C42. Process and realisation

Topic: Dependence along a series · more questions on this topic
C43 ›

What is a stochastic process, and how does an observed time series relate to it?

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Definitions/notation. A stochastic process is a collection of random variables \{X_t:t\in\mathcal T\} indexed by time or another index set \mathcal T. An observed time series is a finite portion of one realisation (sample path), not a collection of independent realisations of the whole process.