Comovement Plot

COMOVEMENT PLOT
Name:
...COMOVEMENT PLOT
Type:
Graphics Command
Purpose:
Generates a comovement plot.
Description:
A comovement plot is a graphical data analysis technique for determining if comovement exists between:

lags for a single time series (an autocomovement plot);
lags for two time series (a cross-comovement plot).

The comovement plot consist of:
Vertical axis = comovement coefficient (a value between -1 and 1);
Horizontal axis = lag (an integer between 1 and n/4 where = number of observations).
The Leigh-Perlman comovement coefficient is the sum of cross products divided by N-1. The equation for the lag k comovement coefficient is:

\( C_k = \frac{\sum_{i=k+1}^{n}{(x_i - x_{i-k})(y_i - y_{i-k})}} {\sqrt{\sum_{i=k+1}^{n}{(x_i - x_{i-k})^2}\sum_{i=k+1}^{n}{(y_i - y_{i-k})^2}}} \)

The computed coefficient has a value between -1 and +1.
Syntax 1:
AUTOCOMOVEMENT PLOT <y> <SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Syntax 2:
CROSS-COMOVEMENT PLOT <y1> <y2> <SUBSET/EXCEPT/FOR qualification>
where <y1> is the first response variable;
<y2> is the second response variable;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
AUTOCOMOVEMENT PLOT Y
CROSS COMOVEMENT PLOT Y1 Y2

Note:
After generating an autocomovement or cross-comovement plot, the variable YPLOT contains the numerical values for the correlations. If you need to do additional analysis, or simply wish to print the numeric values, copy this variable to a user variable (e.g., LET COMOVE = YPLOT). The YPLOT variable is overwritten when the next plot is generated.
Note:
The LINE, CHARACTER, SPIKE, and BAR commands can be used to control the appearance of the comovement plot. For example, some analysts prefer to draw comovements as spikes from the zero baseline. Trace 1 is the comovement line and trace 2 is the line at zero.
Note:
The number of lags is determined automatically. If you want to override the default, enter one of the following commands:

LET LAGS = <value>
LET LAG = <value>
LET NUMLAG = <value>

Default:
None
Synonyms:
None
Related Commands:

COMOVEMENT = Compute the comovement statistic.

CORRELATION PLOT = Generates an auto or cross correlation plot.

SPECTRUM = Generates a spectral plot.

CHARACTERS = Sets types for plot characters.

LINES = Sets types for plot lines.

SPIKES = Sets on/off switches for plot spikes.

Reference:

"An Index for Comovement of Time Sequences with Geophysical Applications: A Working Paper", Penn State Interface Conference on Astronomy, August, 1991. Applications:

Time Series Analysis Implementation Date:

1997/12 Program 1:

Program 2: