The Aggregate command takes a TimeSeries data set, and transforms it into a data set with a different (typically lower) frequency. For example, it transforms weekly into monthly data.

The Aggregate command examines the first and last time point for which data exist in timeseries. It then divides the time in between up into periods corresponding to the frequency argument; for example, if frequency is monthly, it looks at the month including the first data point up to the month including the last data point. The existing data for each period are combined in a way determined by the combine option; by default, by just taking the last data value from that period. Finally, a new TimeSeries object is created that contains the combined data, and associated time points chosen according to the date option.

The frequency parameter determines the new frequency of the data.

Possible values are the names hourly, daily, weekly, monthly, quarterly, yearly, or annual; or equivalently, the same as strings, "hourly", etc. The values yearly and annual are the same.

Another option is to use a positive integer for this parameter. This represents a time period of that number of seconds. For example, using 3600 would have the same result as hourly.

The combine option can take a few keyword values, or a user-supplied procedure. The keywords are max, min, sum, mean, weightedmean, first, and last; or equivalently, the same strings, "max", etc. The name or string weightedmean can be indexed by the name first, last, or middle (but not strings - one cannot index strings by strings).

With combine = max or combine = min or combine = sum, the value for the new data set is the maximum or minimum or sum of the values for the given period, respectively.

With combine = mean or combine = weightedmean, the value for the new data set is the arithmetic mean of the values for the given period; in the first case, unweighted, and in the second case, weighted by the length of the interval. If weightedmean is indexed by first, then it is assumed that the dates for the time series are the first in their period, and the weight of a value is the length of the period between the current date and the next one. If weightedmean is indexed by last, then it is assumed that the dates for the time series are the last in their period, and the weight of a value is the length of the time period between the previous date and the current one. If weightedmean is indexed by middle, or not indexed at all, then it is assumed that the period boundaries are in the middle between the specified dates, and the weight of a value is half the length of the time period between the previous date and the next one.

With combine = first or combine = last (the default), the value for the new data set is the first or last of the values for the given period, respectively.

When using combine = p or combine = [p, nodates] or combine = [p, dates], where p is a custom procedure and the names nodates and dates are included literally, the procedure p is called for every period. When using combine = p or combine = [p, nodates], it is called as p(v), and when using combine = [p, dates], it is called as p(v, d); the values of the parameters are as follows:

v is Vector of the n data values for the given period; n is zero or more.

d is the Vector of n+2 dates corresponding to the data in v, and the last date before it and the first date after it, in order, expressed as the number of seconds elapsed since January 1st, 1970. For the purposes of this argument d, the sequence of dates in the time series is temporarily extended by an interval at the beginning equal to the first interval, and an interval at the end equal to the last interval.

p should return the value to be used for the given period. This should be a value that can be stored in a Matrix with datatype float. If it throws an error for any value, $\mathrm{undefined}$ will be used (that is, the data will be considered missing).

For all of the combining methods, if there are no data points for any period, the result will be obtained from applying the given procedure to a Vector with zero entries. In particular, max will use $-\mathrm{\infty }$, min will use $\mathrm{\infty }$, sum will use $0$, and mean, first, and last will all use $\mathrm{undefined}$.

The date option (which can also be spelled dates) can have the values first, last, or default; or equivalently, the same strings, "first", etc. This option determines the time points with which the given periods are marked in the resulting TimeSeries.

With dates = first, the resulting data are considered to occur at the first second of the given period.

With dates = last, the resulting data are considered to occur at the last second of the given period.

The option dates = default (the default) works like dates = last, unless combine = first is given, in which case it works like dates = first.

You can specify extra options, such as period or headers, that are accepted by the TimeSeries constructor. These are passed on to that constructor.

