Ichimoku Kinko Hyo — five formulas, plotting shifts and full windows

Ichimoku combines five plots derived from the same instrument’s prices. Before interpreting their arrangement, identify which candles supplied a number and where it is drawn. Forward placement does not reveal a future price, and a back-plotted current Close was not available earlier. This lesson checks the formulas and chronology using hypothetical inputs.

Windows, candles and explicit indices

Use settings 9, 26 and 52 with exactly 26 index shifts in this model. That parameter set appears in the MQL5 reference example. The numbers count timeframe candles, not calendar dates. Weekends and the feed’s candle construction prevent treating 26 bars as one calendar month.

Let t be the last completed candle, H its high, L its low and C its close. HHn(t) is the highest High and LLn(t) the lowest Low from t−n+1 through t inclusive. At t=100, the 9-, 26- and 52-bar windows are 92–100, 75–100 and 49–100. Indices increase chronologically.

The five lines — what each one actually calculates

Tenkan and Kijun are range midpoints. Span A averages those two numbers; Span B uses a longer high/low window. Chikou copies Close. This formula description does not treat the five plots as independent statistical evidence of a profitable trade.

None of the Ichimoku lines is a classic moving average. Tenkan-sen and Kijun-sen are midpoints of a range — the average of the highest high and the lowest low, not of every close. The practical difference from an EMA or an SMA is this: such a line changes when the rolling window’s highest high or lowest low changes, including when an old extreme leaves the window. It may stay flat without proving that the market is consolidating, and can move without a new breakout. Senkou Span A and B form the two edges of the Kumo cloud, which deserves a section of its own. Chikou Span is the oddest of the group — it is not derived from any average; it is simply the current closing price drawn backwards on the chart, used as a reference for comparison.

Tenkan-sen and Kijun-sen — the market's fast and slow pulse

Assume complete, nested EUR/USD windows at t=100, in USD per EUR: HH9=1.1120, LL9=1.1040; HH26=1.1180, LL26=1.1000; HH52=1.1240, LL52=1.0920. Tenkan=1.1080 and Kijun=1.1090 are plotted at 100. Span A=(1.1080+1.1090)/2=1.1085 and Span B=(1.1240+1.0920)/2=1.1080 are plotted at 126. Close=1.1100 is drawn as Chikou at 74.

Compare Tenkan with a separate SMA example: eight closes in 92–100 are 1.1050 and the final close is 1.1100. Their mean is (8×1.1050+1.1100)/9 ≈ 1.105556, while Tenkan remains 1.1080 because it uses the window extremes. A generic “average” label does not identify which calculation was performed.

Now let High 1.1120 occur only at 92. When the window moves to 93–101, that bar leaves. Assume remaining highest High 1.1105, unchanged lowest Low 1.1040, and the new candle confined to 1.1060–1.1100. Tenkan becomes 1.10725, down 7.5 pips at 0.0001 without a new outer extreme. A midpoint can move because an old observation expired.

Senkou Span A and B — the birth of the Kumo cloud

Span A and B enclose the Kumo. In our example the fresh bounds 1.1080–1.1085 are drawn at 126, not beneath current candle 100. The cloud at 100 needs A and B calculated at 74, which the supplied numbers do not specify. Both sets can share a colour while representing different source windows.

Cloud colour represents the chosen A/B ordering and can be customized. Thickness is |A−B| at that plotted location. It is not an order-volume measure, the full high/low range, or a wall guaranteed to stop price. In the separate diagram, A=B=105 but HH52−LL52=112−98=14.

A method may classify price above, below or inside the applicable cloud. Equality on a boundary needs its own rule. Such a classification is not automatically a long/short instruction or a universally reliable trading exclusion; define execution and costs separately.

Chikou Span — the lagging line as a trend reality check

Chikou is current Close displayed backwards, not a delayed calculation of an old Close. The value 1.1100 drawn at 74 in our example is final only after candle 100 closes. Using it to decide at 74 would import later information into a historical decision.

A Chikou comparison must name the earlier field: Close, High, Low or a range. A current value above a historical Close need not exceed that candle’s High. It does not establish that buying pressure persisted throughout the interval or provide an independent dataset.

Changing the historical comparison or adding a Chikou filter creates another rule variant. Record it before evaluating results. Neither “clear air” nor agreement with the other price-derived plots guarantees a more profitable entry.

Bullish and bearish clouds — what the colours tell you

A/B ordering describes calculated numbers, not who controls price 26 days later. An A line can remain unchanged while B changes because a rolling window loses an old extreme. Record the calculation and plotting indices before interpreting a colour change.

Kumo twist is a change of sign in the A−B ordering under your equality convention. A future chart location does not specify a future trend-change date. An exit based on that event would need its own execution rule and test.

Defined comparisons are separate strategy variants

State which price fields, current or freshly computed cloud, completed candle and displacement each comparison uses. Adding conditions can change entry chronology and exposure; it does not automatically reduce chance or improve net results.

1. Four-filter bullish variant. Price is above the displayed Kumo, Tenkan-sen is above Kijun-sen, Chikou is above the selected earlier price and the forward-shifted cloud is green. These are aligned checks derived from overlapping price inputs, not independent statistical confirmations. Define all four conditions before testing their effect, including costs and cases excluded by the filters.
2. Cloud breakout. Define the previous and current Close-to-boundary relations and any buffer. The current cloud comes from earlier span calculations. An added Chikou condition must be tested as a separate filter.
3. Retest of Kijun. Define a contact zone, waiting window, cancellation and later execution. A touch or bounce does not by itself justify a position, a cloud-edge stop or a preset target.
4. Tenkan–Kijun cross. Distinguish a new crossover from the state Tenkan above Kijun. Cloud context is another specified condition; none is ranked by a demonstrated hit rate here.

Practical takeaway: Zero cloud thickness means equal span values at that location; it does not mean there was no underlying price range.

Common mistakes and your first steps with Ichimoku

Before interpreting a plot, confirm that every required full window exists. In a hypothetical history starting at index 0 with no earlier bars, the first Tenkan is at 8, Kijun and calculated A at 25, and calculated B at 51. With exact 26-index displacement, A first appears beneath price at 51 and both cloud boundaries at 77: 78 recorded candles are needed.

• Confusing current B with the current cloud. At index 51, fresh B exists, but B beneath 51 would require calculation at 25 using a 52-bar window extending before the history began. Missing data is not zero.
• Mixing full and partial windows. A platform using shorter startup windows is not calculating the full-window definition used here. Record the initialization policy and do not count a missing plot as a real zero.
• Substituting thickness for range. Calculate |A−B| and HH−LL separately. Equal spans can coexist with a wide underlying range; neither tells you the future path.
• Mixing unfinished and final candles. An active candle’s High, Low and Close may change, so dependent values can change as well. Save the timeframe, feed and completed-candle convention rather than assigning universally unsuitable periods.

Recheck one changed input: at t=100, raise only HH26 to 1.1200 while LL26=1.1000, Tenkan=1.1080 and Close=1.1100 remain. Kijun becomes 1.1100 at 100 and Span A becomes 1.1090 at 126. Chikou remains 1.1100 at 74 because Close did not change. This calculation does not establish performance or a mandatory month-by-month learning schedule.

Related reading: full overview of the Ichimoku system — a companion piece with deeper configuration detail; moving averages, EMA and SMA — a comparison with the most common alternatives; multi-timeframe analysis — how to combine Ichimoku on D1 and H4 at the same time.