Ichimoku: Five Lines, Two of Which Are the Same Line Twice

Five names, and the one operation underneath all of them

Start with the definitions, because almost every difficulty on this page comes from them and almost no presentation states them together. The conversion line is the highest high of the last nine bars plus the lowest low of the last nine bars, divided by two. The base line is that same calculation over twenty-six bars. Leading span B is that same calculation again over fifty-two bars. Leading span A is the conversion line plus the base line, divided by two. The lagging span is the closing price, with nothing done to it at all.

Read that list twice and the structure becomes hard to unsee. Three of the five are the identical operation at three different lookbacks. That operation is the midpoint of a rolling high-low range: find the extremes of a window, take the point halfway between them, and plot it. It is not an average of prices. It ignores every bar inside the window except the two that made the extremes, which is a genuinely unusual property and worth knowing about, because it means the line is insensitive to what happens in the middle of a range and jumps when a new extreme prints. The fourth is an average of two of the first three. The fifth is the raw close.

The periods themselves have a specific origin. They are conventionally explained by a trading calendar that included a Saturday session, so a week was six sessions rather than five. On that calendar twenty-six sessions is roughly a month, because 4.33 weeks of six days is 26, nine is about a week and a half, and fifty-two is about two months. Scaled to the five-day week that Indian and most other markets now run, the same intervals would be about 7.5, 21.7 and 43.3 bars. Nobody rescales them. The numbers are used as though they were discovered rather than inherited, which is worth noticing but turns out not to matter much: repeating every measurement on this page with 8, 22 and 43 moves the variance shares by less than one percentage point in every position.

Two of the five are then displaced before they are drawn. Both leading spans are plotted twenty-six bars to the right of the bar they were computed on, which is what creates the shaded cloud extending past the last candle. The lagging span is plotted twenty-six bars to the left, so today's close appears beside the price of twenty-six bars ago. Those two shifts are the source of both the system's visual appeal and the one genuine trap in it, and they get a section to themselves further down.

Nothing in that table is contentious. Every line of it can be checked against any published description of the system. What is unusual is putting the five side by side, because side by side the claim that a reader is looking at five independent signals stops being plausible before any data has been touched. This is a different kind of subjectivity from the one that afflicts a hand-drawn line: our page on what a trendline actually is makes the case that a drawn line encodes five separate choices made by the person drawing it. Ichimoku has the opposite problem. Nothing here is drawn by hand and nothing is ambiguous, which is precisely why the redundancy is measurable instead of arguable.

Two of the five are settled before you look at any data

Leading span A is not approximately the average of the conversion and base lines. It is defined as that average. This is checkable rather than assertable, so it was checked: computing all three independently across 200 generated instruments and 570,800 bar readings, the largest absolute difference between leading span A and the average of the other two was 0.000. Not small, not within tolerance. Zero, in double precision, on every one of those readings, which is what an identity looks like when a computer confirms it.

The consequence is a hard ceiling on the information content of the drawn set. Given the conversion line and the base line, leading span A is fully determined. It can be drawn, it can be shaded against, it can be crossed, and none of that changes the fact that it carries no reading the other two did not already carry. The visual weight it gets on a chart, as one of the two edges of the cloud, is out of all proportion to its content.

The lagging span is the second case, and it is different in kind. It is the close, which is already on the chart as the right edge of every candle. It adds no new series either. What it adds is an alignment: it invites a comparison between today's close and the price of twenty-six bars ago by putting them next to each other. That comparison is a real one and it is not available anywhere else on the chart at a glance, so the lagging span is not empty. But it is not a fifth measurement of the market. It is the first measurement, moved.

Strip both out and three series remain: a rolling high-low midpoint over nine bars, over twenty-six bars, and over fifty-two bars. One transformation, three horizons. Whether that is a rich enough description of a market to justify five lines and a colour-filled region is a question of taste. Whether the five lines carry five independent readings is a question of arithmetic, and the arithmetic has already answered it.

The figure above is the whole system drawn on generated bars, and it is worth spending a moment on the two ends of it. To the right of the last candle the cloud continues for twenty-six bars. Nothing about that region is a projection. Both spans there were computed from bars that have already printed and then shifted right, so the forward cloud is fully determined and has been since the day it was calculated. To the left, the lagging span simply stops twenty-six bars before the last candle, because its final twenty-six values would have to be closes that do not exist yet. Those two facts are the same fact seen from two sides, and the second one is where the trouble lives.