$\mathrm{with}\left(\mathrm{TimeSeriesAnalysis}\right)\:$

$\mathrm{sales\_numbers}≔⟨150\,147\,114\,113\,91\,164\,56\,39\,32\,86\,91\,125\,100\,106\,88\,151\,90\,104\,86\,103\,96\,77\,90\,94\,88\,86\,87\,113\,100\,93\,97\,99\,95\,92\,81\,89\,71\,110\,127\,105⟩$

$\mathrm{sales}≔\mathrm{TimeSeries}\left(\mathrm{sales\_numbers}\,\mathrm{startdate}=''2010-01-01''\,\mathrm{frequency}=''weekly''\,\mathrm{header}=''Weekly\; Sales''\right)$

$\mathrm{sales}≔\left[\begin{array}{c}\mathrm{Time\; series}\\ \mathrm{Weekly\; Sales}\\ \mathrm{40\; rows\; of\; data:}\\ \mathrm{2010-01-01\; -\; 2010-10-01}\end{array}\right]$

$\mathrm{GetData}\left(\mathrm{sales}\right)\left[..5\right]$

$\left[\begin{array}{c}150.\\ 147.\\ 114.\\ 113.\\ 91.\end{array}\right]$

$\mathrm{TimeSeriesPlot}\left(\mathrm{sales}\right)$

$\mathrm{total\_monthly\_sales}≔\mathrm{Aggregate}\left(\mathrm{sales}\,\mathrm{monthly}\,\mathrm{combine}=\mathrm{sum}\,\mathrm{header}=''Approx.\; Total\; Monthly\; Sales''\right)$

$\mathrm{total\_monthly\_sales}≔\left[\begin{array}{c}\mathrm{Time\; series}\\ \mathrm{Approx.\; Total\; Monthly\; Sales}\\ \mathrm{10\; rows\; of\; data:}\\ \mathrm{2010-01-31\; -\; 2010-10-31}\end{array}\right]$

$\mathrm{GetData}\left(\mathrm{total\_monthly\_sales}\right)\left[..5\right]$

$\left[\begin{array}{c}615.\\ 291.\\ 402.\\ 539.\\ 362.\end{array}\right]$

$\mathrm{GetDates}\left(\mathrm{total\_monthly\_sales}\right)\left[..5\right]$

$\left[\begin{array}{c}''2010-01-31''\\ ''2010-02-28''\\ ''2010-03-31''\\ ''2010-04-30''\\ ''2010-05-31''\end{array}\right]$

$\mathrm{TimeSeriesPlot}\left(\mathrm{sales}\,\mathrm{total\_monthly\_sales}\right)$

$\mathrm{total\_monthly\_sales\_2}≔\mathrm{Aggregate}\left(\mathrm{sales}\,\mathrm{monthly}\,\mathrm{combine}=\mathrm{sum}\,\mathrm{dates}=\mathrm{first}\,\mathrm{header}=''Approx.\; Total\; Monthly\; Sales''\right)$

$\mathrm{total\_monthly\_sales\_2}≔\left[\begin{array}{c}\mathrm{Time\; series}\\ \mathrm{Approx.\; Total\; Monthly\; Sales}\\ \mathrm{10\; rows\; of\; data:}\\ \mathrm{2010-01-01\; -\; 2010-10-01}\end{array}\right]$

$\mathrm{GetData}\left(\mathrm{total\_monthly\_sales\_2}\right)\left[..5\right]$

$\left[\begin{array}{c}615.\\ 291.\\ 402.\\ 539.\\ 362.\end{array}\right]$

$\mathrm{GetDates}\left(\mathrm{total\_monthly\_sales\_2}\right)\left[..5\right]$

$\left[\begin{array}{c}''2010-01-01''\\ ''2010-02-01''\\ ''2010-03-01''\\ ''2010-04-01''\\ ''2010-05-01''\end{array}\right]$

$\mathrm{TimeSeriesPlot}\left(\mathrm{sales}\,\mathrm{total\_monthly\_sales}\,\mathrm{total\_monthly\_sales\_2}\right)$

$\mathrm{weekly\_sales\_avg\_per\_month}≔\mathrm{Aggregate}\left(\mathrm{sales}\,\mathrm{monthly}\,\mathrm{combine}=\mathrm{mean}\,\mathrm{header}=''Approx.\; Weekly\; Sales,\; Avg.\; per\; Month''\right)$

$\mathrm{weekly\_sales\_avg\_per\_month}≔\left[\begin{array}{c}\mathrm{Time\; series}\\ \mathrm{Approx.\; Weekly\; Sales,\; Avg.\; per\; Month}\\ \mathrm{10\; rows\; of\; data:}\\ \mathrm{2010-01-31\; -\; 2010-10-31}\end{array}\right]$

