My ultimate aim is to obtain a model and data for a single univariate time series for the unobservable true price of an item (with minimum error).
Instead of directly observing this true price, I can observe data with the interpretation of this true price by different entities, each of these making up a timeseries.
The data from these entities at a single point in time do not match (although they all will attempt to follow this true price). Some of these entities give data that is more faithful to the true price, while other entities whose data may contain larger error terms tend to lag behind on the true price (sometimes more, sometimes less).
My problem is to determine how to proceed and what techniques to use.
I was considering to use some sort of multivariate or vector timeseries, introducing a suitable lag operation for the entities that lag behind in time.
As another option, I could build several models for the individual time series and attempt to reconcile the different credible intervals of the true value.
I have not worked with time series before so pointers to the right reading material and outlines of how to work are both useful and highly appreciated,