[{"data":1,"prerenderedAt":7913},["ShallowReactive",2],{"kscript:functions/moving-averages":3},{"slug":4,"filePath":5,"frontmatter":6,"rawMarkdown":9,"tree":10},"functions/moving-averages","functions/moving-averages.md",{"title":7,"description":8},"Moving Averages","Moving averages and price-band helpers — SMA, EMA, ALMA, SWMA, HMA, WMA, VWMA, RMA, LinReg, Bollinger, Keltner, Donchian.","---\ntitle: Moving Averages\ndescription: Moving averages and price-band helpers — SMA, EMA, ALMA, SWMA, HMA, WMA, VWMA, RMA, LinReg, Bollinger, Keltner, Donchian.\n---\n\nThese functions smooth price into a trend line or wrap it in a band. The single-line averages (`sma`, `ema`, `alma`, `swma`, `hma`, `wma`, `vwma`, `rma`, `linreg`) each return one stream. The band helpers (`bb`, `keltner`, `donchian`) return three levels at once; Bollinger and Keltner expose them as **named streams** `.upper` / `.basis` / `.lower`, ready to hand to `fillBetween`.\n\nEvery windowed average is `na` until its window fills. An SMA(20) plots nothing for its first bars, then begins once 20 bars have loaded; HMA warms up a little longer because of its internal weighted sub-windows. Donchian is the exception: it reads the rolling high/low and can be finite from the very first bar.\n\n## Single-line averages\n\n### sma\n\n`sma(source, period?)` — Simple Moving Average, the unweighted mean of the last `period` values.\n\n| Parameter | Type | Description |\n| --- | --- | --- |\n| `source` | TimeSeries | Price series |\n| `period` | number | Window length |\n\nReturns one stream. Warmup is `period` bars.\n\n```javascript\nvar smaValue = sma(source=close, period=20)\n```\n### ema\n\n`ema(source, period?)` — Exponential Moving Average. Weights recent bars more heavily, so it turns faster than `sma`.\n\n| Parameter | Type | Description |\n| --- | --- | --- |\n| `source` | TimeSeries | Price series |\n| `period` | number | Smoothing length |\n\n```javascript\nvar emaValue = ema(source=close, period=20)\n```\n### hma\n\n`hma(source, period?)` — Hull Moving Average. Very low lag and smooth; built from weighted sub-windows, so it warms up a few bars past `period`.\n\n| Parameter | Type | Description |\n| --- | --- | --- |\n| `source` | TimeSeries | Price series |\n| `period` | number | Window length |\n\n```javascript\nvar hmaValue = hma(source=close, period=21)\n```\n### wma\n\n`wma(source, period?)` — Weighted Moving Average. Linear weights favor recent bars, between `sma` and `ema` in responsiveness.\n\n| Parameter | Type | Description |\n| --- | --- | --- |\n| `source` | TimeSeries | Price series |\n| `period` | number | Window length |\n\n```javascript\nvar wmaValue = wma(source=close, period=20)\n```\n### alma\n\n`alma(source, length, offset?, sigma?)` — Arnaud Legoux Moving Average, a Gaussian-weighted smoother. Omitting `offset` and `sigma` is equivalent to `offset=0.85` and `sigma=6`.\n\n| Parameter | Type | Description |\n| --- | --- | --- |\n| `source` | TimeSeries | Price series |\n| `length` | number | Gaussian window length |\n| `offset` | number | Gaussian center offset, default `0.85` |\n| `sigma` | number | Gaussian width, default `6` |\n\n```javascript\nvar almaValue = alma(source=close, length=10, offset=0.85, sigma=6)\n```\n### swma\n\n`swma(source)` — Symmetrically Weighted Moving Average, the fixed four-tap smoother `(source + 2 * source[1] + 2 * source[2] + source[3]) / 6`.\n\n| Parameter | Type | Description |\n| --- | --- | --- |\n| `source` | TimeSeries | Price series |\n\n```javascript\nvar swmaValue = swma(source=close)\n```\n### vwma\n\n`vwma(source, period?)