, since they turn a description into an unfounded extrapolation. As always, shorter windows fit noise, longer windows fit slower structure; there is no correct length.

Strengths

• Grounded in a standard statistical method (ordinary least squares) with well-understood properties, rather than an ad-hoc weighting recipe.
• Less lag than an SMA of equal length, because the fitted endpoint leans toward the direction of the in-window trend.
• The endpoint series is deterministic and non-repainting: each historical value used only the data available on that bar.
• Doubles as a slope estimator — the regression slope behind each point is itself a usable measure of recent drift.
• Built into Pine Script as ta.linreg, so implementations are consistent and easy to verify.

Pitfalls to watch

• The linear model is an assumption: fitting a straight line to a window says nothing about whether price actually moves linearly — in choppy or curved markets the fit, and hence the endpoint, is a poor summary.
• Overshoot at trend breaks: the endpoint extrapolates the window's slope, so when a strong trend ends abruptly the LSMA hooks past price before correcting.
• Repaint confusion: the LSMA endpoint does not repaint, but full regression lines and channels refit every bar — strategies or backtests built on the drawn line's historical appearance are invalid.
• Whipsaw in ranges: like every average, it crosses back and forth over price in sideways markets, generating many noise events, especially at short lengths.
• Settings sensitivity: slope sign and turning points move materially with the window length; a length that looks clean on one chart proves nothing about another.
• No predictive power: least squares describes the best linear fit to past data — extrapolating that fit forward is a choice the data does not justify, and no indicator removes the risk of loss.

Pine v6 example

//@version=6
indicator("Least Squares MA (LSMA)", overlay = true)

length = input.int(25, "Length", minval = 2)
src    = input.source(close, "Source")
offset = input.int(0, "Offset", minval = 0, tooltip = "0 = evaluate the fitted line at the current bar")

// Endpoint of the rolling least-squares regression
lsma = ta.linreg(src, length, offset)

// Slope of the fit: difference between endpoint and the point one bar back
slope = lsma - ta.linreg(src, length, offset + 1)

plot(lsma, "LSMA", color = slope >= 0 ? color.teal : color.maroon, linewidth = 2)
plot(ta.sma(src, length), "SMA (reference)", color = color.gray)

Pro tip: Keep the two regression objects straight in your head: the LSMA endpoint series is honest history (each point used only past data), while a regression channel drawn over the same window silently refits every bar — so never test rules against how a channel looked in hindsight. If you want the trend estimate itself, plot the fitted slope rather than the line; watching its sign and magnitude is often clearer than watching crossovers. Educational information only, not financial advice; a least-squares fit describes the past and predicts nothing, and all trading carries risk of loss.

Educational only — not financial advice, not a recommendation to trade. No indicator is predictive; trading involves substantial risk of loss.