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TimeSeriesEvents [tser,crit]

finds the events for which the criterion crit is satisfied for the values in the time series tser.

TimeSeriesEvents [tser,crit,fun]

finds the events that satisfy the criterion crit for function fun applied to the time series values.

TimeSeriesEvents [tser,crit,fun,cond]

only keeps the events where the condition cond is true.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Crossings  
Extrema  
Applications  
See Also
Related Guides
History
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TimeSeriesEvents [tser,crit]

finds the events for which the criterion crit is satisfied for the values in the time series tser.

TimeSeriesEvents [tser,crit,fun]

finds the events that satisfy the criterion crit for function fun applied to the time series values.

TimeSeriesEvents [tser,crit,fun,cond]

only keeps the events where the condition cond is true.

Details

  • TimeSeriesEvents is also known as peak finding, zero finding, etc.
  • TimeSeriesEvents operates on TimeSeries as if it is a function of time.
  • TimeSeriesEvents views the time series tser as a function of time and finds events such as value crossings and local maxima and minima. These typically correspond to named events in different domains, such as conjunctions in astronomy or reversals in finance.
  • TimeSeriesEvents returns an EventSeries object with the times ti and annotated with event information.
  • Possible crossing criteria crit include:
  • "Crossing" zero crossing value
    "CrossingFromBelow" crossing zero from negative to positive
    "CrossingFromAbove" crossing zero from positive to negative
    {crossing,value} specify the crossing value
  • Possible extrema criteria crit include:
  • "LocalExtremum" local minimum or maximum
    "LocalMaximum" local maximum
    "LocalMinimum" local minimum
  • Possible conditions cond include Boolean expressions such as Function [2<#comp<5] or Function [#Timestamp>Today ].
  • A component "com" in a time series can be used for either fun or condusing the syntax f[…,#com, …]&. #Timestamp may be used to include the timestamps.
  • For a simple time series with no named components, values for either fun or cond can be accessed using either f[…,#,…]& or f[…,#Value,…]&.

Examples

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Basic Examples  (2)

Find the zero crossings for a time series:

Wolfram Language code: ts = TimeSeries[Cos[Range[0, 10, .5]]]
Wolfram Language code: es = TimeSeriesEvents[ts, "Crossing"]
Wolfram Language code: es["Timestamps"]//Normal
Wolfram Language code: ListLinePlot[ts, GridLines -> {%, None}]

Find all local extrema for a time series:

Wolfram Language code: ts = TimeSeries[Table[{x, x ^ 4 - 16x ^ 2}, {x, RandomReal[{-5, 5}, 20]}]]
Wolfram Language code: es = TimeSeriesEvents[ts, "LocalExtremum"]
Wolfram Language code: ListPlot[{ts, es}, Joined -> {True, False}, PlotStyle -> PointSize[.025]]

Scope  (9)

Crossings  (7)

Find all crossings from negative to positive:

Wolfram Language code: tseries = TimeSeries[TimeEventSeries`TimestampData[Association["UniformlySpacedQ" -> True, "Count" -> 21, "Endpoints" -> TabularColumn[Association["Data" -> {{0, 20}, {}, None}, "ElementType" -> "Integer64"]], "MinimumTimeIncrement" -> 1, "Caller" -> TimeSeries]], TabularColumn[Association["Data" -> {{-2, -2, 2, 0, -2, -1, -2, -2, 0, -2, 2, 0, 0, -2, 2, -1, 1, -2, 0, 1, -2}, {}, None}, "ElementType" -> "Integer64"]], Association[]];
Wolfram Language code: events = TimeSeriesEvents[tseries, {"CrossingFromBelow"}]
Wolfram Language code: ListPlot[{tseries, events}, Joined -> {True, False}, PlotStyle -> PointSize[0.035]]

Find all crossings of a given value:

