What are some good techniques for proxying time series? My purpose is for risk management / modelling and I would like proxy to missing series.

Given that I also have to account for volatility, correlation, etc., what methods can I then apply?

I am currently working on some simulated data generated from Geometric Brownian Motions with correlated Wiener processes - i.e. Black Scholes model. So a simple example could be the task of predicting / proxying the red line in the graph below given that the black data is available. Note that often we do not have any data prior to the red period - e.g. if one were to proxy a stock for a period prior for its listing (say Facebook modeled as if it was listed back at the Dot-com bubble) enter image description here



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