# Modelling Time Series of percentages

I am trying to model a multivariate time series of percentages. And here's the kicker, at each point, each of my individual time series are bound between 0 and 1, and their Sum per period equals 1. An example of such time series would be,

Y1={0.1,0.3,0.6}
Y2={0.2,0.3,0.5}
...


I am thinking of using Genetic Programming and compare it with ARIMA to forecast in and out of sample. I was looking for a while on how to model these issues (someone on this forum with a similar problem modeled ratios, which is not an option for me). If there is no way, I will just model the time series as is and then shave off or add the proportional difference, but this seems like a very ad-hoc procedure. Any ideas?

A standard approach is to transform your series in a way that these constraints are satisfied automatically, e.g., by mapping $$y_{it}\mapsto \log(y_{it}/y_{0t})$$ for some base series $$y_{0t}$$. If the transformation, analysis and forecast does not depend on your particular choice of base series, that is a Good Thing.