Wolfram Language code: tseries = TimeSeries[TimeEventSeries`TimestampData[Association["UniformlySpacedQ" -> True, "Count" -> 21, "Endpoints" -> TabularColumn[Association["Data" -> {{0, 20}, {}, None}, "ElementType" -> "Integer64"]], "MinimumTimeIncrement" -> 1, "Caller" -> TimeSeries]], TabularColumn[Association["Data" -> {{-2, -2, 2, 0, -2, -1, -2, -2, 0, -2, 2, 0, 0, -2, 2, -1, 1, -2, 0, 1, -2}, {}, None}, "ElementType" -> "Integer64"]], Association[]];
Wolfram Language code: events = TimeSeriesEvents[tseries, {"Crossing", 1 / 3}]
Wolfram Language code: ListPlot[{tseries, events}, Joined -> {True, False}, PlotStyle -> PointSize[0.035], GridLines -> {{}, {1 / 3}}]

Find the dates where a time series crosses zero:

Wolfram Language code: tseries = TimeSeries[Sin[Subdivide[4. π, 99]], Today]
Wolfram Language code: events = TimeSeriesEvents[tseries, "Crossing"]
Wolfram Language code: ListLinePlot[tseries, GridLines -> {Normal@events["Timestamps"], None}]

Note that the values that the crossings give are not exactly at zero because the dates are given in "Day" granularity, just like the timestamps in the time series:

Wolfram Language code: Tabular[events]

More accurate crossing timestamps can be found by changing to "Instant" granularity:

Wolfram Language code: Tabular[TimeSeriesEvents[TimeSeries[tseries, DateGranularity -> "Instant"], "Crossing"]]

Find all the crossings of a given value:

Wolfram Language code: ts = TimeSeries[Sin[Subdivide[4. π, 99]], {Today}]
Wolfram Language code: es = TimeSeriesEvents[ts, {"Crossing", .9}]
Wolfram Language code: Normal[es]
Wolfram Language code: ListPlot[ts, GridLines -> {Normal[es["Timestamps"]], {{.9, Directive[Thick, Red]}}}]

Find all positive crossings of a given value:

Wolfram Language code: TimeSeriesEvents[ts, {"CrossingFromBelow", .9}]
Wolfram Language code: Normal[%]

Find zero crossings of an interpolated function of the time series:

Wolfram Language code: ts = TimeSeries[Range[10] / 100, {1}]
Wolfram Language code: fun = Sin[1. / #]&; events = TimeSeriesEvents[ts, "Crossing", fun]

Plotting these events shows there is some disagreement:

Wolfram Language code: Plot[fun[ts[x]], {x, 1, 10}, Epilog -> {PointSize[.02], Red, Point[Normal[events]]}]

The crossings are found for fun[ts], which is equivalent to TimeSeriesMap [fun,ts]:

Wolfram Language code: funts = fun[ts]
Wolfram Language code: SameQ[events, TimeSeriesEvents[funts, "Crossing"]]

The two sets of values can be quite different where the function changes rapidly:

Wolfram Language code: Plot[{fun[ts[x]], funts[x]}, {x, 1, 10}, Epilog -> {PointSize[.02], Red, Point[Normal[events]]}, PlotLegends -> {"fun[ ts[x] ]", "fun[ ts ][x]"}]

Find the crossings using a function involving multiple components of a time series:

