# Suggestions for appropriate time series model , continuous outcome, time varying covariates

I am a dealing with a dataset which is as follows

   y       x1    x2    time    n
0.12    1     0     0       18
0.3031  2     0     1       17
.       .     .     .       .
.       .     .     .       .
1.15    3     2     23      17


where

• outcome y (CO2, Carbon DiOxide)

• is continuous
• not independent because, at time = 0 , n = 18 (there were 18 pigs in the study). Then at time = 1, n=17 (one pig was lost, we dont know the reason why but the pig was not part the study at time =1). The Carbon emission was 0.12 at t=0, n=18, at t =1, carbon emission was 0.3031 it could be from the same 17 pigs in t=0 or a combination of old and new pigs we dont know. So for this reason I like to assume that y is not independent
• regressor x

• are time varying
• Error

• Hetroscedastic

Based on these assumptions, what modeling approach should I use if my goal is to predict y ? Any help would be much appreciated. Thanks.