Standard Error Bands: Fit, Not Volatility
Standard error bands sit a multiple of the standard error either side of a linear regression line fitted to recent prices. The width measures how well that line fits, not how far price moves. So an orderly trend narrows them, and a quiet, directionless market widens them.
How it works
Standard error bands are drawn around a fitted line, not an average. The centre is a linear regression through the recent closes, and the bands sit a multiple of that fit’s standard error either side of it.
The width is the error of the regression itself. Standard error summarises how far the actual closes sit from the line drawn through them. Nothing else enters the number.
Which is not the same as price volatility. Bollinger Bands widen when price moves a lot; these widen when price stops following the line, and a fast, orderly trend can produce narrow bands and a large daily range at once.
A good fit gives narrow bands even in a fast market. If every close lands near the sloping line the residuals are small and the channel is tight, however far price has travelled in the meantime.
So they narrow when the trend is orderly. That is the reverse of what a volatility band does, and it is the single fact that makes the indicator worth learning at all.
Reading the width the right way round
And widen when price stops following the line. A quiet, directionless market fits a straight line badly, so the channel can be at its widest while the bars themselves are small.
Most versions smooth the result, which adds lag. Published implementations run a moving average over both the regression line and the error, which steadies the picture and delays every change in it.
Participation is nowhere in the calculation. Volume enters neither the regression nor the error, so a tight channel says the closes were orderly, not that anyone was trading them.
In practice
A longer window makes everything steadier and later. The lookback is a free parameter, and lengthening it flattens the slope and calms the width at the cost of reacting a good deal later.
And one gap inflates the error for the whole window. A single opening gap leaves a large residual that widens the channel for as long as that bar stays inside the lookback.
The opposite band is the only level on offer. Nothing in a regression channel marks where orders rest, so any stop loss other than the far band is a number you chose yourself.
Every round trip costs 2% of a bar. research/series-measurements.json puts round-trip cost at
0.0098 price units, which is 2% of a median bar’s range on this series and 45% of the smallest bar.
It is a goodness-of-fit measure wearing a channel. The whole regression is recomputed every bar, so the historical portion of the channel is not sitting where it sat yesterday.
Reading both band families at once
The two families answer different questions, so read them side by side. Bollinger Bands and Keltner channels both scale with movement — one from standard deviation, one from the average true range, or ATR. Standard error bands scale with disorder.
Volatility bands widening while error bands narrow is the clearest reading available. Price is moving hard and moving straight, which is what an orderly trend looks like from both angles at once. It is also the point at which the Bollinger squeeze idea inverts.
Both widening is the genuinely disorderly case. Large bars going nowhere in particular: historical volatility is up and the fit is poor, which is the condition that punishes trend analysis and flatters mean reversion.
And a trader treating the two as interchangeable is reading different things off the same-looking picture. A narrowing means a coming move on one and settled order on the other. The picture is identical; the meaning is inverted.
What standard error bands are not
- Not a volatility measure. The width scores fit quality, which is a different quantity entirely.
- Not a squeeze indicator. Narrowing here describes an orderly trend, not a move about to arrive.
- Not a support and resistance tool. The lines are computed each bar and nobody is defending them.
- Not a fixed channel. The fit is redrawn every bar, so the history you are looking at moves.
When it fails
- In a range the fit is poor and the bands are wide. A straight line through sideways trade leaves large residuals in both directions, so the channel is at its widest exactly where there is least to trade. Read as expanding volatility, that is precisely backwards.
- When the window is chosen after the event. The lookback has no natural value, and a channel that fits beautifully at one length is ragged at another. Nothing in the indicator says which length is right.
- When a single outlier dominates. Standard error is built from squared residuals, so one violent bar can widen the entire channel and hold it wide until that bar leaves the window.
- When the historical portion is read as fixed. The fit is recomputed every bar, so the channel on screen is not the channel that existed when those bars printed. Testing it by eye flatters it.
- When smoothing hides the change you needed. The lag applied to both line and error means the bands look steadiest at the moment an orderly trend is coming apart.
- When direction does not persist. Direction runs here average 2.01 bars, with a longest of 11 across 286 runs, so the orderly condition these bands reward is a short-lived one.
The original data
The coverage figures come from research/broker-coverage.json. A scan of the 31,760 videos in
research/search-study-corpus.jsonl finds “bollinger bands” in 311 titles from 173 channels, median
3,816 views, against a single “standard error” title, 2,309 views, one channel. Both draw a channel;
only one has a memorable name.
The more useful comparison is between the two measurements. research/series-measurements.json
puts the average true range at a factor of 2.82 between quiet and active conditions, and the
efficiency ratio at a median of 0.34. Before acting on any band width, ask which quantity it
measures — if the answer is fit quality, a narrowing describes order, not a coming move.
Related
Linear regression is the line these bands are drawn around, and the width is nothing more than how badly it fits.
Bollinger Bands measure dispersion around a moving average instead, which is why the two families widen at opposite moments.
Standard deviation is the quantity that separates them, since one applies it to price and the other to the residuals of a fit.
I put these on a chart years ago expecting them to behave like Bollinger Bands, and spent a fortnight reading them backwards. Every time they pinched in I braced for a breakout, and what was actually happening was a trend behaving itself. Once I understood that the width was scoring the fit rather than the movement, the indicator stopped lying to me. It never had lied; I had simply assumed all bands measure the same thing.
— Michael Whitman
This page is educational, not financial advice. Test every idea on your own charts before risking money.