Wolfram Language code: tseries = TimeSeries[Tabular[Association["RawSchema" -> Association["ColumnProperties" -> Association["Timestamp" -> Association["ElementType" -> TypeSpecifier["Date"]["Integer32", "Day", "Gregorian", -7.]], "k" -> Association["ElementType" -> "Integer64"], "w" -> Association["ElementType" -> "String"]], "KeyColumns" -> {"Timestamp"}, "Backend" -> "WolframKernel"], "Options" -> {MetaInformation -> Association[MetaInformation -> Association[]]}, "BackendData" -> Association["ColumnData" -> DataStructure["ColumnTable", {{TabularColumn[Association["Data" -> {5, {{NumericArray[{20475, 20484, 20497, 20500, 20570}, "Integer32"], {}, None}}, None}, "ElementType" -> TypeSpecifier["Date"]["Integer32", "Day", "Gregorian", -7.]]], TabularColumn[Association[ "Data" -> {{2, 0, 10, 3, 3}, {}, None}, "ElementType" -> "Integer64"]], TabularColumn[Association["Data" -> {{3, {0, 9, 14, 21, 26, 37}, "melodramastoopculvertshootunpopulated"}, {}, None}, "ElementType" -> "String"]]}}]]]]];
Wolfram Language code: f = Function[#k - StringLength[#w]];
Wolfram Language code: DateListPlot@TimeSeriesMap[f, tseries]
Wolfram Language code: TimeSeriesEvents[tseries, "Crossing", f] //Normal

Find only the crossings that happen in the first two weeks of the month:

Wolfram Language code: tseries = TimeSeries[Sinc[Subdivide[47., 364]], {DateObject[{2026, 1, 1}]}]
Wolfram Language code: events = TimeSeriesEvents[tseries, "Crossing", Identity, DateValue[#Timestamp, "Day"] <= 14 &]
Wolfram Language code: firsts = DateRange[DateObject[{2026, 1, 1}, "Day"], DateObject[{2026, 12, 31}, "Day"], Quantity[1, "Months"]];
Wolfram Language code: DateListPlot[{tseries, events}, Joined -> {True, False}, PlotStyle -> PointSize[0.025], GridLines -> {firsts, {0}}]

Extrema  (2)

Find the local maxima and local minima separately:

Wolfram Language code: ts = TimeSeries[TimeEventSeries`TimestampData[Association["UniformlySpacedQ" -> False, "Timestamps" -> TabularColumn[Association[ "Data" -> {25, {{{1767602823435, 1768686930089, 1769047268361, 1770622834401, 1772353465297, 17741088 ... ", "Gregorian", -7.]]], "Caller" -> TimeSeries]], TabularColumn[ Association["Data" -> {{-2, 0, -3, -3, 2, 2, 2, 3, 0, -2, 1, 2, 0, -2, 2, -2, -1, -1, -2, 1, -1, -2, -3, 2, 1}, {}, None}, "ElementType" -> "Integer64"]], Association[]];
Wolfram Language code: maxima = TimeSeriesEvents[ts, "LocalMaximum"]
Wolfram Language code: minima = TimeSeriesEvents[ts, "LocalMinimum"]
Wolfram Language code: DateListPlot[{ts, maxima, minima}, Joined -> {True, False, False}, PlotStyle -> PointSize[.025]]

The combination of these is the local extrema:

Wolfram Language code: SameQ[Join[minima, maxima], TimeSeriesEvents[ts, "LocalExtremum"]]

Find the local extrema for the automatic value of scale:

Wolfram Language code: tseries = TimeSeries[TimeEventSeries`TimestampData[Association["UniformlySpacedQ" -> True, "Count" -> 251, "Endpoints" -> TabularColumn[Association["Data" -> {{0., 1.}, {}, None}, "ElementType" -> "Real64"]], "MinimumTimeIncrement" -> 0.004, "Call ... 8304225, 0.3695749700876914, 0.33287032525155513, 0.29081418681721904, 0.24371561122423627, 0.19201917641207317, 0.13628850592901354, 0.07718559115778553, 0.015446640343153}, {}, None}, "ElementType" -> "Real64"]], Association[]];
Wolfram Language code: evA = TimeSeriesEvents[tseries, {"LocalExtremum", Automatic}]

In this case, some extrema between times 0.4 and 0.5 were not identified:

Wolfram Language code: ListPlot[{tseries, evA}, Joined -> {True, False}, PlotStyle -> PointSize[.025]]

Increasing the scale will typically reduce the number of peaks:

