[{"data":1,"prerenderedAt":9986},["ShallowReactive",2],{"wrun-open-editor-url":3,"indicators:functions/moving-averages":4},"https://openmarket.xyz/chart/#wrun-open=v1",{"slug":5,"filePath":6,"frontmatter":7,"rawMarkdown":12,"tree":13},"functions/moving-averages","functions/moving-averages.md",{"title":8,"description":9,"order":10,"section":11},"Moving averages","These classes smooth price into a trend line or wrap it in a band. Every one of them ships with the editor in the ./sdk/ta module (Sma, Ema, Wma, Hma, Alma…",42,"functions","---\ntitle: \"Moving averages\"\ndescription: \"These classes smooth price into a trend line or wrap it in a band. Every one of them ships with the editor in the ./sdk/ta module (Sma, Ema, Wma, Hma, Alma…\"\norder: 42\nsection: \"functions\"\n---\n\n\u003C!-- source: docs/indicators/functions/moving-averages.md; generated by packages/cli/scripts/gen-indicator-docs.ts, do not edit -->\n\n# Moving averages\n\nThese classes smooth price into a trend line or wrap it in a band. Every\none of them ships with the editor in the `./sdk/ta` module (`Sma`,\n`Ema`, `Wma`, `Hma`, `Alma`, `Swma`, `Vwma`, `Rma`, `Linreg`, `Bb`,\n`Keltner`, `Donchian`), each one built the same way: allocate in the\nconstructor, fold one bar per `update()`, return `NaN` until the window is\nfull, restore with `reset()`. Name the class you need (nothing to import),\nconstruct it in `onStart()`, and call `update()` once per bar in `onBar()`.\nEvery class has fixed arithmetic and edge rules, named in its section\n([TA library](ta-library.md) lists the full catalog and the proof).\n\nEvery windowed average is `NaN` until its window fills. An `Sma(20)` draws\nnothing for its first 19 bars, then begins once the 20th has loaded; the\nHull average warms up a little longer because of its internal weighted\nsub-windows. Donchian is the exception: it reads the rolling extreme of\nwhatever has loaded from the very first bar. `NaN` is the warm-up signal,\nso a `NaN` written to one output and an early `return` from `onBar()`\nthat leaves every output unwritten are the two honest ways to say \"not\nyet\" ([Execution model](../core-concepts/execution-model.md)).\n\nThe shape every class shares:\n\n| Member | Meaning |\n| --- | --- |\n| `new X(period)` | allocates the window once; a `period` below 1 is clamped to 1 |\n| `.update(x): f64` | folds one bar, returns the current value, `NaN` until warm |\n| `.reset(): void` | back to the freshly constructed state; nothing on the chart calls it for you |\n\nA non-finite input (a `NaN` or an infinity) inside a window makes the\nwindowed averages return `NaN` for as long as that bar sits in the window;\nthe two running averages (`Ema`, `Rma`) never recover from one.\n\n## Single-line averages\n\n### Sma\n\n`new Sma(period)`, `.update(x)`: the unweighted mean of the last `period`\nvalues, summed oldest to newest and divided by the period. Warm-up is\n`period` bars (first value at bar `period - 1`).\n\n```typescript\nlet sma = new Sma(20);\nfunction onStart(): void { sma = new Sma(i32(p_period())); }\n```\n\nRead the period through its accessor and cast it: params are `f64`, class\nperiods are `i32`, and AssemblyScript refuses the implicit conversion.\n\n### Ema\n\n`new Ema(period)`, `.update(x)`: the exponential average. Weights recent\nbars more heavily, so it turns faster than `Sma`. The first `period`\nfinite values seed it with their simple mean, then `x * alpha + prev * (1\n- alpha)` with `alpha = 2 / (period + 1)` takes over, so it is `NaN` for\n`period - 1` bars. A non-finite input before the seed completes restarts\nthe seed count; one after the seed sets the value to `NaN` for good (the\nengine never reseeds).