1. Kernel Functions: Assume that trading of a commodity futures contract commenced at a time point that is far away from the current time point: t > 0. Further assume that at exactly the same time point t, a transaction happened with a price of p, > 0, size of V, > 0, and a sign of Et which is +1, -1 or 0. +1 indicates that the trade is buyer-initiated, -1 indicates seller- initiated, and 0 indicates no specific direction can be determined. To understand how all the trades that happened before the trade at time point t (or the "current trade") influenced the market to attain a trade price of p, we consider the following assumptions: (1) First, we assume that all the trades that happened before the trade at time point t should have impact on the current trade, even though we are quite certain that the most recent ones should have higher, more direct impact on the current trade than "older" trades that happened at time points t' with t' G(t') c(t' - 1) - Cost' G(t') c(t')]