How much of the rest is the same line

The identity handles one line. For the remaining four the question is empirical, and the framing of the question decides the answer, so it is worth being careful about how the comparison is set up.

Comparing the raw plotted values is the obvious approach and it is close to useless. Measured that way, the five lines correlate between 0.88 and 0.99 with each other. That number is real but it says nothing about Ichimoku, because every line is a price-scaled quantity sitting on a series that wanders over years. Two unrelated indicators built on the same price would correlate almost as highly. Publishing 0.99 as though it were a finding would be the arithmetic equivalent of noticing that a chart of a stock in rupees correlates with a chart of the same stock in paise.

The informative comparison is the one a reader actually performs. Nobody looks at the base line and reads a price off it. They look at where price is relative to the line: above it, below it, far from it, converging on it. So the measurement here is each line's distance from the close, expressed as a fraction of the close, which is scale-free and is the quantity that carries the reading. Correlations were computed separately on each of the 200 generated instruments and then averaged, so nothing in the result comes from pooling different price levels together.

Among the four components a reader has at the moment of a decision, the mean pairwise correlation is 0.67. The two cloud boundaries, which a reader is invited to treat as the upper and lower edges of a zone, correlate at 0.91. The base line and leading span A correlate at 0.82, which is unsurprising given that one is an input to the other. The loosest pair, the conversion line against leading span B, still reaches 0.41, and that pair is loose only because it compares a nine-bar window with a fifty-two-bar one.

Reducing the four to principal components makes the ceiling explicit. The first accounts for 84.6 percent of the variance, the second brings the running total to 96.4 percent, and the third brings it to 100 percent. Not approximately 100 percent. The fourth eigenvalue comes back as 3.1 divided by ten to the power seventeen, which is the number a computer returns when the true answer is zero and it has done some arithmetic on the way. Four lines, three degrees of freedom, and the missing one is exactly the leading span A identity showing up again from a different direction.

Taking the five drawn lines together, including the lagging span, the shares run 61.2, 20.0, 14.1, 3.5 and 1.1 percent. Three components still reach 95.4 percent. The reason the fifth line lifts the numbers at all is the same reason it is uncorrelated with everything else: its column in the matrix reads 0.01 against every other component, because the quantity it holds is not a transformation of the past at all.

One more control, because a result that depended on the specific numbers 9, 26 and 52 would be a fact about those numbers rather than about the system. Rerunning the entire measurement with the five-day-week equivalents, 8, 22 and 43, with the displacement scaled to 22, gives variance shares of 61.6, 20.0, 13.9, 3.4 and 1.1 percent for the drawn set and 85.2, 11.4, 3.4 and zero for the computed set. Every figure moves by less than one percentage point. The redundancy is structural. It follows from applying one transformation at three nested horizons, and it would survive any reasonable choice of the three.

There is a version of this result that argues in the other direction and it deserves stating. Comparing the one-bar changes of the components rather than their levels or their distances from price, the mean pairwise correlation among the four rises to 0.87, which is higher still. Comparing raw levels it is higher again. There is no framing of the data in which these lines look like independent measurements, which is the point at which the reasonable position stops being that the redundancy might be an artefact of how it was measured. Combining several indicators to form a view is a defensible practice, and our guide to reading the market regime builds exactly that kind of composite from trend, volatility and breadth. The reason that composite is worth building is that its three inputs are genuinely different measurements of different things. A composite of four range midpoints is a different proposition.

The displacement is the part almost nobody states clearly

Both shifts are usually described in a single sentence and then left alone: the cloud is projected forward, the lagging span is plotted back. Neither half of that sentence survives contact with what the shift actually does.

Take the forward shift first, because it is the harmless one and it is almost universally misdescribed. The cloud that extends past the last candle was computed twenty-six bars ago. It is not a projection, a forecast, or a probabilistic statement about anything. It is old arithmetic drawn in an unusual place. The practical consequence runs opposite to how the region is normally read: the forward cloud cannot tell you where price is going, because it does not contain any information that was not already available twenty-six bars ago. What it can do, and this is a real property rather than a dismissal, is tell you today what the boundary will be on a bar four or five weeks out, which is a genuine convenience if you want to know in advance where a level will sit. It is knowable precisely because it is stale.

