Suppose there is a baseball stadium. The stadium has a food stand - let's assume that to make a purchase at the food stand, fans must purchase a ticket to watch the baseball game. This means that all fans who purchased food also purchased a ticket - but not all fans who purchased a ticket, also purchased food.
Let's assume that a private company rents the food stand and is not directly affiliated with the stadium. The food stand is interested in forecasting their future weekly sales (i.e. a univariate time series) - however, let's pretend that the food stand does not have access to the ticket sales information.
Of course, the food stand could use standard ARIMA models to forecast future sales - but could the food stand treat the "ticket sales information" as a "hidden state" and attempt to use this information to create a state-space time series model (e.g. https://sidravi1.github.io/blog/2020/06/20/linear-gaussian-state-space-models)? If the food stand has some very general ideas about the ticket sales (e.g. mean and standard deviation) - could they treat this information as the "initial conditions" for the state space model, and then attempt to better forecast their sales compared to a standard ARIMA model? Maybe the kalman filter can be used for filtration/smoothing, and the hidden markov model can indirectly be used as a proxy to determine how well the home team is playing (e.g. use the following assumption: more wins statistically results in higher attendance, which statistically results in higher sales )?
Can someone please confirm if this general idea describes the "hidden state" concept in state-space models?
Note: Let's assume that the food stand has enough data (e.g. past 10 years)