We present a MIxed DAta Sampling model for one-month- and two-months-ahead forecasts for the monthy changes in the Israel's CPI. This model enables us to incorporate daily financial and commodity price data in a monthly model by imposing a flexible Beta function on the lag distribution of the daily explanatory variables. Given the lag length, the parameters of those distributions can be optimized simultaneously with the regression coefficients. We also consider a more flexible Bayesian model, enabling to evaluate inter alia the most likely lag lengths, based on the frequency of their appearance in the Gibbs sample. We find that the proposed MIDAS specification improves the forecast ability, measured by the RMSFE (Root Mean Square Forecast Error) and MAFE (Mean Absolute Forecast Error), relative to a model with uniformly distributed daily lags and a model with only monthly frequency data. We also find that the preferred timing to perform the one-month-ahead forecast is on the third week of the forecasted month. The first two weeks of daily data and information about the previous month's CPI, both contribute to the improvement of the forecast accuracy. The addition of the two last weeks of the month does not contribute to the performance of the model.