The backward shift is the one that causes damage. The lagging span drawn at chart position t is the close at bar t plus twenty-six. So the comparison a reader is invited to make there, between the lagging span and the price beside it, is a comparison between the close at t plus twenty-six and the close at t. Dividing one by the other does not estimate the forward return. It is the forward return, exactly, with no error term. On the tape used here that quantity came back positive 50.1 percent of the time across 178,440 readings, which is what a coin looks like when it is fair, and which is exactly what it should look like on a series in which nothing makes direction predictable.

That makes the size of the trap measurable rather than a matter of opinion. Take the ordinary description of the condition, that the lagging span is above price, evaluate it at the position where the line is drawn, and measure what followed over the next twenty bars. On a tape where nothing is happening, that reading produced an excess of 2.70 percent over the control, with a t statistic of 55.74 across 20,375 occurrences. Fifty-five standard errors of effect, manufactured entirely by reading a chart in the order the chart invites.

Now move the identical condition to the first bar on which a reader could actually have evaluated it, which is twenty-six bars later, when the close in question finally prints. The excess becomes 0.04 percent below the control with a t statistic of 0.78 below zero. The gap between the two readings is 2.74 percentage points of pure artefact.

It is worth adding the crossing form of the same condition, because it shows that this kind of error does not have a comfortable direction. Reading the bar on which the lagging span first rises above price, again at the drawn position, gives an excess of 0.75 percent below the control with a t statistic of 23.61 below zero. Correctly lagged, the same crossing gives 0.02 percent below the control at a t statistic of 0.33 below zero. The naive reading of the crossing form produces a large negative artefact and the naive reading of the state form produces a large positive one, from the same tape, using the same line. Look-ahead does not reliably flatter a rule. It produces whatever the overlap between the condition and the measurement window happens to imply, and the sign of that is not something a reader can reason about from the outside.

None of this makes the lagging span unusable, and it is important to be precise about what survives. The comparison that is genuinely available at bar t is between today's close and the close twenty-six bars ago, which is a trailing comparison and perfectly legitimate. It is also, stated plainly, a twenty-six-bar momentum check wearing an unfamiliar name. Every test on this page uses that correctly lagged form.

What actually followed each signal

With the components implemented and the displacement handled, the standard signals can be tested. Five were coded from their usual descriptions, plus the conjunction of all of them: price closing above the cloud, the conversion line crossing above the base line, the cloud turning from bearish to bullish, price already sitting above the cloud, and a correctly lagged reading of the lagging span. The outcome measured is the return over the next twenty bars, entering at the open of the bar after the condition became true and exiting at the close twenty bars later. That convention is applied identically to both arms of every comparison, which matters more than the convention itself.

The comparison group is where most tests of this kind go wrong. A signal fires in a particular market at a particular time, so comparing its outcome to the unconditional average of the whole tape compares two different things. The fix is to draw the comparison entries from nearby bars on the same instrument. The fix to the fix, which is less widely appreciated and cost a published finding elsewhere, is that those nearby bars must come only from after the signal. A comparison drawn from before it is drawn from the very stretch of price that produced the signal, so the two arms are not independent and the comparison is circular. Every headline number on this page uses a control drawn only from bars after the event, within 250 bars, at 200 draws per event.

The upper panel is the result on a tape in which nothing makes direction predictable. The two distributions sit on top of each other. Across 8,000 cloud crossings the mean twenty-bar outcome was 0.33 percent and the control mean was 0.36 percent, an excess of 0.03 percent below the control with a standard error of 0.09 percent. That is a null, and a null is only worth reading if the instrument that produced it can detect anything at all, which is what the lower panel is for.

The lower panel is the identical test on a second tape, generated with the same code and the same seed, but with a genuine effect planted in it. The planted mechanism is keyed to a volatility squeeze followed by a breakout of a sixty-bar range, which is an extreme of a rolling window and never a midpoint of one, so no Ichimoku component appears anywhere in its definition. On that tape the same cloud-crossing test returns an excess of 0.39 percent with a t statistic of 3.60. The instrument is not blind.

The left panel of the figure above puts all six tests on one axis, and adds the quantity that turns a null into a bounded statement. The minimum detectable effect is the smallest true effect a sample of that size would have found at the usual thresholds, and here it ranges from 0.18 percent for the largest arm to 0.28 percent for the smallest. Every measured excess sits inside its own band. That is a much stronger statement than saying nothing was found. It says that if an effect of a fifth of a percent per twenty bars had existed in any of these signals, this sample would very probably have seen it, and it did not.

