[{"data":1,"prerenderedAt":8265},["ShallowReactive",2],{"kscript:functions/series-functions":3},{"slug":4,"filePath":5,"frontmatter":6,"rawMarkdown":9,"tree":10},"functions/series-functions","functions/series-functions.md",{"title":7,"description":8},"Series Functions","Crossovers, rolling extremes, change, percentile, correlation, and na handling for time series.","---\ntitle: Series Functions\ndescription: Crossovers, rolling extremes, change, percentile, correlation, and na handling for time series.\n---\n\nSeries functions operate over a stream of bars rather than a single value. They answer the questions that come up constantly when writing indicators: did two lines just cross, is a series rising, what's the highest high in the last 10 bars, how many bars since a condition was true, and is this value real or missing.\n\n## Price-source helpers\n\nSince 3.0.13 (in-flight), `hl2`, `hlc3`, `ohlc4`, and `hlcc4` expose the common OHLC averages as builtins. Each accepts an optional OHLC source; when you omit `source`, the helper reads the chart's current OHLC source. The verified formulas are `hl2 = (high + low) / 2`, `hlc3 = (high + low + close) / 3`, `ohlc4 = (open + high + low + close) / 4`, and `hlcc4 = (high + low + close + close) / 4`.\n\n| Function | Signature | Formula |\n| --- | --- | --- |\n| `hl2` | `hl2(source?)` | `(high + low) / 2` |\n| `hlc3` | `hlc3(source?)` | `(high + low + close) / 3` |\n| `ohlc4` | `ohlc4(source?)` | `(open + high + low + close) / 4` |\n| `hlcc4` | `hlcc4(source?)` | `(high + low + close + close) / 4` |\n\nThe probe below checked explicit-source and implicit-source calls against the manual formulas. The ladder reported `ok: true`; both plotted checks had 300 finite values from bar 0 to 299, moving from `441.6605495613245` to `459.47412156950656`.\n\n```javascript title=\"scripts/probes/series-fns/price_source_helpers.ks\"\n//@version=2\ndefine(title=\"Price Source Helpers\", position=\"offchart\", axis=true)\n\ntimeseries trade = ohlcv(symbol=currentSymbol, exchange=currentExchange)\n\nvar explicitSum = hl2(source=trade) + hlc3(source=trade) + ohlc4(source=trade) + hlcc4(source=trade)\nvar manualSum = ((trade.high + trade.low) / 2) + ((trade.high + trade.low + trade.close) / 3) + ((trade.open + trade.high + trade.low + trade.close) / 4) + ((trade.high + trade.low + trade.close + trade.close) / 4)\nvar implicitSum = hl2() + hlc3() + ohlc4() + hlcc4()\nvar explicitCheck = math.abs(explicitSum - manualSum) \u003C 0.000001 ? explicitSum : na\nvar implicitCheck = math.abs(implicitSum - manualSum) \u003C 0.000001 ? implicitSum : na\n\nplotLine(value=explicitCheck, colors=[\"#2563eb\"], width=2, label=[\"Explicit\"], desc=[\"price helpers with explicit source match manual OHLC formulas\"])\nplotLine(value=implicitCheck, colors=[\"#16a34a\"], width=2, label=[\"Implicit\"], desc=[\"price helpers without source use chart OHLC\"])\n```\n\n## Crossovers and signals\n\nThe crossover family turns two lines into a discrete signal. They're the backbone of almost every entry rule.\n\n- `crossover(a, b)` is true on the single bar where `a` rises above `b`.\n- `crossunder(a, b)` is true on the bar where `a` falls below `b`.\n- `cross(a, b)` is true on either: the bar they touch or swap order.\n\nThis is the classic signal-line pattern. A bullish MACD cross is just `crossover` of the MACD line over its signal:\n\n```javascript\n//@version=2\ndefine(title=\"MACD cross\", position=\"offchart\", axis=true)\n\ntimeseries trade = ohlcv(symbol=currentSymbol, exchange=currentExchange)\nvar m = macd(source=trade.close, fastPeriod=12, slowPeriod=26, signalPeriod=9)\n\n// 1 on the bar MACD crosses up through its signal, otherwise 0.\nvar bullish = crossover(seriesA=m.macd, seriesB=m.signal) ? 