I am interested in an overview over the connection and correspondence between time series models in continuous vs. discrete time in finance. E.g. take ARMA(p,q) or GARCH(s,r) or ARMA(p,q)-GARCH(s,r) from discrete time, list their counterparts in continuous time and show how they are related (e.g. how a continuous time process is a limit for the discrete time process as observation frequency increases without bound, or something like that); and do the same with the popular continuous time models (whatever these are) giving their discrete-time counterparts. It could be a full answer with worked out examples or just a reference to a textbook or a paper.


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