[{"data":1,"prerenderedAt":10184},["ShallowReactive",2],{"wrun-open-editor-url":3,"indicators:functions/trend-indicators":4},"https://openmarket.xyz/chart/#wrun-open=v1",{"slug":5,"filePath":6,"frontmatter":7,"rawMarkdown":12,"tree":13},"functions/trend-indicators","functions/trend-indicators.md",{"title":8,"description":9,"order":10,"section":11},"Trend and volatility","Trend tools read direction and strength, volatility tools read range: the directional movement system, the Ichimoku cloud, the parabolic stop-and-reverse, the…",44,"functions","---\ntitle: \"Trend and volatility\"\ndescription: \"Trend tools read direction and strength, volatility tools read range: the directional movement system, the Ichimoku cloud, the parabolic stop-and-reverse, the…\"\norder: 44\nsection: \"functions\"\n---\n\n\u003C!-- source: docs/indicators/functions/trend-indicators.md; generated by packages/cli/scripts/gen-indicator-docs.ts, do not edit -->\n\n# Trend and volatility\n\nTrend tools read direction and strength, volatility tools read range: the\ndirectional movement system, the Ichimoku cloud, the parabolic\nstop-and-reverse, the ATR trailing stop, the band pair, and the volatility\nprimitives under them. Every one on this page ships as a class in\n`./sdk/ta` (`Adx`, `Ichimoku`, `Psar`, `Supertrend`, `Tr`, `Atr`, `Stdev`,\n`Variance`), and the bands are outputs plus a `range()` declaration. MACD\nis an oscillator and lives on the [Oscillators](oscillators.md#macd) page.\nThe full catalog is on the [TA library](ta-library.md) page.\n\n| System | What it reads |\n| --- | --- |\n| Directional movement (`Adx`) | trend strength as `adx`, with `plusDi` and `minusDi`; above 25 is a strong trend, below 20 often a range |\n| Ichimoku cloud (`Ichimoku`) | five components; the two leading spans come out of the class already shifted, the lagging span is drawn back by declaration |\n| Parabolic SAR (`Psar`) | a dot that trails price and jumps to the other side when the trend flips |\n| Supertrend (`Supertrend`) | an ATR-banded trailing stop with a direction the chart colors by |\n\n## Adx\n\n`new Adx(period = 14)`, `.update(high, low, close)` returns the ADX line;\nafter each update the fields `adx`, `plusDi`, and `minusDi` hold the three\nstreams. The class follows the engine's own arithmetic rather than a\ntextbook Wilder average: the true\nrange and the two directional movements are first summed over the first\n`period` bars (a plain sum, not a mean), then each running sum is smoothed\nas `s = s - s / period + x`; `plusDi` and `minusDi` are the smoothed\nmovements over the smoothed true range times 100 (`0` when that range is\nexactly `0`); DX is the normalized DI difference, `0` when both DI lines\nare `0`; and `adx` seeds on the plain average of the first `period` DX\nvalues before smoothing as `(adx * (period - 1) + dx) / period`. So the DI\nlines appear at bar `period` and `adx` at bar `2 * period - 1`. Bar 0 has\nno previous bar and produces nothing; a non-finite bar before the seed\nclears the partial sums and restarts the run, and a non-finite bar after\nthe seed leaves all three outputs `NaN` for the rest of the series.\n\n```typescript\nlet adx = new Adx(14);\nfunction onStart(): void { adx = new Adx(i32(p_adx_period())); }\n```\n\nRead `adx.plusDi > adx.minusDi` for direction and `adx.adx` rising for\nconviction; a `Cross` object over the two DI lines\n([Series functions](series-functions.md)) turns the crossover into a\nsignal.\n\nPine's `ta.dmi(diLength, adxSmoothing)` takes two lengths: `+DI` and\n`-DI` over `diLength`, ADX over `adxSmoothing`. `Adx` smooths all three\nover one period, so when the two differ reach for `Dmi` in\n`./sdk/ta-plus` ([Extra indicators](extra-indicators.md)), which keeps\nPine's form (Wilder's `Rma` on both) and the same three fields; with\nequal lengths the two classes agree on a series without a hole (`Dmi`\nskips a missing bar the way TradingView's `ta.dmi` does, where `Adx`\nreads `NaN` for good).