I develop a multi-period trading model to analyze how a fundamental trader adjusts his trading strategies and information production decisions to the existence of high frequency trading (HFT). I show that these decisions differ strongly depending on the type of information that the HFT can observe. Information correlated with past trading activity reduces fundamental trading and information production, and leads to lower price informativeness, compared to a benchmark without HFT. HFT information correlated with fundamental information does not induce these effects, and prices may become more informative on average. Moreover, I study the ability of prices to reflect the asset value and produced information over time. My results are consistent with empirical findings highlighting that HFT enhances price discovery in the short run, and others suggesting that HFT reduces the ability of prices to reflect long-term fundamental information.