` — Volume-Weighted Moving Average. Bars with more volume pull the average harder, so it tracks where trading actually happened.\n\n| Parameter | Type | Description |\n| --- | --- | --- |\n| `source` | TimeSeries | OHLC series (needs volume) |\n| `period` | number | Window length |\n\n```javascript\nvar vwmaValue = vwma(source=trade, period=20)\n```\n### rma\n\n`rma(source, period?)` — Running (Wilder) Moving Average, the smoothing used inside RSI and ATR. Smoother and slower than `ema` for the same period.\n\n| Parameter | Type | Description |\n| --- | --- | --- |\n| `source` | TimeSeries | Price series |\n| `period` | number | Smoothing length |\n\n```javascript\nvar rmaValue = rma(source=close, period=20)\n```\n### linreg\n\n`linreg(source, period?, offset?)` — Linear Regression. Fits a least-squares line over the last `period` bars and returns its value; the trend's fitted price rather than an average.\n\n| Parameter | Type | Description |\n| --- | --- | --- |\n| `source` | TimeSeries | Price series |\n| `period` | number | Regression window |\n| `offset` | number | Shift the read point along the fitted line (default `0`) |\n\n```javascript\nvar linregValue = linreg(source=close, period=20, offset=0)\n```\n## Band helpers\n\n### bb\n\n`bb(source, period?, mult?)` — Bollinger Bands. A basis (SMA) with upper and lower bands set `mult` standard deviations away, so the band widens with volatility.\n\n| Parameter | Type | Description |\n| --- | --- | --- |\n| `source` | TimeSeries | Price series |\n| `period` | number | Basis and stdev window (default `20`) |\n| `mult` | number | Standard-deviation multiplier (default `2`) |\n\nReturns `[upper, basis, lower]`, named `.upper`, `.basis`, `.lower`.\n\n```javascript\nvar bands = bb(source=close, period=20, mult=2)\nplotLine(value=bands.upper, colors=[\"#64748b\"], width=1, label=[\"BB upper\"], desc=[\"upper band\"])\nplotLine(value=bands.lower, colors=[\"#64748b\"], width=1, label=[\"BB lower\"], desc=[\"lower band\"])\nfillBetween(bands.upper, bands.lower, \"#2563eb\", 0.12)\n```\n### keltner\n\n`keltner(source, period?, mult?, atrPeriod?)` — Keltner Channels. Like Bollinger, but the band width comes from ATR instead of standard deviation, so it reacts to range rather than dispersion.\n\n| Parameter | Type | Description |\n| --- | --- | --- |\n| `source` | TimeSeries | OHLC series |\n| `period` | number | Basis EMA window (default `20`) |\n| `mult` | number | ATR multiplier (default `1.5`) |\n| `atrPeriod` | number | ATR lookback (default `10`) |\n\nReturns `[upper, basis, lower]`, named `.upper`, `.basis`, `.lower`.\n\n```javascript\nvar kc = keltner(source=trade, period=20, mult=1.5, atrPeriod=10)\n```\n### donchian\n\n`donchian(source, period?)` — Donchian Channel. The highest high and lowest low over `period` bars, with their midpoint as the basis.\n\n| Parameter | Type | Description |\n| --- | --- | --- |\n| `source` | TimeSeries | OHLC series |\n| `period` | number | Lookback for the high/low (default `20`) |\n\nReturns three levels `[upper, basis, lower]`. Because it reads the rolling extreme rather than averaging, it can be finite from the first loaded bar.\n\n```javascript\nvar dc = donchian(source=trade, period=20)\n```\n## Putting them together\n\nEvery average and band on one panel. Band helpers are plotted whole here by passing the value directly; pass `.upper` / `.basis` / `.lower` instead when you want a single level.