--- title: "TimeSeriesWindow" language: "en" type: "Symbol" summary: "TimeSeriesWindow[tseries, {tmin, tmax}] gives the elements of the time series tseries that fall between tmin and tmax. TimeSeriesWindow[tseries, windowspec] gives the elements of the time series tseries that satisfy the window specification windowspec." keywords: - time series part - temporal data part - time series chunk - split time series canonical_url: "https://reference.wolfram.com/language/ref/TimeSeriesWindow.html" source: "Wolfram Language Documentation" related_guides: - title: "Time Series Processing" link: "https://reference.wolfram.com/language/guide/TimeSeries.en.md" related_functions: - title: "MovingMap" link: "https://reference.wolfram.com/language/ref/MovingMap.en.md" - title: "TimeSeriesAggregate" link: "https://reference.wolfram.com/language/ref/TimeSeriesAggregate.en.md" - title: "TimeSeriesResample" link: "https://reference.wolfram.com/language/ref/TimeSeriesResample.en.md" - title: "TimeSeriesThread" link: "https://reference.wolfram.com/language/ref/TimeSeriesThread.en.md" - title: "RegularlySampledQ" link: "https://reference.wolfram.com/language/ref/RegularlySampledQ.en.md" - title: "MinimumTimeIncrement" link: "https://reference.wolfram.com/language/ref/MinimumTimeIncrement.en.md" - title: "TimeSeriesShift" link: "https://reference.wolfram.com/language/ref/TimeSeriesShift.en.md" - title: "TimeSeriesRescale" link: "https://reference.wolfram.com/language/ref/TimeSeriesRescale.en.md" - title: "TimeSeriesMap" link: "https://reference.wolfram.com/language/ref/TimeSeriesMap.en.md" - title: "TimeSeriesMapThread" link: "https://reference.wolfram.com/language/ref/TimeSeriesMapThread.en.md" - title: "TimeSeriesInsert" link: "https://reference.wolfram.com/language/ref/TimeSeriesInsert.en.md" - title: "TimeSeriesModelFit" link: "https://reference.wolfram.com/language/ref/TimeSeriesModelFit.en.md" - title: "TemporalData" link: "https://reference.wolfram.com/language/ref/TemporalData.en.md" - title: "TimeSeries" link: "https://reference.wolfram.com/language/ref/TimeSeries.en.md" - title: "EventSeries" link: "https://reference.wolfram.com/language/ref/EventSeries.en.md" - title: "ResamplingMethod" link: "https://reference.wolfram.com/language/ref/ResamplingMethod.en.md" - title: "IncludeWindowTimes" link: "https://reference.wolfram.com/language/ref/IncludeWindowTimes.en.md" --- # TimeSeriesWindow TimeSeriesWindow[tseries, {tmin, tmax}] gives the elements of the time series tseries that fall between tmin and tmax. TimeSeriesWindow[tseries, windowspec] gives the elements of the time series tseries that satisfy the window specification windowspec. ## Details and Options * ``TimeSeriesWindow`` is used to select a subset of a time series that falls in a given window. [image] * The time series ``tseries`` can be a list of numeric values ``{x1, x2, …}``, a list of time-value pairs ``{{t1, x1}, {t2, x2}, …}``, a ``TimeSeries``, ``EventSeries``, or ``TemporalData``. * The window times ``tmin`` and ``tmax`` can be given as ``Automatic``, numbers, or dates. When ``tmin`` or ``tmax`` are given as ``Automatic``, the first and last times in ``tseries`` are used, respectively. * The window specification ``windowspec`` can be given as: | | | | ------------------- | ---------------------------- | | {tmin, tmax} | time or date limits | | DateObject[_, gran] | a single granular DateObject | | dayspec | use day