This paper considers single-item, periodic review inventory systems with linear procurement, holding and shortage costs, and immediate delivery. Immediate stock disposal with a linear disposal fee may or may not be an option. The demand in each time period is assumed to equal some real- valued function of demand in previous periods, perturbed by a stochastic shock. Both additive and multiplicative stochastic shocks are considered. The former include some familiar linear time series and Bayesian models. The latter subsume some alternate Bayesian models and a style-goods forecasting technique. In all cases, bounds on the value loss relative to optimal cost for using the myopic stocking policy are derived. In particular, i.i.d. additive shock demand models can have random walk characteristics that will mathematically generate negative demand forecasts in finite time. If an endogenous stopping time is defined that prevents the demand process from generating negative values in these models, the myopic policy is precisely optimal up to the stopping time.