\n\n```javascript title=\"all_moving_averages.ks\"\n//@version=2\ndefine(title=\"Moving Averages\", position=\"offchart\", axis=true)\n\ntimeseries trade = ohlcv(symbol=currentSymbol, exchange=currentExchange)\ntimeseries closeSeries = trade.close\n\nvar smaValue = sma(source=closeSeries, period=20)\nvar emaValue = ema(source=closeSeries, period=20)\nvar hmaValue = hma(source=closeSeries, period=21)\nvar wmaValue = wma(source=closeSeries, period=20)\nvar vwmaValue = vwma(source=trade, period=20)\nvar rmaValue = rma(source=closeSeries, period=20)\nvar linregValue = linreg(source=closeSeries, period=20, offset=0)\nvar bands = bb(source=closeSeries, period=20, mult=2)\nvar keltnerBands = keltner(source=trade, period=20, mult=1.5, atrPeriod=10)\nvar donchianBands = donchian(source=trade, period=20)\n\nplotLine(value=smaValue, colors=[\"#2563eb\"], width=2, label=[\"SMA\"], desc=[\"20 period simple moving average\"])\nplotLine(value=emaValue, colors=[\"#dc2626\"], width=2, label=[\"EMA\"], desc=[\"20 period exponential moving average\"])\nplotLine(value=hmaValue, colors=[\"#7c3aed\"], width=2, label=[\"HMA\"], desc=[\"21 period hull moving average\"])\nplotLine(value=wmaValue, colors=[\"#ea580c\"], width=2, label=[\"WMA\"], desc=[\"20 period weighted moving average\"])\nplotLine(value=vwmaValue, colors=[\"#0891b2\"], width=2, label=[\"VWMA\"], desc=[\"20 period volume weighted moving average\"])\nplotLine(value=rmaValue, colors=[\"#059669\"], width=2, label=[\"RMA\"], desc=[\"20 period running moving average\"])\nplotLine(value=linregValue, colors=[\"#4b5563\"], width=2, label=[\"LinReg\"], desc=[\"20 period linear regression\"])\nplotLine(value=bands, colors=[\"#0f766e\", \"#64748b\", \"#be123c\"], width=1, label=[\"Bollinger bands\"], desc=[\"Bollinger bands multi output\"])\nplotLine(value=keltnerBands, colors=[\"#16a34a\", \"#94a3b8\", \"#dc2626\"], width=1, label=[\"Keltner bands\"], desc=[\"Keltner channel multi output\"])\nplotLine(value=donchianBands, colors=[\"#0ea5e9\", \"#94a3b8\", \"#f97316\"], width=1, label=[\"Donchian bands\"], desc=[\"Donchian channel multi output\"])\n```\n\n## Warmup and named streams\n\nThis isolates the two ideas worth seeing: an average is blank until its window fills, and Bollinger's `.upper` / `.basis` / `.lower` are independent streams you can plot one at a time. All four lines here begin together once the 20-bar window completes.\n\n```javascript title=\"warmup_named_streams.ks\"\n//@version=2\ndefine(title=\"Moving Average Warmup Boundary\", position=\"offchart\", axis=true)\n\ntimeseries trade = ohlcv(symbol=currentSymbol, exchange=currentExchange)\ntimeseries closeSeries = trade.close\n\nvar sma20 = sma(source=closeSeries, period=20)\nvar bands = bb(source=closeSeries, period=20, mult=2)\n\nplotLine(value=sma20, colors=[\"#2563eb\"], width=2, label=[\"SMA 20\"], desc=[\"SMA is na until the 20 bar window is complete\"])\nplotLine(value=bands.upper, colors=[\"#16a34a\"], width=2, label=[\"BB upper\"], desc=[\"bb.upper named stream\"])\nplotLine(value=bands.basis, colors=[\"#64748b\"], width=2, label=[\"BB basis\"], desc=[\"bb.basis named stream\"])\nplotLine(value=bands.lower, colors=[\"#dc2626\"], width=2, label=[\"BB lower\"], desc=[\"bb.lower named stream\"])\n```\n\n## ALMA and SWMA boundaries\n\nALMA's omitted `offset` and `sigma` default to `0.85` and `6`, matching the explicit call; SWMA uses the fixed four-tap symmetric weighting. The script below plots each line only where the builtin agrees with the manual form.