specification | * Possible ``dayspec`` types are: ``"Weekday"``, ``"Weekend"``, ``Monday`` through ``Sunday``, ``"BeginningOfMonth"``, ``"EndOfMonth"``, ``"BusinessDay"`` and ``"Holiday"``. * ``TimeSeriesWindow`` takes the following options: | | | | | ------------------- | --------------------------- | --------------------------------------------------------------------------- | | ResamplingMethod | Automatic | the method to use for resampling paths | | IncludeWindowTimes | False | whether to create values at tmin and tmax if not members of the time stamps | | CalendarType | "Gregorian" | the calendar system to interpret the dates | | HolidayCalendar | {"UnitedStates", "Default"} | the holiday calendar schedule for business days | * By default, the window times ``tmin`` and ``tmax`` are included only if they are also members of the times ``{t1, t2, …}`` in ``tseries``. * If ``tmin`` and ``tmax`` are outside the range of the ``{t1, t2, …}``, then the ``t1`` and ``tn`` are used, respectively. --- ## Examples (15) ### Basic Examples (1) Extract a portion of a time series: ```wl In[1]:= ts = TimeSeries[FinancialData["GOOGL", {"1 Jan 2012", "1 Jan 2014"}]]; In[2]:= DateListPlot[ts] Out[2]= [image] ``` Take the elements between May 4 and August 4 of 2012: ```wl In[3]:= win = TimeSeriesWindow[ts, {{2012, 5, 4}, {2012, 8, 4}}]; In[4]:= DateListPlot[win] Out[4]= [image] ``` Extract elements from June 2012: ```wl In[5]:= TimeSeriesWindow[ts, DateObject[{2012, 6}, "Month"]] Out[5]= TemporalData[TimeSeries, {{QuantityArray[StructuredArray`StructuredData[{21}, {{285.7770080566406, 289.5799865722656, 285.47601318359375, 290.58099365234375, 289.3800048828125, 290.4809875488281, 284.5249938964844, 282.8240051269531 ... 3549744000, 3549830400, 3549916800}]}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {DateFunction -> Automatic, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}, TemporalRegularity -> True, ValueDimensions -> 1}}, True, 12.1] ``` Extract elements that fall at the end of each month: ```wl In[6]:= end = TimeSeriesWindow[ts, "EndOfMonth"] Out[6]= TemporalData[TimeSeries, {{{Quantity[290.33599853515625, "USDollars"], Quantity[309.42498779296875, "USDollars"], Quantity[302.7179870605469, "USDollars"], Quantity[290.71099853515625, "USDollars"], Quantity[316.8070068359375, "USDollars" ... 3589488000, 3592166400, 3597436800}}}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {DateFunction -> Automatic, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}, TemporalRegularity -> True, ValueDimensions -> 1}}, True, 314.1] In[7]:= DateListPlot[end, PlotMarkers -> Automatic] Out[7]= [image] ``` ### Scope (8) #### Basic Uses (3) Select a subset of a time series: ```wl In[1]:= data = {{1, Subscript[x, 1]}, {2, Subscript[x, 2]}, {3, Subscript[x, 3]}, {4, Subscript[x, 4]}, {5, Subscript[x, 5]}}; In[2]:= TimeSeriesWindow[data, {2, 4}] Out[2]= {{2, Subscript[x, 2]}, {3, Subscript[x, 3]}, {4, Subscript[x, 4]}} ``` --- Select Fridays from a time series with dates: ```wl In[1]:= ts = TemporalData[TimeSeries, {{{285.775791, 289.584598, 285.490482, 290.575565, 289.404423, 290.515507, 284.53455, 282.832828, 280.82584, 279.804813, 282.53754, 285.710728, 291.056065, 289.044041, 282.887882, 286.026035, 280.630649, 282.62262 ... 