\n\n```typescript\nlet ema = new Ema(20);\n```\n\n### Wma\n\n`new Wma(period)`, `.update(x)`: the linearly weighted average. The newest\nbar carries weight `period`, the oldest weight `1`, so it sits between\n`Sma` and `Ema` in responsiveness. The weighted sum walks oldest to newest\nand is divided by `period * (period + 1) / 2`; `NaN` until `period` bars\nhave been seen and whenever any value in the window is not finite.\n\n```typescript\nlet wma = new Wma(20);\nfunction onStart(): void { wma = new Wma(i32(p_period())); }\n```\n\n### Hma\n\n`new Hma(period)`, `.update(x)`: the Hull average, three `Wma` windows\ncomposed as `WMA(2 * WMA(round(n / 2)) - WMA(n), round(sqrt(n)))`. Very\nlow lag and smooth. The half and square-root lengths are rounded (never\nbelow 1), the inner difference is `NaN` until both inner windows are warm,\nand the outer window then needs `round(sqrt(n))` finite values, so the\nfirst value lands at bar `n - 1 + round(sqrt(n)) - 1`.\n\n```typescript\nlet hma = new Hma(21);\nfunction onStart(): void { hma = new Hma(i32(p_hull_period())); }\n```\n\n### Alma\n\n`new Alma(length, offset = 0.85, sigma = 6)`, `.update(x)`: the Arnaud\nLegoux average, a Gaussian-weighted window. `offset` places the peak of\nthe bell at `offset * (length - 1)` from the oldest bar (near the newest\nbar by default), `sigma` sets its width as `length / sigma`. The weights\nare computed once in the constructor with the engine's arithmetic, so\n`update()` is a single weighted pass, walked oldest to newest. `NaN` until\n`length` bars have been seen and whenever any value in the window is not\nfinite.\n\n```typescript\nlet alma = new Alma(20);              // offset 0.85, sigma 6\nlet sharp = new Alma(20, 0.9, 4.0);   // peak closer to the newest bar, narrower bell\n```\n\nOmitting `offset` and `sigma` is the same as passing `0.85` and `6`.\n\n### Swma\n\n`new Swma()`, `.update(x)`: the symmetrically weighted average, the fixed\nfour-tap smoother `(x[3] + 2 * x[2] + 2 * x[1] + x[0]) / 6` with `x[0]`\nthe newest bar. `NaN` on the first three bars (first value at bar 3) and\nwhenever any of the four values is not finite; no period to choose.\n\n```typescript\nlet swma = new Swma();\n```\n\n### Vwma\n\n`new Vwma(period)`, `.update(price, volume)`: the volume-weighted average\ntakes two values per bar, `sum(price * volume) / sum(volume)` over the\nwindow. Bars with more volume pull the average harder, so it tracks where\ntrading actually happened. It needs the bar's volume beside the price\n(`bar.volume()`). `NaN` until `period` bars have been\nseen, whenever any price or volume in the window is not finite, and when\nthe volume sum is exactly `0`.\n\n```typescript\nlet vwma = new Vwma(20);\nfunction onBar(): void { out_vwma(vwma.update(bar.close(), bar.volume())); }\n```\n\n### Rma\n\n`new Rma(period)`, `.update(x)`: the running (Wilder) average, the\nsmoothing inside RSI and ATR. The first `period` finite values seed it\nwith their simple mean, then `rma = (rma * (period - 1) + x) / period`.\nSmoother and slower than `Ema` for the same period. This is the same\nWilder accumulator `Rsi` and `Atr` use internally, so an RSI built by\nhand over `Rma` and the shipped `Rsi` agree. A non-finite input before the seed completes restarts the seed\ncount; one after the seed sets the value to `NaN` for good.