Good introduction to this topic!

For a new model of time series (including the multivariate case) with exponentially decaying auto-correlations or infinite-range auto-correlations depending on the model parameters, read my article (sections 2 and 4) Some Fun with Gentle Chaos, the Golden Ratio, and Stochastic Number…. I also discuss how to de-correlate these time series, and a business application in the context of gaming.