What is the best statistical test to determine the relationship between the absolute price of a time series compared to the spread, or relative change, in the same time series? For example, time series S1 (spot price of commodity) compared to time series S2 (forward price of same commodity - spot price of commodity)? The test is to determine whether the shape of a price curve S2 (forward - spot) affects the spot price S1.
Relative prices likely work better than absolute prices. Or if you wish, take the logarithm of prices. Consider, for example, that a stock price cannot be negative, so stock prices cannot be normally distributed. But, they can be log normal. So, if you wish to do testing, take the logarithms, and compare those.