SEQUENTIAL DIFFERENCE

SEQUENTIAL DIFFERENCE (LET)

Let Subcommand

Compute the sequential differences (i.e., X(I) - X(I-1)) between the elements of a variable.

Given a data series with N points, the sequential difference will contain the points

         Y(1) = X(2) - X(1)
         Y(2) = X(3) - X(2)
              ...
         Y(N-1) = X(N) - X(N-1)
         

If there are less than two points in the series, nothing will be done.

One use of sequential differencing is to remove trend from time series data.

The 2016/02 version of Dataplot generalized this command in the following two ways.

1. In additon to the difference, the following additional sequential values can also be computed:

   SEQUENTIAL SUM	-	X(I) + X(I-1)
   SEQUENTIAL PRODUCT	-	X(I) * X(I-1)
   SEQUENTIAL MEAN	-	(X(I) + X(I-1))/2
   SEQUENTIAL MINIMUM	-	MIN(X(I), X(I-1))
   SEQUENTIAL MAXIMUM	-	MAX(X(I), X(I-1))
   SEQUENTIAL LOWER	-	X(I-1)
   SEQUENTIAL UPPER	-	X(I)

2. A group-id variable can be included. That is, the data values in each group will differenced. If there are K groups, then the differenced series will have N - K points.

   The original data series does not have to be sorted by group. However, the output series will be sorted as follows:

   • The data will be sorted by group in the order that the groups are detected in the original series.

   • Within a group, the order in the output series will be based on the order of the input series.

   For example, if X is the group-id variable and Y is the response variable

   X(1)	=	1
   X(2)	=	2
   X(3)	=	3
   X(4)	=	1
   X(5)	=	2
   X(6)	=	3
   X(7)	=	1
   X(8)	=	2
   X(9)	=	3

   then the output group-id variable (X2) and differenced variable will be in the order

   X2(1) = 1,		Y2(1) = Y(4) - Y(1)
   X2(2) = 1,		Y2(2) = Y(7) - Y(4)
   X2(3) = 2,		Y2(3) = Y(5) - Y(2)
   X2(4) = 2,		Y2(4) = Y(8) - Y(5)
   X2(5) = 3,		Y2(5) = Y(6) - Y(3)
   X2(6) = 3,		Y2(6) = Y(9) - Y(6)

LET <y> = SEQUENTIAL <stat> <x>             <SUBSET/EXCEPT/FOR qualification>
where <x> is the response variable;
            <stat> is one of
DIFFERENCE
SUM
PRODUCT
MEAN
MINIMUM
MAXIMUM
LOWER
UPPER;

            <y> is a variable containing the differenced series;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET <y2> <x2> = SEQUENTIAL <stat> <y> <x>
                        <SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable;
            <x> is a the group-id variable;
            <stat> is one of
DIFFERENCE
SUM
PRODUCT
MEAN
MINIMUM
MAXIMUM
LOWER
UPPER;

            <y2> is a variable containing the differenced series;
            <x2> is a variable containing the group-id of the differenced series;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET XD = SEQUENTIAL DIFFERENCE PRESSURE
LET XD = SEQUENTIAL MEAN PRESSURE
LET XD = SEQUENTIAL SUM PRESSURE
LET XD = SEQUENTIAL DIFFERENCE PRESSURE SUBSET X > 4
LET YDIFF X2 = SEQUENTIAL DIFFERENCE Y X

None

DIFFERENCE is a synonym for SEQUENTIAL DIFFERENCE
SEQUENTIAL AVERAGE is a synonym for SEQUENTIAL MEAN
SEQUENTIAL MIN is a synonym for SEQUENTIAL MINIMUM
SEQUENTIAL MAX is a synonym for SEQUENTIAL MAXIMUM

CUMULATIVE SUM	= Compute the cumulative sum of the elements of a variable.
SORT	= Sort the elements of a variable.
COCODE	= Generate a cocoded variable.
CODE	= Generate a coded variable.
SEQUENCE	= Generate a sequence of numbers.
PATTERN	= Generate numbers with a specific pattern.

