This paper examines the impact of intraday periodicity on forecasting realized volatility using a heterogeneous autoregressive model (HAR) framework. We show that periodicity inflates the variance of the realized volatility and biases jump estimators. This combined effect adversely affects forecasting. To account for this, we propose a periodicity-adjusted model, HARP, where predictors are built from the periodicity-filtered data. We demonstrate empirically (using 30 stocks from various business sectors and the SPY for the period 2000--2016) and via Monte Carlo simulations that the HARP models produce significantly better forecasts, especially at the 1-day and 5-days ahead horizons.