compute lagged differences between elements in a data set
Difference( X )
Difference( X, options )
data set, DataSeries, DataFrame, or TimeSeries; numeric list of values
(optional) equation(s) of the form option=value where option can be times or lag
times : posint; positive integer value indicating the number of times (order) to perform lagged differences. The default is 1.
lag : posint; positive integer value indicating the lag (staggering) of the differenced elements. The default is 1.
The Difference command is used to compute lagged differences between elements in a data set. If X is a vector of length n and times = 1, then the computed result is equal to the successive differences X[(1+lag)..n] - X[1..(n-lag)]. If X is a multi-column data set, then the differencing algorithm is run on each column of data individually.
Define some data:
x := <seq(i^2, i=1..10)>;
To compute the differences between terms in the data, the Difference command is used.
Difference( x );
The times option makes it possible to apply the difference multiple times.
Difference( x, times=2 );
Note that this is equivalent to running:
Difference( Difference( x ) );
The lag option staggers the differencing. Using a lag of 2 subtracts the first value from the third value, the second from the fourth, and so on:
Difference( x, lag=2 );
The Difference command can also be applied directly to TimeSeries data.
ts := TimeSeriesAnalysis:-TimeSeries([1,4,9,16]);
ts≔Time seriesdata set4 rows of data:2016 - 2019
Time seriesdata set (differenced)3 rows of data:2017 - 2019
The Statistics[Difference] command was introduced in Maple 2019.
For more information on Maple 2019 changes, see Updates in Maple 2019.
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