The right panel is the part that makes the nulls credible, and it goes further than a simple positive control. For each channel it plots the measured excess on the planted tape against a prediction, computed by adding up how much of the planted drift each arm's holding window actually contained and subtracting how much the control's holding window contained. Those predictions were not fitted to anything: they are read straight off the generator. Across the six channels, predicted and measured agree at a correlation of 0.996, with the largest discrepancy anywhere being 0.04 percentage points. The apparatus reports what is in the tape, no more and no less, including for the two channels that fail to detect the planted effect because they do not land on it.

The last row is in the table deliberately, and it is the only row in it that is not a null. It is also the only row that could not have been acted on, because the condition it tests requires a price that had not printed. Placed next to the five honest rows it makes the scale of the difference legible: the artefact is roughly twenty-seven times the largest genuine effect anywhere else in the table, and about ten times the largest effect the sample could have detected.

Slide the control window forward and watch the finding evaporate

One methodological result on this page is worth reporting on its own, because it is a general hazard rather than an Ichimoku one and because it was reproduced here independently.

The same six tests were rerun with only one thing changed: where the comparison entries may be drawn from. Four windows were tried, holding the signals, the outcomes, the holding period and the number of draws all fixed.

For the four-condition conjunction the t statistic reads 7.28 below zero when the comparison comes only from earlier bars, 4.00 below zero from 250 bars either side, 1.66 below zero from 1,000 bars either side, and 1.15 below zero when the comparison comes only from later bars. For the cloud crossing the same progression runs 2.98, 1.60, 0.46 and 0.33, all below zero. Nothing was planted in this tape. Every one of those numbers ought to be near zero, and only the rightmost column is.

A monotone collapse as the window slides forward is the signature of contamination rather than of a real effect that is merely hard to see. The mechanism is not subtle once stated: the backward half of a symmetric window contains the price path that produced the signal in the first place, so the comparison group is partly built out of the thing being compared against. Any test conditioned on what happened before the signal is exposed to this, which covers most reversal claims and most context splits.

Two things make this worth stating rather than quietly fixing. The first is that the correct control is not merely a stricter one. It was calibrated here on the planted tape, where it still detects a real effect at t of 3.60 through the cloud-crossing channel and 6.57 through the conjunction, and where its channel-by-channel results match the planted drift at a correlation of 0.996. It is the right instrument, not a duller one.

The second is about how corroboration works. This progression has been observed on a sibling page using different machinery, a different pattern and a different tape. The harness used here was written from scratch for this page precisely so that the agreement would mean something: two pages that share a harness will agree whether or not the claim is true, so agreement between them is not evidence. Two independent implementations reaching the same qualitative result on different data is a genuine cross-check, and this one held. Where the two differ is in the sign structure of the residual: on this tape the forward-only control leaves the conjunction at 1.15 below zero rather than at a small positive value, which is a difference worth recording rather than smoothing over.

Does the whole system beat its best single part

The claim that gives Ichimoku its appeal is not that any one line is powerful. It is that the components confirm one another, and that a reading taken when all of them agree is worth more than any of them alone. That is a testable proposition and it has a specific failure mode: a rule set that is over-specified will discard occasions without improving on what its best single clause already delivered.

On the tape with nothing planted in it the question cannot be answered, and saying so is more useful than manufacturing an answer. Every clause is null, so a comparison between the conjunction and the strongest clause is a comparison between two nulls. Its point estimate favours neither, at 0.10 percent below the strongest clause with a standard error of 0.14 percent.

The tape with a real effect in it can answer it. There the four-condition conjunction produced an excess of 0.69 percent, and its strongest single clause, price already sitting above the cloud, produced 0.49 percent. The difference of 0.21 percent carries a standard error of 0.13 percent, giving a t statistic of 1.64, which does not clear any conventional threshold. The smallest difference this comparison could have detected is 0.35 percent, so the honest reading is not that the conjunction is worse, it is that on evidence of this size the two cannot be told apart. That standard error is also a conservative one: the two arms share occasions, and shared occasions make the true standard error of a difference smaller than the sum used here, so a real difference would be easier to see than this test implies, not harder.

What can be said without ambiguity is the cost. The conjunction fired on 7,462 occasions against 15,728 for the single clause, so requiring all four conditions discarded 53 percent of the occasions on which the strongest clause alone was true, and bought no measurable improvement in exchange. On this evidence the rule set is over-specified. That is the honest version of the argument, and it is a narrower claim than saying confluence does not work: it says that on this data, these particular four conditions are close enough to being the same condition that requiring all of them mostly just reduces the sample.

