what should be the optimal quantity in theory

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The Newsvendor problem. We know how to model if the demand Y_i is iid. 1. Explore if Y_i are not iid. How should we model this? 2. Let’s start with AR(p) process. What should be the optimal quantity in theory? Is x_{t-1}’ * beta(\tau_n)? 3. I expect it has the format x_{t-1}’ * beta(\tau_n). Then explore how to estimate the beta function (of tau) by quantile regression (use Python packages, Matlab). For instance, if tau=1/2, then we need to find the medium of Y_{n+1}. If tau = 3/4, what should be the 3rd-quartile of Y_{n+1}?

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