--- title: "TimeSeriesShift" language: "en" type: "Symbol" summary: "TimeSeriesShift[tseries, shift] shifts the time series tseries to the left or right according to shift." keywords: - time shift - time series align - time alignment - temporal alignment - shift event series - shift temporal data - realign time series canonical_url: "https://reference.wolfram.com/language/ref/TimeSeriesShift.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: "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: "TimeSeriesWindow" link: "https://reference.wolfram.com/language/ref/TimeSeriesWindow.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" --- # TimeSeriesShift TimeSeriesShift[tseries, shift] shifts the time series tseries to the left or right according to shift. ## Details and Options * ``TimeSeriesShift`` is used to align the start of a time series with a particular time. * [image] * The input ``tseries`` can be a list of values ``{x1, x2, …}``, a list of time-value pairs ``{{t1, x1}, {t2, x2}, …}``, a ``TimeSeries``, an ``EventSeries``, or ``TemporalData``. * Settings for ``shift`` include: | | | | --------- | ------------- | | τ | shift by τ | | {k, step} | shift k steps | | {{tmin}} | set t1 = tmin | * The shift ``τ`` can be any real number or a time ``Quantity``. * For integer ``k``, ``{k}`` is equivalent to giving ``{k, MinimumTimeIncrement[tseries]}``. * The ``step`` can be a number or date step such as ``"Year"``, ``"Month"``, ``"Day"``, etc. * ``TimeSeriesShift`` threads over paths for multipath ``TemporalData``. * ``TimeSeriesShift`` takes the following options: | | | | | ---------------- | --------------------------- | ----------------------------------------------- | | CalendarType | "Gregorian" | the calendar system to interpret the dates | | HolidayCalendar | {"UnitedStates", "Default"} | the holiday calendar schedule for business days | | TimeZone | Automatic | the time zone specification for dates | --- ## Examples (22) ### Basic Examples (3) Shift a time series ahead 2.5: ```wl In[1]:= ts = RandomFunction[ARProcess[{.1}, 1], {1, 10}]; In[2]:= shift = TimeSeriesShift[ts, 2.5]; In[3]:= ListLinePlot[{ts, shift}] Out[3]= [image] ``` Shift backward 2.5: ```wl In[4]:= shift = TimeSeriesShift[ts, -2.5]; In[5]:= ListLinePlot[{ts, shift}] Out[5]= [image] ``` --- Shift a time series ahead 30 days: ```wl In[1]:= ts = FinancialData["GOOGL", {"January 2012", "January 2013"}]; In[2]:= shift = TimeSeriesShift[ts, {30, "Day"}]; In[3]:= DateListPlot[{ts, shift}] Out[3]= [image] ``` --- Set the starting time for a time series to 100: ```wl In[1]:= ts = TimeSeries[Accumulate@RandomReal[{-1, 1}, 100]]; In[2]:= shift = TimeSeriesShift[ts, {{100}}]; In[3]:= ListLinePlot[{ts, shift}] Out[3]= [image] ``` ### Scope (13) #### Basic Uses (7) Shift a time series forward by 3.5: ```wl In[1]:= td = TimeSeries[{Subscript[x, 1], Subscript[x, 2], Subscript[x, 3], Subscript[x, 4], Subscript[x, 5]}, {1}]; In[2]:= TimeSeriesShift[td, 3.5]["Path"] Out[2]= {{4.5, Subscript[x, 1]}, {5.5, Subscript[x, 2]}, {6.5, Subscript[x, 3]}, {7.5, Subscript[x, 4]}, {8.5, Subscript[x, 5]}} ``` --- Shift a time series backward by 3.5: ```wl In[1]:= td = TimeSeries[{Subscript[x, 1], Subscript[x, 2], Subscript[x, 3], Subscript[x, 4], Subscript[x, 5]}, {1}]; In[2]:= TimeSeriesShift[td, -3.5]["Path"] Out[2]= {{-2.5, Subscript[x, 1]}, {-1.5, Subscript[x, 2]}, {-0.5, Subscript[x, 3]}, {0.5, Subscript[x, 4]}, {1.5, Subscript[x, 5]}} ``` --- Shift by two days: ```wl In[1]:= td = TimeSeries[Range[5], {"December 29, 2012"}]; In[2]:= shift = TimeSeriesShift[td, Quantity[2, "Days"]]; In[3]:= DateListPlot[{td, shift}] Out[3]= [image] ``` --- Use business days as an increment: ```wl In[1]:= td = TimeSeries[Range[5], {"December 29, 2012"}]; In[2]:= shift = TimeSeriesShift[td, {4, "BusinessDay"}]; ``` Compare time stamps: ```wl In[3]:= TimelinePlot[{td["Dates"], shift["Dates"]}] Out[3]= [image] In[4]:= DateListPlot[{td, shift}] Out[4]= [image] ``` --- Shift ahead one week and three days: ```wl In[1]:= td = TemporalData[TimeSeries, {{{-0.7300936468626915, -1.4519910060028738, -0.5169470600446475, -0.5865073582473852, -0.3877452738596685, -1.1268832613089939, -1.573832025824792, -1.513287567214887, -0.9281089897453407, -1.51062273515126, -1.1 ... 90256942794819, -0.2908415274027569, -1.1815264644646835}}, {TemporalData`DateSpecification[{2013, 9, 23, 13, 34, 42.7383033}, {2013, 10, 17, 13, 34, 42.7383033}, {1, "Day"}]}, 1, {"Discrete", 1}, {"Discrete", 1}, 1, {}}, True, 10.]; In[2]:= shift = TimeSeriesShift[td, {{1, "Week"}, {3, "Day"}}]; In[3]:= DateListPlot[{td, shift}] Out[3]= [image] ``` --- Shift the start time to 5: ```wl In[1]:= td = TimeSeries[Accumulate@RandomReal[{-1, 1}, 25], {1}]; In[2]:= shift = TimeSeriesShift[td, {{5}}]; In[3]:= ListLinePlot[{td, shift}] Out[3]= [image] ``` --- Shift the dates in a time series to begin on today's date: ```wl In[1]:= td = TimeSeries[Accumulate@RandomReal[{-1, 1}, 25], {DatePlus[DateList[], {-1, "Week"}]}]; In[2]:= shift = TimeSeriesShift[td, {{DateList[]}}]; In[3]:= DateListPlot[{td, shift}] Out[3]= [image] ``` #### Data Types (6) Shift the times for a vector forward 2: ```wl In[1]:= vals = {a, b, c, d, e}; In[2]:= TimeSeriesShift[vals, 2] Out[2]= {{2, a}, {3, b}, {4, c}, {5, d}, {6, e}} ``` --- Shift the times for a series of time-value pairs backward by 2: ```wl In[1]:= vals = {{2, a}, {3, b}, {7, c}, {14, d}, {15, e}}; In[2]:= TimeSeriesShift[vals, -1] Out[2]= {{1, a}, {2, b}, {6, c}, {13, d}, {14, e}} ``` --- Shift the values from a ``TimeSeries`` forward by 10: ```wl In[1]:= ts = TemporalData[TimeSeries, {CompressedData["«1176»"], {{0, 99, 1}}, 1, {"Discrete", 1}, {"Discrete", 1}, 1, {}}, False, 10.]; In[2]:= ts1 = TimeSeriesShift[ts, 10] Out[2]= TemporalData[TimeSeries, {CompressedData["«1174»"], {{10, 109, 1}}, 1, {"Discrete", 1}, {"Discrete", 1}, 1, {}}, False, 14.3] In[3]:= ListLinePlot[{ts, ts1}] Out[3]= [image] ``` --- Shift the values of an ``EventSeries`` forward by 5: ```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}}, {{0, 19, 1}}, 1, {"Discrete", 1}, {"Discrete", 1}, 1, {ResamplingMethod -> None}}, False, 10.]; In[2]:= es1 = TimeSeriesShift[es, 5] Out[2]= TemporalData[EventSeries, {{{1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1}}, {{5, 24, 1}}, 1, {"Discrete", 1}, {"Discrete", 1}, 1, {ResamplingMethod -> None}}, False, 14.3] In[3]:= ListPlot[{es, es1}, Filling -> Axis] Out[3]= [image] ``` --- Shift the paths of ``TemporalData`` ahead 10: ```wl In[1]:= td = RandomFunction[WienerProcess[], {0, 5, 0.1}, 3] Out[1]= TemporalData[Automatic, {CompressedData["«1746»"], {{0, 5, 0.1}}, 3, {"Continuous", 3}, {"Continuous", 1}, 1, {ValueDimensions -> 1, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 14.3] In[2]:= td1 = TimeSeriesShift[td, 10] Out[2]= TemporalData[Automatic, {CompressedData["«1746»"], {{10, 15, 0.1}}, 3, {"Continuous", 3}, {"Continuous", 1}, 1, {ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}, ValueDimensions -> 1}}, False, 14.3] In[3]:= Show[ListLinePlot /@ {td["Paths"], td1["Paths"]}, PlotRange -> {{0, 15}, All}] Out[3]= [image] ``` --- Shift a time series involving quantities: ```wl In[1]:= ts = TimeSeries[Quantity[{0, 16, 9, 3, 7, 2, 17, 10, 6, 12}, "Meters"]]; In[2]:= ts1 = TimeSeriesShift[ts, 1]; In[3]:= ListLinePlot[{ts, ts1}, PlotLegends -> {"original time series", "shifted time series"}, Filling -> Axis, AxesLabel -> Automatic] Out[3]= [image] ``` ### Options (3) #### CalendarType (1) Define a time series: ```wl In[1]:= data = TimeSeries[{{DateObject[{2016, 11, 10}], 1}, {DateObject[{2016, 11, 14}], 2}, {DateObject[{2016, 11, 15}], 3}}]; ``` Shift the data by one day and express the result using the Jewish calendar: ```wl In[2]:= TimeSeriesShift[data, {1, "Day"}, CalendarType -> "Jewish"]//Normal Out[2]= {{DateObject[{5777, 8, 10, 0, 0, 0.}, "Instant", "Jewish", -5.], 1}, {DateObject[{5777, 8, 14, 0, 0, 0.}, "Instant", "Jewish", -5.], 2}, {DateObject[{5777, 8, 15, 0, 0, 0.}, "Instant", "Jewish", -5.], 3}} ``` #### HolidayCalendar (2) Shift a time series by a business day using the default ``HolidayCalendar`` : ```wl In[1]:= data = TimeSeries[{{DateObject[{2016, 11, 10}], 1}, {DateObject[{2016, 11, 14}], 2}, {DateObject[{2016, 11, 15}], 3}}]; In[2]:= TimeSeriesShift[data, {1, "BusinessDay"}]//Normal Out[2]= {{DateObject[{2016, 11, 14, 0, 0, 0.}, "Instant", "Gregorian", -5.], 1}, {DateObject[{2016, 11, 15, 0, 0, 0.}, "Instant", "Gregorian", -5.], 2}, {DateObject[{2016, 11, 16, 0, 0, 0.}, "Instant", "Gregorian", -5.], 3}} ``` Use the NYSE holiday calendar: ```wl In[3]:= TimeSeriesShift[data, {1, "BusinessDay"}, HolidayCalendar -> {"UnitedStates", "NYSE"}]//Normal Out[3]= {{DateObject[{2016, 11, 11, 0, 0, 0.}, "Instant", "Gregorian", -5.], 1}, {DateObject[{2016, 11, 15, 0, 0, 0.}, "Instant", "Gregorian", -5.], 2}, {DateObject[{2016, 11, 16, 0, 0, 0.}, "Instant", "Gregorian", -5.], 3}} ``` --- Use a holiday calendar of a given country: ```wl In[1]:= data = TimeSeries[Range[7], {DateObject[{2017, 4, 13}]}]; In[2]:= TimeSeriesShift[data, {1, "BusinessDay"}, HolidayCalendar -> "Germany"]//Normal Out[2]= {{DateObject[{2017, 4, 18, 0, 0, 0.}, "Instant", "Gregorian", -5.], 1}, {DateObject[{2017, 4, 19, 0, 0, 0.}, "Instant", "Gregorian", -5.], 2}, {DateObject[{2017, 4, 20, 0, 0, 0.}, "Instant", "Gregorian", -5.], 3}, {DateObject[{2017, 4, 21, 0, 0, 0.}, "Instant", "Gregorian", -5.], 4}, {DateObject[{2017, 4, 22, 0, 0, 0.}, "Instant", "Gregorian", -5.], 5}, {DateObject[{2017, 4, 23, 0, 0, 0.}, "Instant", "Gregorian", -5.], 6}, {DateObject[{2017, 4, 24, 0, 0, 0.}, "Instant", "Gregorian", -5.], 7}} In[3]:= TimeSeriesShift[data, {1, "BusinessDay"}, HolidayCalendar -> "UnitedStates"]//Normal Out[3]= {{DateObject[{2017, 4, 14, 0, 0, 0.}, "Instant", "Gregorian", -5.], 1}, {DateObject[{2017, 4, 15, 0, 0, 0.}, "Instant", "Gregorian", -5.], 2}, {DateObject[{2017, 4, 16, 0, 0, 0.}, "Instant", "Gregorian", -5.], 3}, {DateObject[{2017, 4, 17, 0, 0, 0.}, "Instant", "Gregorian", -5.], 4}, {DateObject[{2017, 4, 18, 0, 0, 0.}, "Instant", "Gregorian", -5.], 5}, {DateObject[{2017, 4, 19, 0, 0, 0.}, "Instant", "Gregorian", -5.], 6}, {DateObject[{2017, 4, 20, 0, 0, 0.