\n\n```typescript\nlet rma = new Rma(14);\n```\n\n### Linreg\n\n`new Linreg(period, offset = 0)`, `.update(x)`: linear regression fits a\nleast-squares line over the last `period` bars (x positions `0` oldest to\n`period - 1` newest) and returns its value at the newest bar (`offset`\n`0`) or `offset` bars back along the fitted line: the trend's fitted price\nrather than an average. `offset` is an `f64` truncated to an integer. `NaN`\nuntil `period` bars have been seen and whenever any value in the window\nis not finite; a period of `1` returns the value itself.\n\n```typescript\nlet linreg = new Linreg(20);        // value at the newest bar\nlet lagged = new Linreg(20, 2.0);   // the fitted line two bars back\n```\n\n## Band helpers\n\nA band is three named streams. A wrun indicator has no\ntuple outputs: the class exposes `upper`, `basis`, and `lower` as fields\nafter each `update()`, and you write each one to its own output\n([Named streams](../core-concepts/named-streams.md)). Shading between the\nedges is a `range()` band over the two drawn edges\n([Styling](../presentation/styling.md)) or a `box` on every bar\n([Cards, frames and panels](../presentation/cards-frames-panels.md)).\n\n### Bb\n\n`new Bb(period, mult)`, `.update(x)`: Bollinger bands. `basis` is the\nwindow mean (the same arithmetic as `Sma`), `upper` and `lower` sit `mult`\npopulation standard deviations away (the same arithmetic as `Stdev`, the\ntextbook Bollinger form). `update()` returns the basis and fills the three\nfields. All three are `NaN` until `period` bars exist and whenever any bar\nof the window is not finite; the window heals as soon as the bad bar\nleaves it. Both arguments are required; the usual call is\n`new Bb(20, 2.0)`.\n\n```typescript\nlet bb = new Bb(20, 2.0);\nfunction onBar(): void {\n  bb.update(bar.close());\n  out_bb_upper(bb.upper);\n  out_bb_basis(bb.basis);\n  out_bb_lower(bb.lower);\n}\n```\n\n### Keltner\n\n`new Keltner(period, mult, atrPeriod)`, `.update(x, high, low, close)`:\nlike Bollinger, but the width comes from the average true range instead\nof the standard deviation, so it reacts to range rather than dispersion.\n`basis` is an `Ema(period)` over `x` (usually the close), the width is an\n`Atr(atrPeriod)` over the three prices (the Wilder-smoothed true range;\nits class is on the [Trend and volatility](trend-indicators.md#volatility-primitives) page)\nmultiplied by `mult`. `update()` returns the basis and fills the three\nfields. The basis is reported as soon as the `Ema` is seeded, even while\nthe ATR is still warming up; `upper` and `lower` are `NaN` unless both the\nbasis and the ATR are finite.\n\n```typescript\nlet kc = new Keltner(20, 1.5, 10);\nfunction onBar(): void {\n  const close = bar.close();\n  kc.update(close, bar.high(), bar.low(), close);\n  out_kc_upper(kc.upper);\n  out_kc_basis(kc.basis);\n  out_kc_lower(kc.lower);\n}\n```\n\n### Donchian\n\n`new Donchian(period = 12)`, `.update(high, low)`: the highest high and\nlowest low over `period` bars as `upper` and `lower`, with their midpoint\nas `basis` (the value `update()` returns). Because it reads the rolling\nextreme rather than averaging,\nit is finite from the first loaded bar: the window is partial at the\nstart, and bar 0 returns `(high + low) / 2` of that bar alone. The current\nbar's high and low always take part, even when `NaN` (so a `NaN` bar\npropagates), while non-finite highs or lows of older bars are skipped.\nThe period is used as given: the clamp to 1 the other classes apply does\nnot run here.