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TimeSeries

Represents a series of values paired with time stamps. Descriptive statistics such as Mean and Total operate on the value path.

A time series can be given as a list of {time, value} pairs:

$ wo 'Mean[TimeSeries[{{1, 10.}, {2, 20.}, {3, 30.}}]]'
20.

$ wo 'Total[TimeSeries[{{1, 10}, {2, 20}, {3, 30}}]]'
60

A bare list of values gets integer time stamps 1, 2, 3, …:

$ wo 'Mean[TimeSeries[{10., 20., 30., 40.}]]'
25.

TimeSeriesWindow keeps the points whose time stamps fall in a window, including both endpoints:

$ wo 'TimeSeriesWindow[TimeSeries[{{1, 10}, {2, 20}, {3, 30}, {4, 40}}], {2, 3}]["Path"]'
{{2, 20}, {3, 30}}

Either bound may be infinite to leave that end open:

$ wo 'TimeSeriesWindow[TimeSeries[{{1, 10}, {2, 20}, {3, 30}, {4, 40}}], {3, Infinity}]["Path"]'
{{3, 30}, {4, 40}}

TimeSeriesResample samples the piecewise-linear path at an even step, interpolating exactly:

$ wo 'TimeSeriesResample[TimeSeries[{{1, 10}, {3, 30}, {4, 40}}], 1]["Path"]'
{{1, 10}, {2, 20}, {3, 30}, {4, 40}}

$ wo 'TimeSeriesResample[TimeSeries[{{1, 10}, {2, 15}, {4, 20}}], 1]["Path"]'
{{1, 10}, {2, 15}, {3, 35/2}, {4, 20}}

TimeSeriesShift moves every time stamp, and TimeSeriesMap transforms every value:

$ wo 'TimeSeriesShift[TimeSeries[{{1, 10}, {2, 20}}], 5]["Path"]'
{{6, 10}, {7, 20}}

$ wo 'TimeSeriesMap[# + 1 &, TimeSeries[{{1, 10}, {2, 20}}]]["Path"]'
{{1, 11}, {2, 21}}

TimeSeriesThread hands the function the values the series share at each time stamp:

$ wo 'TimeSeriesThread[Total, {TimeSeries[{{1, 10}, {2, 20}}], TimeSeries[{{1, 1}, {2, 2}}]}]["Path"]'
{{1, 11}, {2, 22}}

RegularlySampledQ asks whether the stamps are evenly spaced, and TimeSeriesInsert keeps the path sorted:

$ wo '{RegularlySampledQ[TimeSeries[{{1, 10}, {2, 20}, {3, 30}}]], RegularlySampledQ[TimeSeries[{{1, 10}, {2, 20}, {4, 40}}]]}'
{True, False}

$ wo 'TimeSeriesInsert[TimeSeries[{{1, 10}, {3, 30}}], {2, 20}]["Path"]'
{{1, 10}, {2, 20}, {3, 30}}

Arithmetic keeps the time stamps and works on the values:

$ wo 'Normal[2*TimeSeries[{{1, 10}, {2, 20}}] + 1]'
{{1, 21}, {2, 41}}

TimeSeriesRescale carries the time stamps linearly onto a given span, keeping their spacing and the values:

$ wo 'TimeSeriesRescale[TimeSeries[{{1, 10}, {2, 20}, {4, 40}}], {0, 1}]["Times"]'
{0, 1/3, 1}

A series runs in time order however its points were written:

$ wo 'TimeSeries[{{1, 10}, {5, 50}, {2, 20}}]["Path"]'
{{1, 10}, {2, 20}, {5, 50}}

MovingMap over a series windows by time rather than by count: the function sees the values whose stamps fall in [t - n, t], and the result is stamped at t. Unevenly spaced stamps therefore put different numbers of points in each window, and one that would reach back past the start of the series is dropped:

$ wo 'MovingMap[Total, TimeSeries[{{1, 1}, {2, 2}, {4, 4}, {7, 7}}], 2]["Path"]'
{{4, 6}, {7, 7}}

A plain list still windows by count:

$ wo 'MovingMap[Total, {1, 2, 3, 4}, 1]'
{3, 5, 7}

EventSeries

An EventSeries records events at particular times rather than a sampled signal. EventSeriesQ recognizes one, and Normal unwraps it back to {time, value} pairs:

$ wo 'EventSeriesQ[EventSeries[{{1, a}, {2, b}}]]'
True

$ wo 'EventSeriesQ[TimeSeries[{{1, 1}, {2, 2}}]]'
False

$ wo 'Normal[EventSeries[{{1, a}, {2, b}}]]'
{{1, a}, {2, b}}

EventSeriesLookup[series, t] gives the events nearest to t. A time between two events picks the closer one, and a time outside the range picks the nearest end:

$ wo 'EventSeriesLookup[EventSeries[{{1, a}, {2, b}, {5, c}}], 3]'
{{2, b}}

$ wo 'EventSeriesLookup[EventSeries[{{1, a}, {2, b}, {5, c}}], 10]'
{{5, c}}

A time exactly between two events is equidistant from both, so both come back:

$ wo 'EventSeriesLookup[EventSeries[{{1, a}, {2, b}, {5, c}}], 7/2]'
{{2, b}, {5, c}}

EventSeriesAccumulate gives the running count of events as a TimeSeries. The values themselves play no part — what accumulates is how many events have occurred:

$ wo 'Normal[EventSeriesAccumulate[EventSeries[{{1, 5}, {2, 7}, {5, 9}}]]]'
{{1, 1}, {2, 2}, {5, 3}}