Estimates of influenza-associated excess mortality have been widely published using different regression models with time series data. These methods result in variability of estimates and few have appropriately addressed limitations with over-dispersion and auto-correlation in a time series. We used United States Census, vital records, and influenza viral surveillance data from 1981-2014 to evaluate two methods to address temporal autocorrelation in residuals and over dispersion in deaths. We used a double bootstrap model that extends existing generalized linear model approaches and a Bayesian hierarchical model. Age-specific seasonal influenza-associated excess deaths were estimated from all respiratory coded-deaths and we assessed model performance using simulation. We found the Bayesian hierarchical model produced smaller estimates compared with the bootstrap, possibly due to better control for unmeasured temporal confounders. While the Bayesian model produced smaller estimates, the bootstrap produced reasonably similar estimates and either method could be used to address the methodological limitations.