Seasonal influenza in the United States is estimated to cause 9-35 million illnesses annually, with resultant economic burden amounting to $47-$150 billion. Reliable real-time forecasts of influenza can help public health agencies better manage these outbreaks. Here, we investigate the feasibility of three autoregressive methods for near-term forecasts: an Autoregressive Integrated Moving Average (ARIMA) model with time-varying order; an ARIMA model fit to seasonally adjusted incidence rates (ARIMA-STL); and a feed-forward autoregressive artificial neural network with a single hidden layer (AR-NN). We generated retrospective forecasts for influenza incidence one to four weeks in the future at US National and 10 regions in the US during 5 influenza seasons. We compared the relative accuracy of the point and probabilistic forecasts of the three models with respect to each other and in relation to two large external validation sets that each comprise at least 20 other models. Both the probabilistic and point forecasts of AR-NN were found to be more accurate than those of the other two models overall. An additional sub-analysis found that the three models benefitted considerably from the use of search trends based 'nowcast' as a proxy for surveillance data, and these three models with use of nowcasts were found to be the highest ranked models in both validation datasets. When the nowcasts were withheld, the three models remained competitive relative to models in the validation sets. The difference in accuracy among the three models, and relative to models of the validation sets, was found to be largely statistically significant. Our results suggest that autoregressive models even when not equipped to capture transmission dynamics can provide reasonably accurate near-term forecasts for influenza. Existing support in open-source libraries make them suitable non-naïve baselines for model comparison studies and for operational forecasts in resource constrained settings where more sophisticated methods may not be feasible.