# ARMA parameters estimation

I'm trying to estimate parameters of ARMA. Ljung-Box statistic reveals no serial correlation in residuals. But one coefficient is statistically insignificant. When I remove the variable corresponding to this coefficient I get a model that is worse than the former one(AIC and SC choose the first model, Ljung-Box statistic reveal serial correlation in residuals for the second(reduced) model). Should I choose the first model with statistically insignificant coefficient? And one more question: if I use assumption about t-distribution of errors then how to check whether a coefficient equals zero(i.e. which statistic should I use and what distribution does it have?)

As regards your second question, you may take as a rough guide a $\sim 95\%$ confidence interval by taking two times the standard error of the parameter estimates and see if zero lies within it, but as said before, this may not give you enough conclusive information.