\n\n```typescript\nlet dmi = new Dmi(14, 14);\nfunction onStart(): void { dmi = new Dmi(i32(p_di_length()), i32(p_adx_smoothing())); }\n// after dmi.update(high, low, close): dmi.adx, dmi.plusDi, dmi.minusDi\n```\n\n## Ichimoku\n\n`new Ichimoku(conversionPeriod = 9, basePeriod = 26, laggingSpanPeriod =\n52, displacement = 26)`, `.update(high, low, close)` returns `tenkan`;\nfields `tenkan`, `kijun`, `senkouA`, `senkouB`, `chikou`. Each line is the\nmidpoint of the highest high and lowest low over its period. The engine\nconventions the class keeps:\n\n- **Partial windows, no warm-up.** Bar 0 already has a value from its own\n  bar; there is no `NaN` lead-in. A `NaN` high or low inside the window is\n  skipped, but the current bar's own `NaN` poisons the value, and every\n  output that comes out `NaN` is reported as `0`.\n- **The displacement is inside the math.** `senkouA` on bar `i` is\n  `(tenkan + kijun) / 2` as it stood `displacement` bars earlier, and\n  `senkouB` is the 52-bar midpoint from `displacement` bars earlier; on\n  the first `displacement` bars both fall back to the current bar's\n  values. The two fields are therefore already the cloud that belongs on\n  the current bar, so write them to plain outputs with no\n  `displacement_bars`. The projection past the newest loaded bar is not\n  emitted, exactly as in the engine.\n- **`chikou` is the current close.** The engine reads the close of bar\n  `i + displacement`, a future bar, and only falls back to the current\n  close on the last `displacement` bars of the series; a class that sees\n  one bar at a time cannot read ahead, so the field is the current close.\n  Declaring `displacement_bars: -26` on its output makes the chart draw\n  that close 26 bars back, which is the lagging span as the engine's\n  chart shows it. That shift is drawing only: the value stays on the bar\n  that computed it.\n\n```typescript\nconst cloud = new Ichimoku(9, 26, 52, 26);\n\n// In onBar(): one update per bar, then read the five lines by name.\ncloud.update(bar.high(), bar.low(), bar.close());\nconst bullish = cloud.senkouA >= cloud.senkouB; // the cloud on this bar, already shifted\n```\n\nThe cloud itself is two boxes: `box(\"cloud_up\", { top: senkouA, bottom:\nsenkouB, when: aAbove })` draws, for each bar, a one-bar slice between the\ntwo spans the class reports for that bar, and a second box gated the other\nway draws the bearish slices in the other color. The declarations are\ncompiled in [Cloud, stop, and dots](#cloud-stop-and-dots) below.\n\n## Psar\n\n`new Psar(start = 0.02, increment = 0.02, maxValue = 0.2)`, `.update(high,\nlow, close)` returns the SAR price for the bar, which jumps to the other\nside of price when the trend flips; there is no direction field, so read\nthe side as `close > sar` (or the SAR against the low), or track the flips\nwith a `Cross` object over price and the SAR. The acceleration factor\nstarts at `start`, grows by `increment` on every new extreme, and caps at\n`maxValue`; the SAR never crosses the two prior bars' lows in an up trend\nor highs in a down trend, and when price trades through it the trend\nflips and the SAR jumps to the last extreme. Engine conventions: bar 0 is\n`NaN`; bar 1 decides the opening trend from `close[1] >= close[0]` and\nreturns `low[0]` for an up trend or `high[0]` for a down one; the close is\nonly read on those two bars; a non-finite high or low (or close on bars 0\nand 1) makes the SAR `NaN` for that bar and every bar after it, because\nthe engine recomputes the whole series and stops at the first bad bar.