\n\n```javascript title=\"alma_swma.ks\"\n//@version=2\ndefine(title=\"ALMA and SWMA\", position=\"offchart\", axis=true)\n\ntimeseries trade = ohlcv(symbol=currentSymbol, exchange=currentExchange)\ntimeseries closeSeries = trade.close\n\nvar almaDefault = alma(source=closeSeries, length=10)\nvar almaExplicit = alma(source=closeSeries, length=10, offset=0.85, sigma=6)\nvar swmaValue = swma(source=closeSeries)\nvar swmaManual = (closeSeries + 2 * closeSeries[1] + 2 * closeSeries[2] + closeSeries[3]) / 6\nvar almaCheck = math.abs(almaDefault - almaExplicit) \u003C 0.000001 ? almaExplicit : na\nvar swmaCheck = math.abs(swmaValue - swmaManual) \u003C 0.000001 ? swmaValue : na\n\nplotLine(value=almaCheck, colors=[\"#2563eb\"], width=2, label=[\"ALMA\"], desc=[\"ALMA default offset 0.85 and sigma 6\"])\nplotLine(value=swmaCheck, colors=[\"#16a34a\"], width=2, label=[\"SWMA\"], desc=[\"SWMA fixed four tap symmetric average\"])\n```\n",{"type":11,"children":12,"data":7906,"position":7908},"root",[13,365,367,402,403,422,423,439,440,488,490,688,689,721,722,791,792,805,806,848,849,1019,1020,1073,1074,1087,1088,1131,1132,1302,1303,1357,1358,1371,1372,1435,1436,1607,1608,1661,1662,1676,1677,1777,1779,2087,2088,2169,2170,2184,2185,2230,2232,2350,2351,2393,2394,2408,2409,2436,2437,2609,2610,2664,2665,2679,2680,2724,2725,2893,2894,2947,2948,2962,2963,3007,3009,3252,3253,3318,3319,3335,3336,3350,3351,3395,3396,3655,3656,3741,3742,4015,4016,4029,4030,4057,4058,4388,4389,4465,4466,4544,4545,4558,4559,4603,4604,4791,4792,4823,4824,4877,4878,4894,4895,4958,4959,6484,6485,6501,6502,6568,6569,7127,7128,7143,7144,7225,7226],{"type":14,"tagName":15,"properties":16,"children":17,"position":362},"element","p",{},[18,28,42,49,62,68,81,87,100,106,119,125,138,144,157,163,176,182,195,202,215,221,234,240,253,260,278,284,297,304,317,323,336,343,356],{"type":19,"value":20,"position":21},"text","These functions smooth price into a trend line or wrap it in a band. The single-line averages (",{"start":22,"end":25},{"line":23,"column":23,"offset":24},1,0,{"line":23,"column":26,"offset":27},96,95,{"type":14,"tagName":29,"properties":30,"children":31,"position":39},"code",{},[32],{"type":19,"value":33,"position":34},"sma",{"start":35,"end":36},{"line":23,"column":26,"offset":27},{"line":23,"column":37,"offset":38},101,100,{"start":40,"end":41},{"line":23,"column":26,"offset":27},{"line":23,"column":37,"offset":38},{"type":19,"value":43,"position":44},", ",{"start":45,"end":46},{"line":23,"column":37,"offset":38},{"line":23,"column":47,"offset":48},103,102,{"type":14,"tagName":29,"properties":50,"children":51,"position":59},{},[52],{"type":19,"value":53,"position":54},"ema",{"start":55,"end":56},{"line":23,"column":47,"offset":48},{"line":23,"column":57,"offset":58},108,107,{"start":60,"end":61},{"line":23,"column":47,"offset":48},{"line":23,"column":57,"offset":58},{"type":19,"value":43,"position":63},{"start":64,"end":65},{"line":23,"column":57,"offset":58},{"line":23,"column":66,"offset":67},110,109,{"type":14,"tagName":29,"properties":69,"children":70,"position":78},{},[71],{"type":19,"value":72,"position":73},"alma",{"start":74,"end":75},{"line":23,"column":66,"offset":67},{"line":23,"column":76,"offset":77},116,115,{"start":79,"end":80},{"line":23,"column":66,"offset":67},{"line":23,"column":76,"offset":77},{"type":19,"value":43,"position":82},{"start":83,"end":84},{"line":23,"column":76,"offset":77},{"line":23,"column":85,"offset":86},118,117,{"type":14,"tagName":29,"properties":88,"children":89,"position":97},{},[90],{"type":19,"value":91,"position":92},"swma",{"start":93,"end":94},{"line":23,"column":85,"offset":86},{"line":23,"column":95,"offset":96},124,123,{"start":98,"end":99},{"line":23,"column":85,"offset":86},{"line":23,"column":95,"offset":96},{"type":19,"value":43,"position":101},{"start":102,"end":103},{"line":23,"column":95,"offset":96},{"line":23,"column":104,"offset":105},126,125,{"type":14,"tagName":29,"properties":107,"children":108,"position":116},{},[109],{"type":19,"value":110,"position":111},"hma",{"start":112,"end":