Nischal Piratla wrote: > Given the random process X = [X1,X2,.Xt,Xt+1..XN]'. I have got scatter > plots with Xt, Xt+i for all i = 1,2,3... If these plots do not have > any pattern and I see a bunch of patches, can I conclude that the > random variables X1, X2, X3, .. are independent? If not, can you > please provide a counter argument. > Being a computer engineer, I would really appreciate a reference. > Nischal Piratla http://lamar.colostate.edu/~nischal
It is a good idea to do the plots you suggested. If one was more paranoid, you could also do plots at lag 2, and at lag 3, etc. If you compute the AutoCorrelation Function (ACF), this will give you the correlation at each lag value. Many programs (such as S/Splus/R) will also draw dashed lines on each side of zero that are significance bands; if the ACF is outside those lines, then it is statistically significantly different from zero. So if the ACF falls within the lines, you can be fairly confident that the random variables are independent (at least linearly, since the usual correlation is a measurement of linear relationship). Depending on the distribution of the X values, you might also want to do your plots after a transformation. In particular, if your variables have an Exponential distribution, they tend to cluster toward the axes, and it's hard to spot any patterns in the mess. However, if you plot exp(-Xt) versus exp(-(Xt+1)), the plot should have a U(0,1) distribution on both axes. Sorry that I don't have any references for you. I look forward to hearing other people's ideas too. Andrew -- Andrew Ross Industrial and Systems Engineering Lehigh University, www.lehigh.edu/~inime/ Bethlehem, Pennsylvania, USA remove all digits <=4 from my e-mail address to reply . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