\nLower acceleration (`0.01` to `0.02`) gives smoother stops with fewer\nreversals; `0.05` and up reacts faster and flips more in ranges.\n\n```typescript\nlet psar = new Psar(0.02, 0.02, 0.2);\n\nfunction onBar(): void {\n  const close = bar.close();\n  const sar = psar.update(bar.high(), bar.low(), close);\n  if (isNaN(sar)) return;\n  const side = close > sar ? 1.0 : -1.0;\n  out_psar(sar);\n  out_side(side);\n}\n```\n\nDraw the SAR as a `scatter` output so it reads as dots, and color the dots\nby `side` through a `color_by` ladder ([Styling](../presentation/styling.md)).\n\n## Supertrend\n\n`new Supertrend(factor, atrPeriod)` (no defaults; `3` and `10` are the\nusual values), `.update(high, low, close)` returns the stop line and fills\nthe fields `line` and `direction` (`1` for an up trend, the line sits\nbelow price; `-1` for a down trend, the line sits above). The bands sit\n`factor` ATRs either side of the bar midpoint `(high + low) / 2`; the\nupper band ratchets down (a lower basic band, or the previous close above\nthe old band, replaces it) and the lower band ratchets up symmetrically;\nthe direction flips to `-1` when the close drops below the lower band in\nan up trend and to `1` when it rises above the upper band in a down\ntrend; the line is the lower band in an up trend and the upper band in a\ndown one. The ATR inside is the same Wilder smoothing as `Atr`, so the\nfirst finite bar is `atrPeriod - 1`, where the direction starts as `1`\nwhen the close is at or above the midpoint. While the ATR is `NaN` both\nfields are `NaN` and the band state is left untouched, so a gap neither\nresets nor advances the bands; a non-finite high, low, or close on a bar\nwith a finite ATR gives `NaN` for that bar alone. Because a shape cannot\nread a bool, the direction is a number, ready to be written to a\ndata-only output and used as a `color_by` index.\n\n```typescript\nlet st = new Supertrend(3.0, 10);\n\nfunction onStart(): void {\n  st = new Supertrend(p_factor(), i32(p_atr_period()));\n}\n\nfunction onBar(): void {\n  st.update(bar.high(), bar.low(), bar.close());\n  if (isNaN(st.line)) return;\n  out_st_line(st.line);\n  out_st_dir(st.direction > 0.0 ? 1.0 : 0.0);\n}\n```\n\n## Bands as outputs\n\n`Bb` and `Keltner` (both described on the [Moving averages](moving-averages.md)\npage) expose `basis`, `upper`, and `lower` fields; each becomes an output.\nA wrun indicator declares the band between them.\n`range(upper, lower, options)` names the two edge outputs (both must\nbe drawn) and the chart draws the band: both edge lines at `edge_width`\nand `edge_line_style` with a tinted interior in `color`, a `colors` +\n`color_by` ladder to tint it per bar, or a vertical `gradient`\n([Styling](../presentation/styling.md)). A `box` on every bar between the\ntwo edge outputs, with `from` and `to` left at `0`, is the other way to\nshade ([Cards, frames and panels](../presentation/cards-frames-panels.md));\nthe slices tile into a channel, and either edge may stay data-only.\n\n## Volatility primitives\n\n| Class | Construct | Per bar | Returns |\n| --- | --- | --- | --- |\n| `Tr` | `new Tr()` | `.update(high, low, close)` | the true range of the current bar: the largest of `high - low`, `abs(high - prevClose)`, `abs(low - prevClose)`, taken pairwise left to right; on bar 0 just `high - low` |\n| `Atr` | `new Atr(period = 14)` | `.update(high, low, close)` | the Wilder-smoothed true range: the seed is the plain average of the first `period` true ranges (first value at bar `period - 1`), then `(prev * (period - 1) + tr) / period` |\n| `Stdev` | `new Stdev(period)` | `.update(x)` | the rolling population standard deviation (divide by `period`, not `period - 1`) |\n| `Variance` | `new Variance(period)` | `.update(x)` | the rolling population variance, the same window arithmetic as `Stdev` without the square root |\n\nAll four ship in `./sdk/ta`;\nthey are the building blocks the band and stop classes use internally,\nexposed so custom volatility logic composes the same way. Their `NaN`\nrules differ, and the differences are the engine's: `Tr` returns `NaN` on\na non-finite high or low and on the bar after a non-finite close; `Atr`\nrestarts its seed when a non-finite true range arrives before the seed\ncompletes, and stays `NaN` for good after one arrives later (the engine\nnever reseeds); `Stdev` and `Variance` are strict windows, `NaN` until\n`period` bars exist and whenever any value in the window is not finite,\nhealing as soon as the bad bar leaves.\n\n```typescript\nconst tr = new Tr();\nlet atr = new Atr(14);\nlet stdev = new Stdev(20);\nlet variance = new Variance(20);\n\nfunction onStart(): void {\n  atr = new Atr(i32(p_atr_period()));\n  stdev = new Stdev(i32(p_period()));\n  variance = new Variance(i32(p_period()));\n}\n\nfunction onBar(): void {\n  const close = bar.close();\n  const trValue = tr.update(bar.high(), bar.low(), close);\n  const atrValue = atr.update(bar.high(), bar.low(), close);\n  const stdevValue = stdev.update(close);\n  const varianceValue = variance.update(close);\n  if (isNaN(atrValue)) return;\n  out_tr(trValue);\n  out_atr(atrValue);\n  out_stdev(stdevValue);\n  out_variance(varianceValue);\n}\n```\n\n`Stdev` is strict: a `NaN` sample anywhere in its window makes the result\n`NaN` until the sample leaves the window; guard the input with `isNaN`\nwhen a sparse source feeds it.\n\n## Putting them together\n\nThe directional system, the SAR, the Supertrend stop, and the volatility\nprimitives in one module. The stop line is colored by its regime through\na `color_by` ladder over a data-only `st_dir` output, the SAR draws as\ndots, and the ADX trio and the four volatility lines share a lower pane.\n\n```typescript sample=fn-trend-kit\nparam(\"adx_period\", 14, { min: 1, max: 200 });\nparam(\"factor\", 3, { min: 0.5, max: 10, description: \"Supertrend ATR multiplier\" });\nparam(\"atr_period\", 10, { min: 1, max: 200, description: \"ATR window for Supertrend and the atr line\" });\noutput(\"st_line\", line, overlay, { width: 2, color_by: \"st_dir\", colors: [\"#dc2626\", \"#16a34a\"], description: \"Supertrend stop, red in a short regime, green in a long one\" });\noutput(\"st_dir\", none, overlay, { description: \"0 short, 1 long: the palette index for st_line\" });\noutput(\"psar\", scatter, overlay, { color: \"#9333ea\", description: \"Parabolic SAR dots\" });\noutput(\"adx\", line, lower, { color: \"#111827\", width: 2, description: \"Average directional index\" });\noutput(\"di_plus\", line, lower, { color: \"#2563eb\", width: 1, description: \"+DI\" });\noutput(\"di_minus\", line, lower, { color: \"#dc2626\", width: 1, description: \"-DI\" });\noutput(\"tr\", line, lower, { color: \"#94a3b8\", width: 1, description: \"True range\" });\noutput(\"atr\", line, lower, { color: \"#f97316\", width: 2, description: \"Average true range\" });\noutput(\"stdev\", line, lower, { color: \"#0891b2\", width: 1, description: \"Rolling standard deviation of the close\" });\noutput(\"variance\", line, lower, { color: \"#7c3aed\", width: 1, description: \"Rolling variance of the close\" });\n\nlet adx = new Adx(14);\nlet psar = new Psar(0.02, 0.02, 0.2);\nlet st = new Supertrend(3.0, 10);\nlet tr = new Tr();\nlet atr = new Atr(10);\nlet stdev = new Stdev(10);\nlet variance = new Variance(10);\n\nfunction onStart(): void {\n  adx = new Adx(i32(p_adx_period()));\n  psar = new