113},{"line":23,"column":104,"offset":105},{"line":23,"column":114,"offset":115},131,130,{"start":117,"end":118},{"line":23,"column":104,"offset":105},{"line":23,"column":114,"offset":115},{"type":19,"value":43,"position":120},{"start":121,"end":122},{"line":23,"column":114,"offset":115},{"line":23,"column":123,"offset":124},133,132,{"type":14,"tagName":29,"properties":126,"children":127,"position":135},{},[128],{"type":19,"value":129,"position":130},"wma",{"start":131,"end":132},{"line":23,"column":123,"offset":124},{"line":23,"column":133,"offset":134},138,137,{"start":136,"end":137},{"line":23,"column":123,"offset":124},{"line":23,"column":133,"offset":134},{"type":19,"value":43,"position":139},{"start":140,"end":141},{"line":23,"column":133,"offset":134},{"line":23,"column":142,"offset":143},140,139,{"type":14,"tagName":29,"properties":145,"children":146,"position":154},{},[147],{"type":19,"value":148,"position":149},"vwma",{"start":150,"end":151},{"line":23,"column":142,"offset":143},{"line":23,"column":152,"offset":153},146,145,{"start":155,"end":156},{"line":23,"column":142,"offset":143},{"line":23,"column":152,"offset":153},{"type":19,"value":43,"position":158},{"start":159,"end":160},{"line":23,"column":152,"offset":153},{"line":23,"column":161,"offset":162},148,147,{"type":14,"tagName":29,"properties":164,"children":165,"position":173},{},[166],{"type":19,"value":167,"position":168},"rma",{"start":169,"end":170},{"line":23,"column":161,"offset":162},{"line":23,"column":171,"offset":172},153,152,{"start":174,"end":175},{"line":23,"column":161,"offset":162},{"line":23,"column":171,"offset":172},{"type":19,"value":43,"position":177},{"start":178,"end":179},{"line":23,"column":171,"offset":172},{"line":23,"column":180,"offset":181},155,154,{"type":14,"tagName":29,"properties":183,"children":184,"position":192},{},[185],{"type":19,"value":186,"position":187},"linreg",{"start":188,"end":189},{"line":23,"column":180,"offset":181},{"line":23,"column":190,"offset":191},163,162,{"start":193,"end":194},{"line":23,"column":180,"offset":181},{"line":23,"column":190,"offset":191},{"type":19,"value":196,"position":197},") each return one stream. The band helpers (",{"start":198,"end":199},{"line":23,"column":190,"offset":191},{"line":23,"column":200,"offset":201},207,206,{"type":14,"tagName":29,"properties":203,"children":204,"position":212},{},[205],{"type":19,"value":206,"position":207},"bb",{"start":208,"end":209},{"line":23,"column":200,"offset":201},{"line":23,"column":210,"offset":211},211,210,{"start":213,"end":214},{"line":23,"column":200,"offset":201},{"line":23,"column":210,"offset":211},{"type":19,"value":43,"position":216},{"start":217,"end":218},{"line":23,"column":210,"offset":211},{"line":23,"column":219,"offset":220},213,212,{"type":14,"tagName":29,"properties":222,"children":223,"position":231},{},[224],{"type":19,"value":225,"position":226},"keltner",{"start":227,"end":228},{"line":23,"column":219,"offset":220},{"line":23,"column":229,"offset":230},222,221,{"start":232,"end":233},{"line":23,"column":219,"offset":220},{"line":23,"column":229,"offset":230},{"type":19,"value":43,"position":235},{"start":236,"end":237},{"line":23,"column":229,"offset":230},{"line":23,"column":238,"offset":239},224,223,{"type":14,"tagName":29,"properties":241,"children":242,"position":250},{},[243],{"type":19,"value":244,"position":245},"donchian",{"start":246,"end":247},{"line":23,"column":238,"offset":239},{"line":23,"column":248,"offset":249},234,233,{"start":251,"end":252},{"line":23,"column":238,"offset":239},{"line":23,"column":248,"offset":249},{"type":19,"value":254,"position":255},") return three