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Statistics

  

Difference

  

compute lagged differences between elements in a data set

 

Calling Sequence

Parameters

Options

Description

Examples

Compatibility

Calling Sequence

Difference( X )

Difference( X, options )

Parameters

X

-

data set, DataSeries, DataFrame, or TimeSeries; numeric list of values

options

-

(optional) equation(s) of the form option=value where option can be times or lag

Options

• 

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.

Description

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.

Examples

with(Statistics):

Define some data:

x := <seq(i^2, i=1..10)>;

149162536496481100

(1)

To compute the differences between terms in the data, the Difference command is used.

Difference( x );

35791113151719

(2)

The times option makes it possible to apply the difference multiple times.

Difference( x, times=2 );

22222222

(3)

Note that this is equivalent to running:

Difference( Difference( x ) );

22222222

(4)

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 );

812162024283236

(5)

The Difference command can also be applied directly to TimeSeries data.

ts := TimeSeriesAnalysis:-TimeSeries([1,4,9,16]);

tsTime seriesdata set4 rows of data:2016 - 2019

(6)

Difference(ts);

Time seriesdata set (differenced)3 rows of data:2017 - 2019

(7)

GetData(%);

3.05.07.0

(8)

 

Compatibility

• 

The Statistics[Difference] command was introduced in Maple 2019.

• 

For more information on Maple 2019 changes, see Updates in Maple 2019.

See Also

Statistics

TimeSeriesAnalysis[Difference]