12000, 3549571200, 3549657600, 3549744000, 3549830400, 3549916800}}}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {ValueDimensions -> 1, DateFunction -> Automatic, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, True, 314.1]; In[2]:= fridays = TimeSeriesWindow[ts, Friday] Out[2]= TemporalData[TimeSeries, {{{285.775791, 290.515507, 282.53754, 286.026035, 290.325321}}, {{{3547497600, 3548102400, 3548707200, 3549312000, 3549916800}}}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {ValueDimensions -> 1, DateFunction -> Automatic, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, True, 14.3] In[3]:= DateListPlot[{ts, fridays}, Joined -> {True, False}, Filling -> 2 -> 0, FillingStyle -> Directive[Gray, Thick]] Out[3]= [image] ``` --- Visualize different subsets of a time series: ```wl In[1]:= data = TimeSeries[RandomFunction[ARIMAProcess[{.1}, 1, {.2}, 1], {1000}]]; In[2]:= ListLinePlot[data] Out[2]= [image] ``` Split the data into three parts: ```wl In[3]:= win1 = TimeSeriesWindow[data, {Automatic, 300}]; win2 = TimeSeriesWindow[data, {300, 700}]; win3 = TimeSeriesWindow[data, {700, Automatic}]; In[4]:= ListLinePlot[{win1, win2, win3}, PlotLegends -> {"win1", "win2", "win3"}] Out[4]= [image] ``` #### Data Types (5) Extract three elements from a vector: ```wl In[1]:= v = {a, b, c, d, e}; In[2]:= TimeSeriesWindow[v, {2, 4}] Out[2]= {c, d, e} ``` --- Select the values for a specific interval of times in a list of time-value pairs: ```wl In[1]:= v = {{1, a}, {3, b}, {7, c}, {14, d}, {15, e}}; In[2]:= TimeSeriesWindow[v, {2, 8}] Out[2]= {{3, b}, {7, c}} ``` --- Extract 50 values from a ``TimeSeries`` : ```wl In[1]:= ts = TemporalData[TimeSeries, {CompressedData["«1176»"], {{0, 99, 1}}, 1, {"Discrete", 1}, {"Discrete", 1}, 1, {}}, False, 10.]; In[2]:= win = TimeSeriesWindow[ts, {10, 59}] Out[2]= TemporalData[TimeSeries, {CompressedData["«612»"], {{10, 59, 1}}, 1, {"Discrete", 1}, {"Discrete", 1}, 1, {}}, False, 10.] ``` Overlay the window over the original data: ```wl In[3]:= ListLinePlot[{ts, win}] Out[3]= [image] ``` --- Extract 30 values from an ``EventSeries`` : ```wl In[1]:= es = TemporalData[EventSeries, {{{-1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1}}, {{0, 49, 1}}, 1, {"Discrete", 1}, {"Discrete", 1}, 1, {ResamplingMethod -> None}}, False, 10.]; In[2]:= win = TimeSeriesWindow[es, {10, 39}] Out[2]= TemporalData[EventSeries, {{{1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1}}, {{10, 39, 1}}, 1, {"Discrete", 1}, {"Discrete", 1}, 1, {ResamplingMethod -> None}}, False, 10.] ``` Overlay the window over the original data: ```wl In[3]:= ListPlot[{es, win}, Filling -> Axis] Out[3]= [image] ``` --- Restrict the paths of ``TemporalData`` to a smaller interval: ```wl In[1]:= td = RandomFunction[WienerProcess[], {0, 20, 0.01}, 5] Out[1]= TemporalData[Automatic, {CompressedData["«107648»"], {{0, 20, 0.01}}, 5, {"Continuous", 5}, {"Continuous", 1}, 1, {ValueDimensions -> 1, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 14.3] In[2]:= win = TimeSeriesWindow[td, {3, 15}] Out[2]= TemporalData[Automatic, {CompressedData["«64936»"], {{3., 15., 0.01}}, 5, {"Continuous", 5}, {"Continuous", 1}, 1, {ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}, ValueDimensions -> 1}}, False, 14.3] In[3]:= ListLinePlot[#, PlotRange -> {{0, 20}, {-10, 10}}]& /@ {td, win} Out[3]= {[image], [image]} ``` ### Options (4) #### IncludeWindowTimes (1) By default, the window times are included only if they are among the time stamps: ```wl In[1]:= ts = {{1, 1}, {2, 2}, {3, 3}, {4, 4}}; In[2]:= TimeSeriesWindow[ts, {2, 3}] Out[2]= {{2, 