}, "Instant", "Gregorian", -5.], 7}} ``` ### Applications (1) Specify rates for ``TimeValue`` : ```wl In[1]:= ts = TemporalData[TimeSeries, {{{0.04, 0.05, 0.06, 0.07, 0.08}}, {{4, 8, 1}}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 10.1]; ``` Note that the first time step must be 0 to define the initial rate. Shift the time series: ```wl In[2]:= rates = TimeSeriesShift[ts, {{0}}] Out[2]= TemporalData[TimeSeries, {{{0.04, 0.05, 0.06, 0.07, 0.08}}, {{0, 4, 1}}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 14.3] ``` Calculate the time value: ```wl In[3]:= TimeValue[1, rates, 10] Out[3]= 1.96542 ``` ### Possible Issues (2) ``TimeSeriesShift`` may break temporal regularity: ```wl In[1]:= data = TimeSeries[Range[7], {DateObject[{2017, 4, 13}], Automatic, "BusinessDay"}, HolidayCalendar -> "Germany"]; ``` Shift by a day: ```wl In[2]:= ts1 = TimeSeriesShift[data, {1, "Day"}] Out[2]= TemporalData[TimeSeries, {{{1, 2, 3, 4, 5, 6, 7}}, {{{3701116800, 3701548800, 3701635200, 3701721600, 3701808000, 3702067200, 3702153600}}}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {HolidayCalendar -> "Germany", ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}, ValueDimensions -> 1}}, True, 14.3] In[3]:= RegularlySampledQ[ts1] Out[3]= False ``` The next day in Germany is not a business day: ```wl In[4]:= DayMatchQ[DatePlus[data["FirstDate"], {1, "Day"}], "BusinessDay", HolidayCalendar -> "Germany"] Out[4]= False ``` Preserve temporal regularity by shifting by a business day: ```wl In[5]:= ts2 = TimeSeriesShift[data, {1, "BusinessDay"}] Out[5]= TemporalData[TimeSeries, {{{1, 2, 3, 4, 5, 6, 7}}, {TemporalData`DateSpecification[{2017, 4, 18, 0, 0, 0.}, {2017, 4, 26, 0, 0, 0.}, "BusinessDay", "DayRange"]}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {HolidayCalendar -> "Germany", ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}, ValueDimensions -> 1}}, True, 14.3] In[6]:= RegularlySampledQ[ts2] Out[6]= True ``` Compare the time series: ```wl In[7]:= DateListPlot[{data, ts1, ts2}, PlotLegends -> {"data", "ts1", "ts2"}] Out[7]= [image] ``` --- Specifying a new ``HolidayCalendar`` overrides that option in the input: ```wl In[1]:= data = TimeSeries[Range[7], {DateObject[{2017, 4, 13}], Automatic, "BusinessDay"}, HolidayCalendar -> "UnitedStates"]; ``` Shift by one business day with the same ``HolidayCalendar`` : ```wl In[2]:= res1 = TimeSeriesShift[data, {1, "BusinessDay"}] Out[2]= TemporalData[TimeSeries, {{{1, 2, 3, 4, 5, 6, 7}}, {TemporalData`DateSpecification[{2017, 4, 14, 0, 0, 0.}, {2017, 4, 24, 0, 0, 0.}, "BusinessDay", "DayRange"]}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {HolidayCalendar -> "UnitedStates", ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}, ValueDimensions -> 1}}, True, 14.3] ``` Specify a new ``HolidayCalendar`` : ```wl In[3]:= res2 = TimeSeriesShift[data, {1, "BusinessDay"}, HolidayCalendar -> "Germany"] Out[3]= TemporalData[TimeSeries, {{{1, 2, 3, 4, 5, 6, 7}}, {TemporalData`DateSpecification[{2017, 4, 18, 0, 0, 0.}, {2017, 4, 26, 0, 0, 0.}, "BusinessDay", "DayRange"]}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {HolidayCalendar -> "Germany", ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}, ValueDimensions -> 1}}, True, 14.3] In[4]:= TimelinePlot[{res1["Dates"], res2["Dates"]}, PlotLegends -> Placed[{"United States", "Germany"}, Below]] 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) * [`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) * [`TimeSeriesWindow`](https://reference.wolfram.com/language/ref/TimeSeriesWindow.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) ## 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 2017 (11.2)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn112.en.md)