The dynamics of consumption and stocks are crucial for analysis of commodity prices and policies. But empirical application of the standard storage model has been derailed by failure to replicate high real price autocorrelation. Our proposed storage model is the first empirical model to recognize the full implications of nonstationarity for price behavior and speculative arbitrage with an occasionally binding non-negativity constraint, a challenge shared by DSGE models in macroeconomics and growth. Our consistent least squares strategy estimates first the endogenous price trend induced by a latent trend in production and then the interest rate and a target separating two distinct dynamic regimes. In one, price has a stochastic trend with drift equal to the interest rate; in the other, price exhibits expected jumps from current price to a trending target price in the stockout region. Neglect of small trends can increase measured price autocorrelation and variation to the high observed levels.