$\mathrm{GetData}\left(\mathrm{weekly\_sales\_avg\_per\_month}\right)\left[..5\right]$

$\left[\begin{array}{c}123.\\ 72.7500000000000\\ 100.500000000000\\ 107.800000000000\\ 90.5000000000000\end{array}\right]$

$\mathrm{TimeSeriesPlot}\left(\mathrm{sales}\,\mathrm{weekly\_sales\_avg\_per\_month}\right)$

$\mathrm{sales\_variability}≔\mathrm{Aggregate}\left(\mathrm{sales}\,\mathrm{monthly}\,\mathrm{combine}=\mathrm{Statistics}:-\mathrm{StandardDeviation}\,\mathrm{header}=''Sales\; Variability''\right)$

$\mathrm{sales\_variability}≔\left[\begin{array}{c}\mathrm{Time\; series}\\ \mathrm{Sales\; Variability}\\ \mathrm{10\; rows\; of\; data:}\\ \mathrm{2010-01-31\; -\; 2010-10-31}\end{array}\right]$

$\mathrm{TimeSeriesPlot}\left(\mathrm{sales}\,\mathrm{weekly\_sales\_avg\_per\_month}\,\mathrm{sales\_variability}\right)$

$\mathrm{results}≔⟨15\,30\,26\,43\,39\,76\,9\,74\,47\,65\,51\,18\,47\,49\,49\,47\,56\,51\,52\,52\,59\,43\,49\,77\,69\,87\,67\,62\,55\,42⟩$

$\mathrm{ts}≔\mathrm{TimeSeries}\left(\mathrm{results}\,\mathrm{startdate}=''2010-01-01''\,\mathrm{frequency}=''monthly''\,\mathrm{header}=''Results''\right)$

$\mathrm{ts}≔\left[\begin{array}{c}\mathrm{Time\; series}\\ \mathrm{Results}\\ \mathrm{30\; rows\; of\; data:}\\ \mathrm{2010-01-01\; -\; 2012-06-01}\end{array}\right]$

$\mathrm{GetData}\left(\mathrm{ts}\right)\left[..5\right]$

$\left[\begin{array}{c}15.\\ 30.\\ 26.\\ 43.\\ 39.\end{array}\right]$

$\mathrm{TimeSeriesPlot}\left(\mathrm{ts}\right)$

$\mathrm{umean\_results}≔\mathrm{Aggregate}\left(\mathrm{ts}\,\mathrm{quarterly}\,\mathrm{combine}=\mathrm{mean}\,\mathrm{header}=''Unweighted''\right)$

$\mathrm{umean\_results}≔\left[\begin{array}{c}\mathrm{Time\; series}\\ \mathrm{Unweighted}\\ \mathrm{10\; rows\; of\; data:}\\ \mathrm{2010-03-31\; -\; 2012-06-30}\end{array}\right]$

$\mathrm{wmean\_results}≔\mathrm{Aggregate}\left(\mathrm{ts}\,\mathrm{quarterly}\,\mathrm{combine}=\mathrm{weightedmean}\left[\mathrm{first}\right]\,\mathrm{header}=''Weighted''\right)$

$\mathrm{wmean\_results}≔\left[\begin{array}{c}\mathrm{Time\; series}\\ \mathrm{Weighted}\\ \mathrm{10\; rows\; of\; data:}\\ \mathrm{2010-03-31\; -\; 2012-06-30}\end{array}\right]$

$\mathrm{GetData}\left(\mathrm{umean\_results}\right)\left[..5\right]$

$\left[\begin{array}{c}23.6666666666667\\ 52.6666666666667\\ 43.3333333333333\\ 44.6666666666667\\ 48.3333333333333\end{array}\right]$

$\mathrm{GetData}\left(\mathrm{wmean\_results}\right)\left[..5\right]$

$\left[\begin{array}{c}23.4543770264011\\ 52.5164835164835\\ 43.2934782608696\\ 44.6007243096424\\ 48.3107920333488\end{array}\right]$

$\mathrm{TimeSeriesPlot}\left(\mathrm{ts}\,\mathrm{umean\_results}\,\mathrm{wmean\_results}\right)$

The TimeSeriesAnalysis[Aggregate] command was introduced in Maple 2015.

For more information on Maple 2015 changes, see Updates in Maple 2015.