\n\n```typescript\nlet dc = new Donchian(20);\nfunction onBar(): void {\n  dc.update(bar.high(), bar.low());\n  out_dc_upper(dc.upper);\n  out_dc_basis(dc.basis);\n  out_dc_lower(dc.lower);\n}\n```\n\n## Putting them together\n\nEvery average and band on one chart: the nine single-line averages on the\nprice pane, the three band helpers as nine more outputs. Every class is\nused by name with nothing to import. Each class is constructed in\n`onStart()` from a param, then updated once and its value written in\n`onBar()`.\n\n```typescript sample=fn-moving-averages\nparam(\"period\", 20, { min: 2, max: 400, description: \"Window for every average and band\" });\nparam(\"hull_period\", 21, { min: 4, max: 400, description: \"Hull average window\" });\nparam(\"mult\", 2, { min: 0.5, max: 5, description: \"Bollinger standard-deviation multiplier\" });\nparam(\"kc_mult\", 1.5, { min: 0.5, max: 5, description: \"Keltner ATR multiplier\" });\nparam(\"atr_period\", 10, { min: 1, max: 200, description: \"Keltner ATR window\" });\noutput(\"sma\", line, overlay, { color: \"#2563eb\", width: 2, description: \"Simple moving average\" });\noutput(\"ema\", line, overlay, { color: \"#dc2626\", width: 2, description: \"Exponential moving average\" });\noutput(\"hma\", line, overlay, { color: \"#7c3aed\", width: 2, description: \"Hull moving average\" });\noutput(\"wma\", line, overlay, { color: \"#ea580c\", width: 2, description: \"Weighted moving average\" });\noutput(\"alma\", line, overlay, { color: \"#0891b2\", width: 2, description: \"Arnaud Legoux moving average\" });\noutput(\"swma\", line, overlay, { color: \"#0f766e\", width: 1, description: \"Symmetrically weighted moving average\" });\noutput(\"vwma\", line, overlay, { color: \"#b45309\", width: 2, description: \"Volume-weighted moving average\" });\noutput(\"rma\", line, overlay, { color: \"#059669\", width: 2, description: \"Wilder running moving average\" });\noutput(\"linreg\", line, overlay, { color: \"#4b5563\", width: 2, description: \"Least-squares regression value\" });\noutput(\"bb_upper\", line, overlay, { color: \"#0f766e\", width: 1, description: \"Bollinger upper band\" });\noutput(\"bb_basis\", line, overlay, { color: \"#64748b\", width: 1, description: \"Bollinger basis\" });\noutput(\"bb_lower\", line, overlay, { color: \"#be123c\", width: 1, description: \"Bollinger lower band\" });\noutput(\"kc_upper\", line, overlay, { color: \"#16a34a\", width: 1, description: \"Keltner upper channel\" });\noutput(\"kc_basis\", line, overlay, { color: \"#94a3b8\", width: 1, description: \"Keltner basis\" });\noutput(\"kc_lower\", line, overlay, { color: \"#dc2626\", width: 1, description: \"Keltner lower channel\" });\noutput(\"dc_upper\", line, overlay, { color: \"#0ea5e9\", width: 1, description: \"Donchian upper band\" });\noutput(\"dc_basis\", line, overlay, { color: \"#94a3b8\", width: 1, description: \"Donchian midpoint\" });\noutput(\"dc_lower\", line, overlay, { color: \"#f97316\", width: 1, description: \"Donchian lower band\" });\n\nlet sma = new Sma(20);\nlet ema = new Ema(20);\nlet hma = new Hma(21);\nlet wma = new Wma(20);\nlet alma = new Alma(20);\nlet swma = new Swma();\nlet vwma = new Vwma(20);\nlet rma = new Rma(20);\nlet linreg = new Linreg(20);\nlet bb = new Bb(20, 2.0);\nlet kc = new Keltner(20, 1.5, 10);\nlet dc = new Donchian(20);\n\nfunction onStart(): void {\n  const period = i32(p_period());\n  sma = new Sma(period);\n  ema = new Ema(period);\n  hma = new Hma(i32(p_hull_period()));\n  wma = new