We want language for recording the elements of some set that appear at regular intervals of time.

Let $A$ be a set. An observation sequence (or time series) in $A$ is a mapping $a: \Z \to A$.

If $A = \R ^d$ in which case we call $a$ a vector-valued observation sequence or vector-valued time series.

Examples include temperature readings, seismograph readings, sunspot numbers, export quantities, and so on.

The most basic assumption we can make is that
the observation sequence $a$ exhibits some
regularity over time.
This assumption is naturally related to the
assumption of time-invariance in physical laws.^{1}

- Future editions will expand on this discussion. ↩︎