1 : 0\n\nplotLine(value=bullish, colors=[\"#16a34a\"], width=2, label=[\"Bull cross\"], desc=[\"MACD crossing above its signal line\"])\n```\n\nCrossovers return a boolean, so a plot value of `cond ? 1 : 0` gives you a clean 0/1 step you can see on the chart. To place a marker on price instead, feed the price to `plotShape` on signal bars and `na` otherwise: `plotShape(value=bullish ? trade.low : na, ...)`.\n\n{% hint style=\"info\" %}\nThe crossover family expects `timeseries` inputs (it needs the previous bar to detect the turn). Declare the two lines as `timeseries`, or pass indicator outputs that already carry history.\n\n\n{% endhint %}\n## Trend, extremes, and counting\n\n| Function | Signature | Returns |\n| --- | --- | --- |\n| `rising` | `rising(source, period)` | true if `source` rose over the last `period` bars |\n| `falling` | `falling(source, period)` | true if `source` fell over the last `period` bars |\n| `change` | `change(source, n)` | `source` now minus `source` `n` bars ago |\n| `highest` | `highest(source, period, priceIndex?)` | highest value in the window |\n| `lowest` | `lowest(source, period, priceIndex?)` | lowest value in the window |\n| `highestbars` | `highestbars(source, period, priceIndex?)` | bar offset back to the window's high |\n| `lowestbars` | `lowestbars(source, period, priceIndex?)` | bar offset back to the window's low |\n| `pivothigh` | `pivothigh(source, leftbars, rightbars, priceIndex)` | pivot high value, emitted at confirmation |\n| `pivotlow` | `pivotlow(source, leftbars, rightbars, priceIndex)` | pivot low value, emitted at confirmation |\n| `barssince` | `barssince(condition)` | bars elapsed since `condition` was last true |\n| `percentile` | `percentile(source, period, pct)` | the `pct`-th percentile over the window |\n| `correlation` | `correlation(s1, s2, period)` | rolling correlation of two series (`-1` to `1`) |\n\n`highest`/`lowest` take an OHLCV source plus a `priceIndex` to pick the field (`2` = high, `3` = low). `highestbars`/`lowestbars` return how many bars back the extreme sits, handy for \"is the high in the window recent?\" logic. `barssince` counts up from the last time a condition fired, which is perfect for cooldowns and recency checks.\n\n```javascript\n//@version=2\ndefine(title=\"Donchian breakout\", position=\"onchart\", axis=true)\n\ntimeseries trade = ohlcv(symbol=currentSymbol, exchange=currentExchange)\n\n// 20-bar high && low channel.\nvar hi = highest(source=trade, period=20, priceIndex=2)\nvar lo = lowest(source=trade, period=20, priceIndex=3)\n\nplotLine(value=hi, colors=[\"#16a34a\"], width=1, label=[\"20-bar high\"], desc=[\"Upper Donchian band\"])\nplotLine(value=lo, colors=[\"#dc2626\"], width=1, label=[\"20-bar low\"], desc=[\"Lower Donchian band\"])\n```\n## Pivot confirmation\n\nSince 3.0.13 (in-flight), `pivothigh` and `pivotlow` are causal confirmation signals. A pivot only emits after `rightbars` later bars have closed, so the emitted value appears on the confirmation bar and lags the true pivot bar by `rightbars`. The function does not read future bars and does not repaint a prior bar; if you want a continuous line, forward-fill the sparse confirmation series yourself.\n\nThe probe below uses `leftbars=2` and `rightbars=2`, then checks each emitted value against `trade.high[2]` or `trade.low[2]` on the confirmation bar. The ladder reported `ok: true`; pivot highs produced 6 sparse finite confirmations from bar 43 to 263, pivot lows produced 7 from bar 14 to 278, and the forward-filled stability lines remained finite from their first confirmed pivot through bar 299.