Wma(period);\n  alma = new Alma(period);\n  swma = new Swma();\n  vwma = new Vwma(period);\n  rma = new Rma(period);\n  linreg = new Linreg(period, 0.0);\n  bb = new Bb(period, p_mult());\n  kc = new Keltner(period, p_kc_mult(), i32(p_atr_period()));\n  dc = new Donchian(period);\n}\n\nfunction onBar(): void {\n  const close = bar.close();\n  const high = bar.high();\n  const low = bar.low();\n  const smaValue = sma.update(close);\n  const emaValue = ema.update(close);\n  const hmaValue = hma.update(close);\n  const wmaValue = wma.update(close);\n  const almaValue = alma.update(close);\n  const swmaValue = swma.update(close);\n  const vwmaValue = vwma.update(close, bar.volume());\n  const rmaValue = rma.update(close);\n  const linregValue = linreg.update(close);\n  bb.update(close);\n  kc.update(close, high, low, close);\n  dc.update(high, low);\n  // Donchian is finite from the first bar, so its band draws at once;\n  // the slower lines simply write NaN until their own windows fill.\n  out_sma(smaValue);\n  out_ema(emaValue);\n  out_hma(hmaValue);\n  out_wma(wmaValue);\n  out_alma(almaValue);\n  out_swma(swmaValue);\n  out_vwma(vwmaValue);\n  out_rma(rmaValue);\n  out_linreg(linregValue);\n  out_bb_upper(bb.upper);\n  out_bb_basis(bb.basis);\n  out_bb_lower(bb.lower);\n  out_kc_upper(kc.upper);\n  out_kc_basis(kc.basis);\n  out_kc_lower(kc.lower);\n  out_dc_upper(dc.upper);\n  out_dc_basis(dc.basis);\n  out_dc_lower(dc.lower);\n}\n```\n\nThe whole module is one chart overlay with eighteen legend entries, and\nonce the indicator is published every one of them is an output an alert\ncan follow ([Alerts](alerts.md)).\n\n## Warm-up and named streams\n\nTwo ideas worth seeing on their own: an average is blank until its window\nfills, and a band's three levels are three independent outputs you can\ndraw or hide one at a time. The Bollinger edges below are drawn while the\nbasis stays data-only (`none`): it still computes and you can read it at\nthe Console prompt, but the chart shows only the two bands. All three\nbegin together once the 20-bar window completes, because one `Bb` feeds\nthem.\n\n```typescript sample=fn-warmup-streams\nparam(\"period\", 20, { min: 2, max: 400 });\noutput(\"sma20\", line, overlay, { color: \"#2563eb\", width: 2, description: \"NaN until the window is complete\" });\noutput(\"bb_upper\", line, overlay, { color: \"#16a34a\", width: 2, description: \"Bollinger upper band\" });\noutput(\"bb_basis\", none, overlay, { description: \"Computed, never drawn: a value without a line\" });\noutput(\"bb_lower\", line, overlay, { color: \"#dc2626\", width: 2, description: \"Bollinger lower band\" });\n\nlet sma = new Sma(20);\nlet bb = new Bb(20, 2.0);\n\nfunction onStart(): void {\n  sma = new Sma(i32(p_period()));\n  bb = new Bb(i32(p_period()), 2.0);\n}\n\nfunction onBar(): void {\n  const close = bar.close();\n  const value = sma.update(close);\n  bb.update(close);\n  // Return before writing while the window is filling: no legend value, nothing drawn.\n  if (isNaN(value)) return;\n  out_sma20(value);\n  out_bb_upper(bb.upper);\n  out_bb_basis(bb.basis);\n  out_bb_lower(bb.lower);\n}\n```\n\n## Alma and Swma boundaries\n\n`Alma`'s omitted `offset` and `sigma` default to `0.85` and `6`, so a\ndefault construction and an explicit one agree to the last bit; `Swma`\nuses the fixed four-tap weighting, so it agrees with the arithmetic\nspelled out by hand over the last four closes. The module below computes\nboth forms and writes each line only where the class agrees with the\nmanual form, which is every bar once the windows are warm: a `NaN`\nwritten on a disagreeing bar would leave a visible hole.