Q: Load curves: similarity check-up

[netstrider]

Hi,
I have to compare different load curves (electricity), eg. curves 2-20 with a curve 1. Every curve is represented as array of 24 values (hourly values), with no discontinuity (all values are above 0). I have to find which curve 2-20 is most similar to curve 1. I'm using Excel, but other tools are in as well (Matlab, Mathematica, pen & paper). As you can see, my knowledge of math is very limited. I've found two
functions in Excel, CORREL (correlation ratio, I presume it is linear
correlation ratio) and COVAR. I also tried my formula which is
=ABS((B2-C2)*(B3-C3)*(B4-C4)...(B25-C25)), that is |Product(xi-yi)|, Vi<n

Please tell me which is best formula to determine shape similarity (from my point of view, CORREL seems the best) and why. Also, if it isn't the same formula, which formula would be best to determine similarity overall (two curves of same shape don't have to overlap, e.g. if they same relativedistance between all of the 24 values)?
Thanks to you all

 

[Valkarie]

in advance.The best formula to determine shape similarity would be to use a correlation coefficient, such as the Pearson correlation coefficient. This is because correlation coefficients measure the strength of the relationship between two variables, and they take into account the magnitude of the differences between the points. The Pearson correlation coefficient can range from -1 to 1, with -1 representing a perfect negative correlation (i.e., one point goes up as the other goes down), 0 representing no correlation, and 1 representing a perfect positive correlation (i.e., both points move in the same direction). Therefore, if two load curves have a high Pearson correlation coefficient, then it is likely that they have similar shapes. For determining overall similarity, you could use the Euclidean distance or the Manhattan distance. The Euclidean distance is the straight line distance between two points, while the Manhattan distance is the sum of the absolute values of the differences between the points. For example, if you have two curves that have 24 points each, then the Euclidean distance would be the sum of the squares of the differences between the 24 points. The Manhattan distance would be the sum of the absolute values of the differences between the 24 points. Both of these measures give an indication of how close the two curves are overall, even if they do not have the exact same shape.