statement of purpose I am currently finishing my MS in Economics and Finances and I intend to apply for a PhD in statistics. There are many reasons why I did not make an undergrad and grad in statistics but in economics, first of all the fact that in my previous university there was no statistics department. 

I'm searching for some advice regarding my statement of purpose since my previous experience is not necessary connected with Statistics. Should I make more emphasis on my quantitative background, on my motivation, on the reasons why I want to apply for this particular program, even though my background might not be entirely relevant?

Is there some advice you can give a student making this sort of "field-shift"?
Your CV should explain well what you have done in the past. Your SOP should be more future directed while also attempting to bridge the past and future. But don't think you just need to explain what is in your CV and neglect what you see as your future. Think about what you want to do and what you have already done that puts you on the path to achieving your future plans. So, yes, say something about your quantitative abilities and such. 

People will understand that others may want to change fields for a variety of reasons. You aren't unique in that so don't dwell too much on it. Say where you want to go, what you've done to get there already, and how this program will help you even more. But put the focus on the future, and not just the program you are applying for, but beyond that.