Wolfram Language code: Table[TimeSeriesEvents[tseries, {"LocalExtremum", s}], {s, {0, 0.04, 0.1}}]

Use scale 0 to find all the extrema, including the sharp peaks missed before:

Wolfram Language code: all = TimeSeriesEvents[tseries, {"LocalExtremum", 0}]
Wolfram Language code: ListPlot[{tseries, all}, Joined -> {True, False, False}, PlotStyle -> PointSize[.025], PlotRange -> {{.4, .51}, {0, .9}}]

Applications  (2)

Find the high and low elevation points of a GPS track for a bicycle ride:

Wolfram Language code: track = TimeSeries[«3»];
Wolfram Language code: highs = TimeSeriesEvents[track -> "Elevation", "LocalMaximum"]; lows = TimeSeriesEvents[track -> "Elevation", "LocalMinimum"];

Show the elevation profile with the high and low points:

Wolfram Language code: ListPlot[{track -> "Elevation", highs, lows}, Joined -> {True, False, False}, PlotStyle -> PointSize[0.01]]

Since GPS has relatively high error in elevation, it is important to use a scale:

Wolfram Language code: highs1 = TimeSeriesEvents[track -> "Elevation", {"LocalMaximum", Quantity[1, "Minutes"]}]; lows1 = TimeSeriesEvents[track -> "Elevation", {"LocalMinimum", Quantity[1, "Minutes"]}];
Wolfram Language code: ListPlot[{track -> "Elevation", highs1, lows1}, Joined -> {True, False, False}, PlotStyle -> PointSize[0.02]]

Find the total climbing elevation gain:

Wolfram Language code: Total[Table[Last[highs1[[i]]] - Last[lows1[[i]]], {i, Length[highs1]}]]

Find highs and lows of NViDIA stock on a quarterly scale:

Wolfram Language code: nvda = FinancialData["NASDAQ:NVDA", DateObject[{2000, 1, 1}]]
Wolfram Language code: lows = TimeSeriesEvents[nvda, {"LocalMinimum", Quantity[1, "Quarters"]}]
Wolfram Language code: highs = TimeSeriesEvents[nvda, {"LocalMaximum", Quantity[1, "Quarters"]}]

Show on a logarithmic scale so the earlier values are more apparent:

Wolfram Language code: DateListPlot[{nvda, highs, lows}, ScalingFunctions -> "Log", PlotStyle -> PointSize[0.02]]

Get the annualized return for each bullish (price trending up) period:

Wolfram Language code: Tabular[Table[ {lt, lv} = lows[[i]]; {ht, hv} = highs[[i]]; dt = ht - lt; {lt, dt, Quantity[(1 + hv / lv) ^ (Quantity[1, "Years"] / dt) - 1, "%"]}, {i, 9}], {"low date", "time to high", "return"}]
Wolfram Research (2026), TimeSeriesEvents, Wolfram Language function, https://reference.wolfram.com/language/ref/TimeSeriesEvents.html.

Text

Wolfram Research (2026), TimeSeriesEvents, Wolfram Language function, https://reference.wolfram.com/language/ref/TimeSeriesEvents.html.

CMS

Wolfram Language. 2026. "TimeSeriesEvents." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/TimeSeriesEvents.html.

APA

Wolfram Language. (2026). TimeSeriesEvents. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TimeSeriesEvents.html

BibTeX

@misc{reference.wolfram_2026_timeseriesevents, author="Wolfram Research", title="{TimeSeriesEvents}", year="2026", howpublished="\url{https://reference.wolfram.com/language/ref/TimeSeriesEvents.html}", note=[Accessed: 15-August-2026]}

BibLaTeX

@online{reference.wolfram_2026_timeseriesevents, organization={Wolfram Research}, title={TimeSeriesEvents}, year={2026}, url={https://reference.wolfram.com/language/ref/TimeSeriesEvents.html}, note=[Accessed: 15-August-2026]}
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