Psar(0.02, 0.02, 0.2);\n  st = new Supertrend(p_factor(), i32(p_atr_period()));\n  tr = new Tr();\n  atr = new Atr(i32(p_atr_period()));\n  stdev = new Stdev(i32(p_atr_period()));\n  variance = new Variance(i32(p_atr_period()));\n}\n\nfunction onBar(): void {\n  const close = bar.close();\n  const high = bar.high();\n  const low = bar.low();\n  adx.update(high, low, close);\n  const psarValue = psar.update(high, low, close);\n  st.update(high, low, close);\n  const trValue = tr.update(high, low, close);\n  const atrValue = atr.update(high, low, close);\n  const stdevValue = stdev.update(close);\n  const varianceValue = variance.update(close);\n  out_st_line(st.line);\n  out_st_dir(st.direction > 0.0 ? 1.0 : 0.0);\n  out_psar(psarValue);\n  out_adx(adx.adx);\n  out_di_plus(adx.plusDi);\n  out_di_minus(adx.minusDi);\n  out_tr(trValue);\n  out_atr(atrValue);\n  out_stdev(stdevValue);\n  out_variance(varianceValue);\n}\n```\n\n## Cloud, stop, and dots\n\nIchimoku with its two-color cloud and the lagging span drawn back, the\nSupertrend stop colored by regime, and the SAR as dots, in one overlay.\n\n```typescript sample=fn-special-trio\nparam(\"factor\", 3, { min: 0.5, max: 10, description: \"Supertrend ATR multiplier\" });\nparam(\"atr_period\", 10, { min: 1, max: 200, description: \"Supertrend ATR window\" });\noutput(\"tenkan\", line, overlay, { color: \"#0891b2\", width: 1, description: \"Conversion line, 9-bar midpoint\" });\noutput(\"kijun\", line, overlay, { color: \"#be123c\", width: 1, description: \"Base line, 26-bar midpoint\" });\n// The spans are already shifted inside the class: the value on a bar is the cloud for that bar.\nconst senkouA = output(\"senkou_a\", line, overlay, { color: \"#0f766e\", width: 1, description: \"Leading span A, the class shifts it 26 bars ahead\" });\nconst senkouB = output(\"senkou_b\", line, overlay, { color: \"#b45309\", width: 1, description: \"Leading span B, the class shifts it 26 bars ahead\" });\noutput(\"chikou\", line, overlay, { color: \"#64748b\", width: 1, displacement_bars: -26, description: \"Lagging span, the close drawn 26 bars back\" });\nconst aAbove = output(\"a_above\", none, overlay, { description: \"1 where span A is above span B: the bullish cloud gate\" });\nconst bAbove = output(\"b_above\", none, overlay, { description: \"1 where span B is above span A: the bearish cloud gate\" });\n// The cloud: one slice per bar between the two spans, tinted by which span is on top.\nbox(\"cloud_up\", { top: senkouA, bottom: senkouB, when: aAbove, color: \"#16a34a\", opacity: 0.12, borderWidth: 0 });\nbox(\"cloud_down\", { top: senkouB, bottom: senkouA, when: bAbove, color: \"#dc2626\", opacity: 0.12, borderWidth: 0 });\noutput(\"st_line\", line, overlay, { width: 2, color_by: \"st_dir\", colors: [\"#dc2626\", \"#16a34a\"], description: \"Supertrend stop, colored by regime\" });\noutput(\"st_dir\", none, overlay, { description: \"0 short, 1 long\" });\noutput(\"psar\", scatter, overlay, { color: \"#9333ea\", description: \"Parabolic SAR\" });\n\nlet cloud = new Ichimoku(9, 26, 52, 26);\nlet st = new Supertrend(3.0, 10);\nlet psar = new Psar(0.02, 0.02, 0.2);\n\nfunction onStart(): void {\n  cloud = new Ichimoku(9, 26, 52, 26);\n  st = new Supertrend(p_factor(), i32(p_atr_period()));\n  psar = new Psar(0.02, 0.02, 0.2);\n}\n\nfunction onBar(): void {\n  const close = bar.close();\n  const high = bar.high();\n  const low = bar.low();\n  cloud.update(high, low, close);\n  st.update(high, low, close);\n  const psarValue = psar.update(high, low, close);\n  out_tenkan(cloud.tenkan);\n  out_kijun(cloud.kijun);\n  out_senkou_a(cloud.senkouA);\n  out_senkou_b(cloud.senkouB);\n  out_chikou(cloud.chikou);\n  out_a_above(cloud.senkouA >= cloud.senkouB ? 