Data Transformations

Pre-1987
2016/02: Support for SUM, PRODUCT, MEAN
2016/02: Support for MINIMUM, MAXIMUM, LOWER, and UPPER
2016/02: Support for group-id variable<

LET X1 = DATA 12 4 2 3 9 7
LET XD = SEQUENTIAL DIFFERENCE X1
    

The variable XD will contain the following values:
8, 2, 1, 6, 2

 
. Step 1:   Define the data
.
let y = sequence 1 1 10
.
. Step 2:   Compute the sequential statistics
.
let ydiff = sequential difference y
let ysum  = sequential sum        y
let yprod = sequential product    y
let ymean = sequential mean       y
let ymin  = sequential min        y
let ymax  = sequential max        y
.
. Step 3:   Print the results
.
set write decimals 1
print y ydiff ysum yprod ymean ymin ymax
    

The following output is generated.

------------------------------------------------------------
              Y          YDIFF           YSUM          YPROD
------------------------------------------------------------
            1.0            1.0            3.0            2.0
            2.0            1.0            5.0            6.0
            3.0            1.0            7.0           12.0
            4.0            1.0            9.0           20.0
            5.0            1.0           11.0           30.0
            6.0            1.0           13.0           42.0
            7.0            1.0           15.0           56.0
            8.0            1.0           17.0           72.0
            9.0            1.0           19.0           90.0
           10.0            0.0            0.0            0.0
 
 
------------------------------------------------------------
              Y          YMEAN           YMIN           YMAX
------------------------------------------------------------
            1.0            1.5            1.0            2.0
            2.0            2.5            2.0            3.0
            3.0            3.5            3.0            4.0
            4.0            4.5            4.0            5.0
            5.0            5.5            5.0            6.0
            6.0            6.5            6.0            7.0
            7.0            7.5            7.0            8.0
            8.0            8.5            8.0            9.0
            9.0            9.5            9.0           10.0
           10.0            0.0            0.0            0.0
    

 
. Step 1:   Define the data
.
dimension 40 columns
let y = sequence 1 1 10
let x = sequence 1 5 1 2
.
. Step 2:   Compute the sequential statistics
.
let ydiff ygroup = sequential difference y x
let ysum  ygroup = sequential sum        y x
let yprod ygroup = sequential product    y x
let ymean ygroup = sequential mean       y x
let ymin  ygroup = sequential min        y x
let ymax  ygroup = sequential max        y x
let ylow  ygroup = sequential lower      y x
let yupp  ygroup = sequential upper      y x
.
. Step 3:   Print the results
.
set write decimals 1
print ygroup ydiff ysum yprod ymean ymin ymax ylow yupp
    

The following output is generated.

---------------------------------------------------------------------------
         YGROUP          YDIFF           YSUM          YPROD          YMEAN
---------------------------------------------------------------------------
            1.0            1.0            3.0            2.0            1.5
            1.0            1.0            5.0            6.0            2.5
            1.0            1.0            7.0           12.0            3.5
            1.0            1.0            9.0           20.0            4.5
            2.0            1.0           13.0           42.0            6.5
            2.0            1.0           15.0           56.0            7.5
            2.0            1.0           17.0           72.0            8.5
            2.0            1.0           19.0           90.0            9.5
 
 
---------------------------------------------------------------------------
         YGROUP           YMIN           YMAX           YLOW           YUPP
---------------------------------------------------------------------------
            1.0            1.0            2.0            1.0            2.0
            1.0            2.0            3.0            2.0            3.0
            1.0            3.0            4.0            3.0            4.0
            1.0            4.0            5.0            4.0            5.0
            2.0            6.0            7.0            6.0            7.0
            2.0            7.0            8.0            7.0            8.0
            2.0            8.0            9.0            8.0            9.0
            2.0            9.0           10.0            9.0           10.0