Lets say I am trying to find patterns in pricing of a commodity such as corn and I have monthly time series data on the demand, the temperature, cost of water, and the current market supply.
What methods would I use to detect patterns such as:
*Corn will cost less during harvesting in October and November when temperatures are around X.
*Corn prices are less when the supply goes up on the month of the Corn festival.
*Last year corn prices are high because there is a drought and the cost of water and the temperature is high in the summer.
What would I use for these types of patterns in a time series? Usually you would use a correlation matrix for linear data. But what do you use for seasonal and stochastic data where there are patterns like these exist but you do not know what they are? Are these types of cases for cointegration and vector autoregression (my guess)?