How do I get the proper p-value of a time series average of regression coefficients?

Question

I have run cross-sectional regression on the returns of 50 companies on 16 regressors, for 128 days. The regression output looks something like this:

          Day1       Day2   ...   Day128 
Var1      c_1,1      c_1,2        c_1,128
Var2      c_2,1      c_2,2        c_2,128
 .
 .
 .
Var 16   c_16,1     c_16,2        c_16,128

Also for each coefficient I have the p_value availlable. Next I want to take the time series average of the coefficient for each regression variable, that is I want to take te average across all days of the regression estimates.

The main question I have is, how do i get the p-value (or t-statistic) of these time series averages?

Any help would be much appreciated