As the interest rates in the United States move up, so must the value of the U.S. dollar, otherwise it would create arbitrage opportunities. There is a formal mathematical relationship between currencies and interest rates called the interest rate parity. In other cases, two variables may exhibit some correlation, although it is difficult to explicitly connect the two through cause-effect relationships. For example, oil and natural gas prices move independently, although they exhibit some correlation. Reflecting these relationships is vital to the generation of scenarios for all the variables that are internally consistent.
Many commodities exhibit seasonal cycles in their price movement.
For example, natural gas cycles between summer and winter prices as the demand shifts each season. Even after accounting for the above characteristics, most variables still exhibit a significant degree of uncertain behavior because of noise. The noise is the aggregate effect of a multitude of small causal factors. It results in many temporary and independent movements that are uncertain in both direction and size. Thus, the process of generating scenarios involves starting with the current value and using the differential equation to generate by iteration the values for each subsequent time period.