That result also sits naturally with the correlation matrix. Four conditions built on four lines that share 0.67 of their variance are not four independent votes. They agree most of the time by construction, so the conjunction is close to the single clause with the strictest threshold, and requiring the others adds selection without adding information.

What this establishes, and what it does not

The results on this page split cleanly into two groups, and conflating them would be the easiest way to overclaim.

The first group does not depend on any data at all. Leading span A is the average of the conversion and base lines, so the drawn set contains at most four distinct series. The lagging span is the close, so it introduces an alignment rather than a measurement. The lagging span at the position where it is drawn is the close from twenty-six bars later, so reading it there uses a price that has not printed. Three of the five components are the same operation, a rolling high-low midpoint, at three lookbacks. None of that is a finding about markets. It is a description of the definitions, and it would be equally true of Indian equities, of a foreign index, or of a column of random numbers.

The second group does depend on data, and the data here is generated rather than observed. The correlations, the variance shares, the null results and the size of the look-ahead artefact were all measured on 600,000 simulated daily bars built from a stated model with symmetric drift regimes and clustered volatility. That choice is deliberate: it makes the exercise reproducible, it lets the absence of any real effect be a known property rather than an assumption, and it avoids implying that any particular Indian stock or index would have produced any particular outcome. It also means these numbers are not evidence about Indian market data, and this page does not claim they are. What generated data can establish is what a method does when there is nothing there, which is exactly the question a base rate is for.

There are narrower limits worth naming. Every test used one holding period of twenty bars and the long side only. Signals were deduplicated so that no two occasions on one instrument fell within twenty bars of each other, which keeps the arms from being one window counted many times but also discards clusters. The cloud was treated as a level to be crossed and as a state to be inside or outside, and no test asked about its thickness, which is a reading some descriptions place weight on. Any of those could be varied and any of them could change a result.

What remains after all of that is a modest and durable conclusion. The system carries fewer independent readings than its five lines suggest, and the shortfall is structural rather than incidental. Its most distinctive visual feature, the displacement, makes one region of the chart look confirmed for reasons that are arithmetic rather than evidential. Whether the shaded region functions as support or resistance is a separate question that turns on what a level is made of rather than on how the boundary was computed, and our page on how levels actually form takes that up in the terms it belongs in: resting orders, absorption and the memory of trapped participants, none of which is a property of a range midpoint.

If the arithmetic on this page was the interesting part rather than the tedious part, that instinct is the whole of it. Learning to read a chart properly starts with what price and volume can and cannot tell you, which is where our introduction to technical analysis begins, and it ends with the habit of asking of every indicator what it is a function of, whether that function is available at the moment of the decision, and what it would look like if it were worth nothing. Those three questions are cheap to ask and awkward to answer, and they are most of the method we teach.

Every figure comes from a single deterministic simulation, seeded so it reproduces identically on each run. Two tapes were generated by the same code: 200 instruments of 3,000 daily bars each, 600,000 bars in total, built from four symmetric drift states, an autoregressive log-volatility process and heavy-tailed innovations. The first tape contains nothing that makes direction predictable. The second is identical except that a drift is planted after a volatility squeeze followed by a breakout of a sixty-bar range, a trigger defined on the extreme of a rolling window and never on a midpoint of one, so no Ichimoku component appears in it.

All five components are computed from their published definitions with periods 9, 26 and 52 and a displacement of 26. Outcomes are measured over 20 bars, entering at the open of the bar after a condition became true and exiting at the close 20 bars later, with the identical convention applied to the comparison arm. Comparison entries are drawn only from bars after the event, within 250 bars on the same instrument, at 200 draws per event. Occurrences are deduplicated so no two on one instrument fall within 20 bars. Minimum detectable effect is 2.802 standard errors, which is the 5 percent threshold plus 80 percent power. The control machinery is itself tested against a tape carrying a known painted effect, which it recovers, and against the same tape with the effect removed, where it returns zero; a test that can only pass would not be a test.

All results are illustrative and simulated. They are not a track record, they are not a forecast, and they are not an indication of what any indicator or rule would produce in a live account. Nothing on this page is a recommendation to buy, sell or hold anything, and no part of it should be read as describing a way to trade.

• What a moving average is a function of →
• Supertrend, and what an overlay can and cannot know →
• The eight ways a backtest can lie →
• Measuring whether an edge exists →