This paper introduces a parsimonious and yet flexible nonnegative semiparametric model to forecast financial volatility. The new model extends the linear nonnegative autoregressive model of Barndorff-Nielsen & Shephard (2001) and Nielsen & Shephard (2003) by way of a power transformation. It is semiparametric in the sense that the dependency structure and distributional form of its error component are left unspecified. The statistical properties of the model are discussed and a novel estimation method is proposed. Simulation studies validate the new estimation method and suggest that it works reasonably well in finite samples. The out-of-sample performance of the proposed model is evaluated against a number of standard methods, using data on S&P 500 monthly realized volatilities. The competing models include the exponential smoothing method, a linear AR(1) model, a log-linear AR(1) model, and two long-memory ARFIMA models. Various loss functions are utilized to evaluate the predictive accuracy of the alternative methods. It is found that the new model generally produces highly competitive forecasts.