levels at once; Bollinger and Keltner expose them as ",{"start":256,"end":257},{"line":23,"column":248,"offset":249},{"line":23,"column":258,"offset":259},302,301,{"type":14,"tagName":261,"properties":262,"children":263,"position":273},"strong",{},[264],{"type":19,"value":265,"position":266},"named streams",{"start":267,"end":270},{"line":23,"column":268,"offset":269},304,303,{"line":23,"column":271,"offset":272},317,316,{"start":274,"end":275},{"line":23,"column":258,"offset":259},{"line":23,"column":276,"offset":277},319,318,{"type":19,"value":279,"position":280}," ",{"start":281,"end":282},{"line":23,"column":276,"offset":277},{"line":23,"column":283,"offset":276},320,{"type":14,"tagName":29,"properties":285,"children":286,"position":294},{},[287],{"type":19,"value":288,"position":289},".upper",{"start":290,"end":291},{"line":23,"column":283,"offset":276},{"line":23,"column":292,"offset":293},328,327,{"start":295,"end":296},{"line":23,"column":283,"offset":276},{"line":23,"column":292,"offset":293},{"type":19,"value":298,"position":299}," / ",{"start":300,"end":301},{"line":23,"column":292,"offset":293},{"line":23,"column":302,"offset":303},331,330,{"type":14,"tagName":29,"properties":305,"children":306,"position":314},{},[307],{"type":19,"value":308,"position":309},".basis",{"start":310,"end":311},{"line":23,"column":302,"offset":303},{"line":23,"column":312,"offset":313},339,338,{"start":315,"end":316},{"line":23,"column":302,"offset":303},{"line":23,"column":312,"offset":313},{"type":19,"value":298,"position":318},{"start":319,"end":320},{"line":23,"column":312,"offset":313},{"line":23,"column":321,"offset":322},342,341,{"type":14,"tagName":29,"properties":324,"children":325,"position":333},{},[326],{"type":19,"value":327,"position":328},".lower",{"start":329,"end":330},{"line":23,"column":321,"offset":322},{"line":23,"column":331,"offset":332},350,349,{"start":334,"end":335},{"line":23,"column":321,"offset":322},{"line":23,"column":331,"offset":332},{"type":19,"value":337,"position":338},", ready to hand to ",{"start":339,"end":340},{"line":23,"column":331,"offset":332},{"line":23,"column":341,"offset":342},369,368,{"type":14,"tagName":29,"properties":344,"children":345,"position":353},{},[346],{"type":19,"value":347,"position":348},"fillBetween",{"start":349,"end":350},{"line":23,"column":341,"offset":342},{"line":23,"column":351,"offset":352},382,381,{"start":354,"end":355},{"line":23,"column":341,"offset":342},{"line":23,"column":351,"offset":352},{"type":19,"value":357,"position":358},".",{"start":359,"end":360},{"line":23,"column":351,"offset":352},{"line":23,"column":361,"offset":351},383,{"start":363,"end":364},{"line":23,"column":23,"offset":24},{"line":23,"column":361,"offset":351},{"type":19,"value":366},"\n",{"type":14,"tagName":15,"properties":368,"children":369,"position":399},{},[370,379,392],{"type":19,"value":371,"position":372},"Every windowed average is ",{"start":373,"end":376},{"line":374,"column":23,"offset":375},3,384,{"line":374,"column":377,"offset":378},27,410,{"type":14,"tagName":29,"properties":380,"children":381,"position":389},{},[382],{"type":19,"value":383,"position":384},"na",{"start":385,"end":386},{"line":374,"column":377,"offset":378},{"line":374,"column":387,"offset":388},31,414,{"start":390,"end":391},{"line":374,"column":377,"offset":378},{"line":374,"column":387,"offset":388},{"type":19,"value":393,"position":394}," until its window fills. An SMA(20) plots nothing for its first bars, then begins once 20 bars have loaded; HMA warms up a little longer because of its internal weighted sub-windows. 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