Definition:Successive Values of Time Series/Equispaced
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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 $z_t$.
Sources
- 1994: George E.P. Box, Gwilym M. Jenkins and Gregory C. Reinsel: Time Series Analysis: Forecasting and Control (3rd ed.) ... (previous) ... (next):
- Part $\text {I}$: Stochastic Models and their Forecasting:
- $2$: Autocorrelation Function and Spectrum of Stationary Processes:
- $2.1$ Autocorrelation Properties of Stationary Models:
- $2.1.1$ Time Series and Stochastic Processes: Time series
- $2.1$ Autocorrelation Properties of Stationary Models:
- $2$: Autocorrelation Function and Spectrum of Stationary Processes:
- Part $\text {I}$: Stochastic Models and their Forecasting: