Below is an example of data output. It represents indicies [y-axis] calculated for 52 weeks in a range of 64 years. Group of 64 years is classified and several years are represented with blue, some with red, and remaining largest portion with black. For each week, there is a distribution of values observed in the past in respective group and the mean is represented with the line and cloud represents SE. My question is - what is the methodology that can be used to say, some week ranges are significantly different from others? Do I make 52 tests or is there something more compact? What test would be most appropriate?
The graph looks like you made it with an R? Did you make it with 'geom_plot' from 'ggplot2'? If so you could use the grey confidence intervalls. In VAR analysis it is mostly argued that if the areas do NOT overlap there is a significant difference. (Of course, the width of the intervals can and should be discussed.)