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Partly inspired by the following post: Relation and difference between time series and regression?

After thinking carefully into these two subjects, I kind of wondering for what kind of data/situation time series analysis is more suitable? (or conversely, stochastic processes will be more suitable) There are some examples (e.g. Auto-regression in the post cited above) where the time series are more suitable; but stochastic processes could as well depict them in terms of filtration. And in other examples (e.g. Poisson process) where stochastic methods dominates but it seems time series specialist in economics could analyze them equally well.

Therefore, is there an example that only one of these two methods works? (I know their relation are vague, so any comments are welcome.)

Henry.L
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  • As far as I can tell, stochastic processes describe a much broader set of probability models like control systems, where there are inputs, states, noise, and dynamical properties. Time series often describes a set of (discrete- or continuous-time) observations for a single variable, so that the observation of a stochastic process may result in one or more time series. In a car, for instance, a stochastic process may describe *how* throttle position engine temperature. Whereas the throttle position and engine temperature are specific time series instances. – AdamO Dec 05 '17 at 19:30
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    The first order of business is to understand what a time series is: please read https://stats.stackexchange.com/questions/126791. The second thing is to clarify the distinction between a *model* and a *statistical procedure*. Once you do that, you might feel inspired to clarify your question--or you might even discover you know the answer. – whuber Dec 05 '17 at 20:17

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