Definition:Successive Values of Time Series/Equispaced

Definition
Let $T$ be a time series whose observations are $\map z {\tau_1}, \map z {\tau_2}, \dotsb, \map z {\tau_t}, \dotsb$ at an unbroken sequence of timestamps $\tau_1, \tau_2, \dotsb, \tau_t, \dotsb$. Let $T$ be equispaced with time interval $h$ between adjacent observations.

Then $N$ successive observations, written as:
 * $z_1, z_2, \dotsb, z_t, \dotsb, z_N$

occur at timestamps:
 * $\tau_0 + h, \tau_0 + 2 h, \dotsb, \tau_0 + t h, \dotsb, \tau_0 + N h$

Hence we can refer to the observations at timestamp $\tau_0 + t h$ as $z_t$.