2}, {3, 3}} ``` If the window times are not time stamps, they are excluded: ```wl In[3]:= TimeSeriesWindow[ts, {1.5, 3.5}] Out[3]= {{2, 2}, {3, 3}} ``` Specify that window times should be included: ```wl In[4]:= TimeSeriesWindow[ts, {1.5, 3.5}, IncludeWindowTimes -> True] Out[4]= {{1.5, 1}, {2, 2}, {3, 3}, {3.5, 3}} ``` Include only the right window time: ```wl In[5]:= TimeSeriesWindow[ts, {1.5, 3.5}, IncludeWindowTimes -> {False, True}] Out[5]= {{2, 2}, {3, 3}, {3.5, 3}} ``` #### ResamplingMethod (1) Specify what values to assign to window times that are not among the time stamps: ```wl In[1]:= s = {Subscript[x, 1], Subscript[x, 2], Subscript[x, 3], Subscript[x, 4]}; t = {2, 4, 6, 8}; In[2]:= td = TemporalData[s, {t}]; td//Normal Out[2]= {{{2, Subscript[x, 1]}, {4, Subscript[x, 2]}, {6, Subscript[x, 3]}, {8, Subscript[x, 4]}}} ``` By default, a resampling method of the input data is used: ```wl In[3]:= win1 = TimeSeriesWindow[td, {4, 6.4}, IncludeWindowTimes -> True]; In[4]:= win1//Normal Out[4]= {{{4., Subscript[x, 2]}, {6., Subscript[x, 3]}, {6.4, Subscript[x, 3]}}} ``` Use interpolation of order 1: ```wl In[5]:= win2 = TimeSeriesWindow[td, {4, 6.4}, IncludeWindowTimes -> True, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}]; In[6]:= win2//Normal Out[6]= {{{4., Subscript[x, 2]}, {6., Subscript[x, 3]}, {6.4, 0.8 (Subscript[x, 3] - Subscript[x, 4]) + Subscript[x, 4]}}} ``` Use a fixed constant: ```wl In[7]:= win3 = TimeSeriesWindow[td, {4, 6.4}, ResamplingMethod -> {"Constant", c}, IncludeWindowTimes -> True]; In[8]:= win3//Normal Out[8]= {{{4., Subscript[x, 2]}, {6., Subscript[x, 3]}, {6.4, c}}} ``` #### CalendarType (1) Use the Jewish calendar: ```wl In[1]:= data = {{{5777, 1, 10}, 1}, {{5777, 1, 11}, 2}, {{5777, 1, 12}, 3}, {{5777, 1, 13}, 4}, {{5777, 1, 14}, 5}, {{5777, 1, 15}, 6}}; In[2]:= TimeSeriesWindow[data, "Weekend", CalendarType -> "Jewish"] Out[2]= {{DateObject[{9537, 10, 4, 0, 0, 0.}, "Instant", "Jewish", -6.], 1}, {DateObject[{9537, 10, 5, 0, 0, 0.}, "Instant", "Jewish", -6.], 2}} ``` #### HolidayCalendar (1) Extract business days: ```wl In[1]:= ts = TimeSeries[Range[20], {{2017, 4, 10}}]; In[2]:= res = TimeSeriesWindow[ts, "BusinessDay", HolidayCalendar -> "Germany"] Out[2]= TemporalData[TimeSeries, {{{1, 2, 3, 4, 9, 10, 11, 12, 15, 16, 17, 18, 19}}, {{{3700771200, 3700857600, 3700944000, 3701030400, 3701462400, 3701548800, 3701635200, 3701721600, 3701980800, 3702067200, 3702153600, 3702240000, 3702326400}}}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, True, 314.1] In[3]:= DateListPlot[{ts, res}, Joined -> False, Filling -> 2 -> 0] Out[3]= [image] ``` ### Applications (2) This time series contains the number of steps taken daily by a person during a period of five months: ```wl In[1]:= stepdata = TemporalData[TimeSeries, {CompressedData["«674»"], {TemporalData`DateSpecification[{2013, 4, 1, 0, 0, 0.}, {2013, 9, 1, 0, 0, 0.}, {1, "Day"}]}, 1, {"Discrete", 1}, {"Discrete", 1}, 1, {ValueDimensions -> 1}}, True, 10.]; ``` Display the daily step counts for each of the months: ```wl In[2]:= monthlyTS = Table[TimeSeriesWindow[stepdata, DateObject[{2013, k}]], {k, 4, 8}]; In[3]:= months = {"April", "May", "June", "July", "August"};DateListPlot[monthlyTS, PlotLegends -> months] Out[3]= [image] ``` Display the total number of steps for each month: ```wl In[4]:= monthlyTotals = Total /@ monthlyTS; In[5]:= PieChart[monthlyTotals, ChartLabels -> Placed[{monthlyTotals, months}, {"RadialCenter", "RadialCallout"}]] Out[5]= [image] ``` --- Visualize the temperature in Champaign during the summer of 2014: ```wl In[1]:= td = TemporalData[TimeSeries, {{QuantityArray[StructuredArray`StructuredData[{365}, {{-2.94, -7.28, -14.94, -3.39, -2.56, -21, -23.06, -14.33, -6.5, 1.33, 3.22, 1.67, 5, -1.72, -2.33, -7.78, -0.5, -9, -4.28, 1.83, -0.94, -17, -12.17, -18 ... cation[{2014, 1, 1, 0, 0, 0.