Definition:Independent Shocks

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Let $M$ be a stochastic model which describes a time series in which adjacent observations are highly dependent.

Then $M$ may be able to be modelled by a time series whose elements are of the form:

$\map z t = \map {z_d} t + \map {z_r} t$


$\map {z_d} t$ has a deterministic model
$\map {z_r} t$ has a stochastic model which consists of a sequence of independent random variables from a specified probability distribution (usually a white noise process).

The terms of the sequence $\sequence {z_r}$ are known as independent shocks.


  • 1927: On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer's Sunspot Numbers (Phil. Trans. Ser. A Vol. 226: pp. 267 – 298)
$1$: Introduction:
$1.2$ Stochastic and Deterministic Dynamic Mathematical Models
$1.2.1$ Stationary and Nonstationary Stochastic Models for Forecasting and Control: Linear filter model