\n\n```javascript title=\"scripts/probes/series-fns/pivot_confirmation_stability.ks\"\n//@version=2\ndefine(title=\"Pivot Confirmation Stability\", position=\"offchart\", axis=true)\n\ntimeseries trade = ohlcv(symbol=currentSymbol, exchange=currentExchange)\ntimeseries pivotHigh = pivothigh(source=trade, leftbars=2, rightbars=2, priceIndex=2)\ntimeseries pivotLow = pivotlow(source=trade, leftbars=2, rightbars=2, priceIndex=3)\n\nvar highAtConfirmation = isna(pivotHigh) ? na : math.abs(pivotHigh - trade.high[2]) \u003C 0.000001 ? pivotHigh : na\nvar lowAtConfirmation = isna(pivotLow) ? na : math.abs(pivotLow - trade.low[2]) \u003C 0.000001 ? pivotLow : na\nvar stableHigh = fixnan(source=pivotHigh)\nvar stableLow = fixnan(source=pivotLow)\n\nplotLine(value=highAtConfirmation, colors=[\"#2563eb\"], width=2, label=[\"Pivot high\"], desc=[\"pivothigh emits the pivot value on the confirmation bar\"])\nplotLine(value=lowAtConfirmation, colors=[\"#dc2626\"], width=2, label=[\"Pivot low\"], desc=[\"pivotlow emits the pivot value on the confirmation bar\"])\nplotLine(value=stableHigh, colors=[\"#16a34a\"], width=2, label=[\"Stable high\"], desc=[\"confirmed pivot high remains readable through history\"])\nplotLine(value=stableLow, colors=[\"#ea580c\"], width=2, label=[\"Stable low\"], desc=[\"confirmed pivot low remains readable through history\"])\n```\n## Handling missing values (`na`)\n\nIndicators return `na` during their warmup window, and any arithmetic involving `na` stays `na`. These helpers let you test for it and recover:\n\n- `isna(x)` / `isnan(x)`: true when `x` is missing. (`NaN` is an alias of `na`, so both report it.)\n- `isnum(x)`: true when `x` is a real, finite number.\n- `nz(x, replacement)`: `x` if it's a number, otherwise `replacement`. The standard way to fill gaps before plotting.\n- `fixnan(source)`: carries the last real value forward across `na` bars, leaving no holes once data starts.\n\nSee [na & Scalar Types](../core-concepts/na-and-scalar-types.md) for how `na` propagates through expressions.\n\n## Every series function in one script\n\nA `sparse` series (forced `na` for the first 10 bars) drives the `na` helpers so you can watch them flip; the rest run over real OHLCV.\n\n```javascript title=\"scripts/probes/series-fns/all_series_functions.ks\"\n//@version=2\ndefine(title=\"Verified Series Functions\", position=\"offchart\", axis=true)\n\ntimeseries trade = ohlcv(symbol=currentSymbol, exchange=currentExchange)\ntimeseries closeSeries = trade.close\ntimeseries fast = sma(source=closeSeries, period=5)\ntimeseries slow = sma(source=closeSeries, period=13)\ntimeseries aboveFast = closeSeries > fast\ntimeseries sparse = barIndex \u003C 10 ? na : closeSeries\n\nplotLine(value=crossover(seriesA=fast, seriesB=slow) ? 1 : 0, colors=[\"#2563eb\"], label=[\"crossover\"], desc=[\"crossover boolean as 1 or 0\"])\nplotLine(value=crossunder(seriesA=fast, seriesB=slow) ? 1 : 0, colors=[\"#dc2626\"], label=[\"crossunder\"], desc=[\"crossunder boolean as 1 or 0\"])\nplotLine(value=cross(seriesA=fast, seriesB=slow) ? 1 : 0, colors=[\"#7c3aed\"], label=[\"cross\"], desc=[\"cross boolean as 1 or 0\"])\nplotLine(value=rising(source=closeSeries, period=3), colors=[\"#16a34a\"], label=[\"rising\"], desc=[\"rising over 3 bars\"])\nplotLine(value=falling(source=closeSeries, period=3), colors=[\"#ea580c\"], label=[\"falling\"], desc=[\"falling over 3 bars\"])\nplotLine(value=barssince(condition=aboveFast), colors=[\"#0891b2\"], label=[\"barssince\"], desc=[\"bars since close was above fast average\"])\nplotLine(value=change(source=closeSeries, n=3), colors=[\"#4b5563\"], label=[\"change\"], desc=[\"3 bar change\"])\nplotLine(value=highest(source=trade, period=10, priceIndex=2), colors=[\"#0f766e\"], label=[\"highest\"], desc=[\"10 bar highest high\"])\nplotLine(value=lowest(source=trade, period=10, priceIndex=3), colors=[\"#be123c\"], label=[\"lowest\"], desc=[\"10 bar lowest low\"])\nplotLine(value=highestbars(source=trade, period=10, priceIndex=2), colors=[\"#9333ea\"], label=[\"highestbars\"], desc=[\"offset to 10 bar highest