computes the mean value of tseries over non-overlapping windows of width dt.


applies the function f to the values of tseries in non-overlapping windows of width dt.


  • TimeSeriesAggregate is often used in time series analysis to compute aggregated statistics like yearly averages or monthly totals.
  • TimeSeriesAggregate breaks the time series tseries into disjoint left-closed and right-open windows of equal width dt and applies a function f to the values in each segment.
  • If there are no values in a segment, the segment is ignored.
  • The time series tseries can be a list of values {x1,x2,}, a list of time-value pairs {{t1,x1},{t2,x2},}, a TimeSeries, EventSeries, or TemporalData.
  • The window width dt can be given as a positive number, a Quantity, or as a date increment.
  • The window specification {dt,align} can be used to determine the alignment of new times within each window.
  • Settings for window alignment align include Left, Center (default), and Right.
  • TimeSeriesAggregate threads pathwise for multipath TemporalData.


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Basic Examples  (3)

Average successive pairs of values:

Compute the quarterly standard deviation for a financial time series:

Aggregate multiple paths simultaneously:

Average over blocks of width 0.15:

Scope  (20)

Basic Uses  (3)

Map a function f over data with blocks of width 2:

Compute the 95^(th) quantile for windows of width 0.05:

Find a quartile envelope for blocks of size 10:

Data Types  (8)

Aggregate a vector in blocks of 4 using a function f:

Find the two-year average for a list of time-value pairs:

Compute the maximum for width-10 segments of a TimeSeries:

Compute a width-10 median for TemporalData:

Compute a width-5 total for an EventSeries:

Compute a six-month variance for multiple paths simultaneously:

Aggregate over vector-valued data:

Componentwise width-5 range:

Visualize the range:

Aggregate over a time series involving quantities:

Window Widths  (5)

Use windows with width 2:


Specify the window width in calendar time:

Average over windows spanning five days:

Specify a window width using Quantity:

Average over windows spanning two quarters:

Specify a mixed radix width:

Average over windows spanning three weeks and two days:

Larger windows smooth more:

Moving averages with increasing window width:

Alignment  (4)

Align new times with the center of the windows:

Center alignment is used by default:

Align new times with the right side of the windows:

Align new times with the left side of the windows:

Compare window alignments:

The values are all equivalent:

The times are not:

A visual comparison:

Applications  (2)

Market Volatility  (1)

Identify periods of high volatility in the S&P 500:

Five-year standard deviation:

Annual interquartile range:

Two-year range:

Labor Force  (1)

Visualize the growth of labor force in California based on monthly data:

Aggregate the data yearly:

Properties & Relations  (1)

Independently of the alignment the windows are closed on the left and open on the right:

It is possible that more time stamps are needed:

Wolfram Research (2014), TimeSeriesAggregate, Wolfram Language function, https://reference.wolfram.com/language/ref/TimeSeriesAggregate.html (updated 2017).


Wolfram Research (2014), TimeSeriesAggregate, Wolfram Language function, https://reference.wolfram.com/language/ref/TimeSeriesAggregate.html (updated 2017).


@misc{reference.wolfram_2021_timeseriesaggregate, author="Wolfram Research", title="{TimeSeriesAggregate}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/TimeSeriesAggregate.html}", note=[Accessed: 21-June-2021 ]}


@online{reference.wolfram_2021_timeseriesaggregate, organization={Wolfram Research}, title={TimeSeriesAggregate}, year={2017}, url={https://reference.wolfram.com/language/ref/TimeSeriesAggregate.html}, note=[Accessed: 21-June-2021 ]}


Wolfram Language. 2014. "TimeSeriesAggregate." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/TimeSeriesAggregate.html.


Wolfram Language. (2014). TimeSeriesAggregate. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TimeSeriesAggregate.html