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Stochastic Process

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Definition: A stochastic process is an ordered collection of random variables. Discrete ones are indexed, often by the subscript t for time, e.g., yt, yt+1, although such a process could be spatial instead of temporal. Continuous ones can be described as continuous functions of time, e.g. y(t).

A stochastic process is specified by properties of the joint distribution for those random variables. Examples:

  • the random variables are independently and identically distributed (iid).
  • the process is a Markov process
  • the process is a martingale
  • the process is white noise
  • the process is autoregressive (e.g. AR(1))
  • the process has a moving average (e.g. see MA(1))

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