Marine transport has grown rapidly as the result of globalization and sustainable world growth rates. Shipping market risks and uncertainty have also grown and need to be mitigated with the development of a more reliable procedure to predict changes in freight rates. In this paper, we propose a new forecasting model and apply it to the Baltic Dry Index (BDI). Such a model compresses, in an optimal way, information from the past in order to predict freight rates. To develop the forecasting model, we deploy a basic set of predictors, add lags of the BDI and introduce additional variables, in applying Bayesian compressed regression (BCR), with two important innovations. First, we include transition functions in the predictive set to capture both smooth and abrupt changes in the time path of BDI; second, we do not estimate the parameters of the transition functions, but rather embed them in the random search procedure inherent in BCR. This allows all coefficients to evolve in a time-varying manner, while searching for the best predictors within the historical set of data. The new procedures predict the BDI with considerable success.