high\"])\nplotLine(value=lowestbars(source=trade, period=10, priceIndex=3), colors=[\"#1d4ed8\"], label=[\"lowestbars\"], desc=[\"offset to 10 bar lowest low\"])\nplotLine(value=percentile(source=closeSeries, period=20, pct=80), colors=[\"#b45309\"], label=[\"percentile\"], desc=[\"80th percentile over 20 bars\"])\nplotLine(value=correlation(s1=trade.open, s2=trade.close, period=20), colors=[\"#15803d\"], label=[\"correlation\"], desc=[\"20 bar correlation between open and close\"])\nplotLine(value=nz(x=sparse, replacement=trade.open), colors=[\"#6d28d9\"], label=[\"nz\"], desc=[\"nz replacement for leading na values\"])\nplotLine(value=isna(sparse) ? 1 : 0, colors=[\"#0e7490\"], label=[\"isna\"], desc=[\"isna result for sparse series\"])\nplotLine(value=isnan(sparse) ? 1 : 0, colors=[\"#991b1b\"], label=[\"isnan\"], desc=[\"isnan result for sparse series\"])\nplotLine(value=isnum(sparse) ? 1 : 0, colors=[\"#374151\"], label=[\"isnum\"], desc=[\"isnum result for sparse series\"])\nplotLine(value=fixnan(source=sparse), colors=[\"#3b82f6\"], label=[\"fixnan\"], desc=[\"fixnan result for sparse series\"])\n```\n\n\n## Warmup and the na window\n\nWindowed functions can't produce a value until they've seen enough bars: a 20-bar `percentile` or `correlation` returns `na` until 20 bars exist, just as a 20-bar SMA does. When the underlying series is itself `na` for a stretch, that warmup shifts forward by the same amount.\n\nThe script below makes the warmup visible. It feeds a `sparse` series that's `na` for the first 10 bars into a 5-bar `percentile` and `correlation`, plotting `1` while each is still warming up. `fixnan` shows the recovery: it produces its first real value the moment the source has one (bar 10 here), then holds steady.\n\n```javascript title=\"scripts/probes/series-fns/na_window_boundary.ks\"\n//@version=2\ndefine(title=\"Series NA Window Boundary\", position=\"offchart\", axis=true)\n\ntimeseries trade = ohlcv(symbol=currentSymbol, exchange=currentExchange)\ntimeseries closeSeries = trade.close\ntimeseries sparse = barIndex \u003C 10 ? na : closeSeries\nvar percentileWarmup = isna(percentile(source=sparse, period=5, pct=50)) ? 1 : 0\nvar correlationWarmup = isna(correlation(s1=sparse, s2=trade.open, period=5)) ? 1 : 0\nvar fixed = fixnan(source=sparse)\n\nplotLine(value=percentileWarmup, colors=[\"#2563eb\"], label=[\"Percentile warmup\"], desc=[\"1 while percentile lacks a finite 5 bar window\"])\nplotLine(value=correlationWarmup, colors=[\"#dc2626\"], label=[\"Correlation warmup\"], desc=[\"1 while correlation lacks a finite 5 bar window\"])\nplotLine(value=fixed, colors=[\"#16a34a\"], label=[\"Fixnan\"], desc=[\"fixnan after leading na values\"])\n```\n",{"type":11,"children":12,"data":8259,"position":8261},"root",[13,31,33,52,53,245,247,608,609,682,683,1473,1474,1489,1490,1504,1505,1676,1677,1710,1711,2056,2057,2148,2149,2206,2207,2222,2224,3246,3247,3397,3398,3806,3807,3823,3824,3908,3909,4013,4014,4852,4853,4885,4886,4953,4954,5212,5213,5266,5267,5283,5284,5351,5352,7457,7458,7474,7475,7560,7561,7682,7683],{"type":14,"tagName":15,"properties":16,"children":17,"position":28},"element","p",{},[18],{"type":19,"value":20,"position":21},"text","Series functions operate over a stream of bars rather than a single value. They answer the questions that come up constantly when writing indicators: did two lines just cross, is a series rising, what's the highest high in the last 10 bars, how many bars since a condition was true, and is this value real or missing.",{"start":22,"end":25},{"line":23,"column":23,"offset":24},1,0,{"line":23,"column":26,"offset":27},318,317,{"start":29,"end":30},{"line":23,"column":23,"offset":24},{"line":23,"column":26,"offset":27},{"type":19,"value":32},"\n",{"type":14,"tagName":34,"properties":35,"children":37,"position":48},"h2",{"id":36},"price-source-helpers",[38],{"type":19,"value":39,"position":40},"Price-source