}, {2014, 12, 31, 0, 0, 0.}, {1, "Day"}]}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {ValueDimensions -> 1, DateFunction -> Automatic, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, True, 10.1]; ``` Extract the temperatures for summer months: ```wl In[2]:= summer = TimeSeriesWindow[td, {DateObject[{2014, 6, 1}, "Day", "Gregorian", -6.], DateObject[{2014, 9, 1}, "Day", "Gregorian", -6.]}] Out[2]= TemporalData[TimeSeries, {{QuantityArray[StructuredArray`StructuredData[{93}, {{23.83, 22.44, 25.17, 23.44, 17.67, 19, 21.22, 20, 17.5, 20.11, 19.11, 18.94, 19.28, 16.28, 17.11, 25, 26.22, 26.22, 26.44, 24.94, 22.33, 21.22, 23.17, 2 ... on[{2014, 6, 1, 0, 0, 0.}, {2014, 9, 1, 0, 0, 0.}, {1, "Day"}]}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {ValueDimensions -> 1, DateFunction -> Automatic, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, True, 10.1] ``` Find some basic descriptive statistics: ```wl In[3]:= {Min[#], Mean[#], Max[#]}&@summer Out[3]= {Quantity[14.67, "DegreesCelsius"], Quantity[21.293440860215053, "DegreesCelsius"], Quantity[26.44, "DegreesCelsius"]} In[4]:= DateListPlot[{td, summer}, FrameLabel -> Automatic] Out[4]= [image] ``` ## See Also * [`MovingMap`](https://reference.wolfram.com/language/ref/MovingMap.en.md) * [`TimeSeriesAggregate`](https://reference.wolfram.com/language/ref/TimeSeriesAggregate.en.md) * [`TimeSeriesResample`](https://reference.wolfram.com/language/ref/TimeSeriesResample.en.md) * [`TimeSeriesThread`](https://reference.wolfram.com/language/ref/TimeSeriesThread.en.md) * [`RegularlySampledQ`](https://reference.wolfram.com/language/ref/RegularlySampledQ.en.md) * [`MinimumTimeIncrement`](https://reference.wolfram.com/language/ref/MinimumTimeIncrement.en.md) * [`TimeSeriesShift`](https://reference.wolfram.com/language/ref/TimeSeriesShift.en.md) * [`TimeSeriesRescale`](https://reference.wolfram.com/language/ref/TimeSeriesRescale.en.md) * [`TimeSeriesMap`](https://reference.wolfram.com/language/ref/TimeSeriesMap.en.md) * [`TimeSeriesMapThread`](https://reference.wolfram.com/language/ref/TimeSeriesMapThread.en.md) * [`TimeSeriesInsert`](https://reference.wolfram.com/language/ref/TimeSeriesInsert.en.md) * [`TimeSeriesModelFit`](https://reference.wolfram.com/language/ref/TimeSeriesModelFit.en.md) * [`TemporalData`](https://reference.wolfram.com/language/ref/TemporalData.en.md) * [`TimeSeries`](https://reference.wolfram.com/language/ref/TimeSeries.en.md) * [`EventSeries`](https://reference.wolfram.com/language/ref/EventSeries.en.md) * [`ResamplingMethod`](https://reference.wolfram.com/language/ref/ResamplingMethod.en.md) * [`IncludeWindowTimes`](https://reference.wolfram.com/language/ref/IncludeWindowTimes.en.md) ## Related Guides * [Time Series Processing](https://reference.wolfram.com/language/guide/TimeSeries.en.md) ## History * [Introduced in 2014 (10.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn100.en.md) \| [Updated in 2019 (12.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn120.en.md)