\n\n```typescript sample=fn-alma-swma\nparam(\"length\", 10, { min: 2, max: 200 });\noutput(\"alma_check\", line, lower, { color: \"#2563eb\", width: 2, description: \"ALMA with the default offset 0.85 and sigma 6\" });\noutput(\"swma_check\", line, lower, { color: \"#16a34a\", width: 2, description: \"SWMA against the four-tap arithmetic\" });\n\nlet almaDefault = new Alma(10);\nlet almaExplicit = new Alma(10, 0.85, 6.0);\nlet swma = new Swma();\n// The manual SWMA keeps the last four closes by hand: x0 is the newest.\nlet x0: f64 = NaN;\nlet x1: f64 = NaN;\nlet x2: f64 = NaN;\nlet x3: f64 = NaN;\n\nfunction onStart(): void {\n  almaDefault = new Alma(i32(p_length()));\n  almaExplicit = new Alma(i32(p_length()), 0.85, 6.0);\n  swma = new Swma();\n}\n\nfunction onBar(): void {\n  const close = bar.close();\n  const a = almaDefault.update(close);\n  const b = almaExplicit.update(close);\n  const s = swma.update(close);\n  x3 = x2;\n  x2 = x1;\n  x1 = x0;\n  x0 = close;\n  const manual = (x3 + 2.0 * x2 + 2.0 * x1 + x0) / 6.0;\n  const almaCheck = Math.abs(a - b) \u003C 0.000001 ? b : NaN;\n  const swmaCheck = Math.abs(s - manual) \u003C 0.000001 ? s : NaN;\n  out_alma_check(almaCheck);\n  out_swma_check(swmaCheck);\n}\n```\n\n## Points to remember\n\n- An average is an object you own: construct it in `onStart()`, keep it\n  in a module-level `let`, feed it in `onBar()`. There is no series to\n  pass in; the class sees one value per bar, which is the whole\n  [execution model](../core-concepts/execution-model.md).\n- A band's `upper` / `basis` / `lower` streams are three fields read\n  after `update()` and three outputs. Nothing indexes into a tuple.\n- `Vwma` reads volume through `bar.volume()` and a two-argument\n  `update(price, volume)`: a wrun indicator names every field it reads.\n- Warm-up is `NaN`, and `NaN` propagates through arithmetic. `isNaN(x)`\n  is the test; a two-line `nz` helper is on the\n  [Series functions](series-functions.md) page.\n- Every class here is checked bit-exact against the reference run\n  described on the [TA library](ta-library.md) page, edge rules included.\n",{"type":14,"children":15,"data":9979,"position":9981},"root",[16,26,29,30,437,438,584,585,599,601,814,815,898,899,915,916,930,931,1027,1028,1160,1161,1211,1212,1225,1226,1303,1304,1400,1401,1447,1448,1461,1462,1627,1628,1735,1736,1750,1751,1882,1883,1992,1993,2007,2008,2180,2181,2295,2296,2377,2378,2392,2393,2491,2492,2531,2532,2546,2547,2678,2679,2794,2795,2809,2810,2996,2997,3044,3045,3059,3060,3295,3296,3399,3400,3415,3416,3605,3606,3620,3621,3839,3840,4000,4001,4015,4016,4258,4259,4470,4471,4485,4486,4671,4672,4829,4830,4845,4846,4895,4896,7630,7631,7666,7667,7682,7683,7734,7735,8370,8371,8386,8387,8515,8516,9573,9574,9589,9590],{"type":17,"value":18,"position":19},"comment"," source: docs/indicators/functions/moving-averages.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},132,131,{"type":27,"value":28},"text","\n",{"type":27,"value":28},{"type":31,"tagName":32,"properties":33,"children":34,"position":434},"element","p",{},[35,44,58,65,78,85,97,104,117,123,136,142,155,161,174,180,193,199,212,218,230,236,249,254,267,273,285,293,306,313,326,332,345,353,365,372,384,390,403,410,427],{"type":27,"value":36,"position":37},"These classes smooth price into a trend line or wrap it in a band. 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