1.0 : 0.0);\n  out_b_above(cloud.senkouB > cloud.senkouA ? 1.0 : 0.0);\n  out_st_line(st.line);\n  out_st_dir(st.direction > 0.0 ? 1.0 : 0.0);\n  out_psar(psarValue);\n}\n```\n\n## Bands: outputs, a range, and a shaded box\n\nThe Bollinger pair as three outputs, a `range()` declaration recording the\nband in the sheet, and a `box` on every bar shading the same pair on the\nchart, gated so the shade only shows while the basis is rising.\n\n```typescript sample=fn-trend-bands\nparam(\"period\", 20, { min: 2, max: 400 });\nparam(\"mult\", 2, { min: 0.5, max: 5, description: \"Standard-deviation multiples\" });\nconst upper = output(\"upper_band\", line, overlay, { color: \"#64748b\", width: 1, description: \"Basis plus mult deviations\" });\noutput(\"basis\", line, overlay, { color: \"#2563eb\", width: 1, description: \"20-bar simple average\" });\nconst lowerBand = output(\"lower_band\", line, overlay, { color: \"#64748b\", width: 1, description: \"Basis minus mult deviations\" });\nconst rising = output(\"rising\", none, overlay, { description: \"1 while the basis rises: the shade gate\" });\n// The sheet-level band: honored by hosts that draw ranges, ignored by the chart lane today.\nrange(\"upper_band\", \"lower_band\", { color: \"#2563eb\", edge_width: 1, edge_line_style: \"dotted\" });\n// The chart-drawn band: one slice per bar between the same two outputs, tiling into a channel.\nbox(\"band_shade\", { top: upper, bottom: lowerBand, when: rising, color: \"#2563eb\", opacity: 0.12, borderWidth: 0 });\n\nlet sma = new Sma(20);\nlet stdev = new Stdev(20);\nlet mult: f64 = 2.0;\nlet mid: f64 = NaN;\nlet prevMid: f64 = NaN;\n\nfunction onStart(): void {\n  sma = new Sma(i32(p_period()));\n  stdev = new Stdev(i32(p_period()));\n  mult = p_mult();\n}\n\nfunction onBar(): void {\n  const close = bar.close();\n  prevMid = mid;\n  mid = sma.update(close);\n  const sd = stdev.update(close);\n  if (isNaN(mid) || isNaN(sd)) return;\n  out_upper_band(mid + mult * sd);\n  out_basis(mid);\n  out_lower_band(mid - mult * sd);\n  out_rising(!isNaN(prevMid) && mid > prevMid ? 1.0 : 0.0);\n}\n```\n\n## Reading them\n\n- **Ichimoku.** Price above the cloud (both spans) is an uptrend, below it\n  a downtrend; a `tenkan` over `kijun` cross that agrees with the cloud is\n  the classic entry.\n- **Supertrend.** The flip of `direction` is the signal; the line itself is\n  the trailing stop for the position the regime implies.\n",{"type":14,"children":15,"data":10177,"position":10179},"root",[16,26,29,30,293,295,617,618,635,636,995,996,1127,1128,1221,1222,1489,1490,1634,1635,1648,1649,1795,1796,2198,2199,2372,2373,2427,2428,2442,2443,2727,2728,3035,3036,3126,3127,3141,3142,3491,3492,3808,3809,3824,3825,4186,4187,4202,4204,4724,4725,4913,4914,5537,5538,5615,5616,5631,5632,5683,5684,7377,7378,7392,7393,7408,7409,8883,8884,8899,8900,8950,8951,10040,10041,10056,10057],{"type":17,"value":18,"position":19},"comment"," source: docs/indicators/functions/trend-indicators.md; generated by packages/cli/scripts/gen-indicator-docs.ts, do not edit ",{"start":20,"end":23},{"line":21,"column":21,"offset":22},1,0,{"line":21,"column":24,"offset":25},133,132,{"type":27,"value":28},"text","\n",{"type":27,"value":28},{"type":31,"tagName":32,"properties":33,"children":34,"position":290},"element","p",{},[35,44,58,65,78,85,98,104,117,123,136,142,155,161,174,180,193,200,212,219,232,239,257,265,283],{"type":27,"value":36,"position":37},"Trend tools read direction and strength, volatility tools read range: the\ndirectional movement system, the Ichimoku cloud, the parabolic\nstop-and-reverse, the ATR trailing stop, the band pair, and the volatility\nprimitives under them. 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