helpers",{"start":41,"end":45},{"line":42,"column":43,"offset":44},3,4,322,{"line":42,"column":46,"offset":47},24,342,{"start":49,"end":51},{"line":42,"column":23,"offset":50},319,{"line":42,"column":46,"offset":47},{"type":19,"value":32},{"type":14,"tagName":15,"properties":54,"children":55,"position":242},{},[56,65,79,86,99,105,118,125,138,145,158,165,178,184,197,203,216,222,235],{"type":19,"value":57,"position":58},"Since 3.0.13 (in-flight), ",{"start":59,"end":62},{"line":60,"column":23,"offset":61},5,344,{"line":60,"column":63,"offset":64},27,370,{"type":14,"tagName":66,"properties":67,"children":68,"position":76},"code",{},[69],{"type":19,"value":70,"position":71},"hl2",{"start":72,"end":73},{"line":60,"column":63,"offset":64},{"line":60,"column":74,"offset":75},32,375,{"start":77,"end":78},{"line":60,"column":63,"offset":64},{"line":60,"column":74,"offset":75},{"type":19,"value":80,"position":81},", ",{"start":82,"end":83},{"line":60,"column":74,"offset":75},{"line":60,"column":84,"offset":85},34,377,{"type":14,"tagName":66,"properties":87,"children":88,"position":96},{},[89],{"type":19,"value":90,"position":91},"hlc3",{"start":92,"end":93},{"line":60,"column":84,"offset":85},{"line":60,"column":94,"offset":95},40,383,{"start":97,"end":98},{"line":60,"column":84,"offset":85},{"line":60,"column":94,"offset":95},{"type":19,"value":80,"position":100},{"start":101,"end":102},{"line":60,"column":94,"offset":95},{"line":60,"column":103,"offset":104},42,385,{"type":14,"tagName":66,"properties":106,"children":107,"position":115},{},[108],{"type":19,"value":109,"position":110},"ohlc4",{"start":111,"end":112},{"line":60,"column":103,"offset":104},{"line":60,"column":113,"offset":114},49,392,{"start":116,"end":117},{"line":60,"column":103,"offset":104},{"line":60,"column":113,"offset":114},{"type":19,"value":119,"position":120},", and ",{"start":121,"end":122},{"line":60,"column":113,"offset":114},{"line":60,"column":123,"offset":124},55,398,{"type":14,"tagName":66,"properties":126,"children":127,"position":135},{},[128],{"type":19,"value":129,"position":130},"hlcc4",{"start":131,"end":132},{"line":60,"column":123,"offset":124},{"line":60,"column":133,"offset":134},62,405,{"start":136,"end":137},{"line":60,"column":123,"offset":124},{"line":60,"column":133,"offset":134},{"type":19,"value":139,"position":140}," expose the common OHLC averages as builtins. Each accepts an optional OHLC source; when you omit ",{"start":141,"end":142},{"line":60,"column":133,"offset":134},{"line":60,"column":143,"offset":144},160,503,{"type":14,"tagName":66,"properties":146,"children":147,"position":155},{},[148],{"type":19,"value":149,"position":150},"source",{"start":151,"end":152},{"line":60,"column":143,"offset":144},{"line":60,"column":153,"offset":154},168,511,{"start":156,"end":157},{"line":60,"column":143,"offset":144},{"line":60,"column":153,"offset":154},{"type":19,"value":159,"position":160},", the helper reads the chart's current OHLC source. The verified formulas are ",{"start":161,"end":162},{"line":60,"column":153,"offset":154},{"line":60,"column":163,"offset":164},246,589,{"type":14,"tagName":66,"properties":166,"children":167,"position":175},{},[168],{"type":19,"value":169,"position":170},"hl2 = (high + low) / 2",{"start":171,"end":172},{"line":60,"column":163,"offset":164},{"line":60,"column":173,"offset":174},270,613,{"start":176,"end":177},{"line":60,"column":163,"offset":164},{"line":60,"column":173,"offset":174},{"type":19,"value":80,"position":179},{"start":180,"end":181},{"line":60,"column":173,"offset":174},{"line":60,"column":182,"offset":183},272,615,{"type":14,"tagName":66,"properties":185,"children":186,"position":194},{},[187],{"type":19,"value":188,"position":189},"hlc3 = (high + low + close) / 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