Definition:Independent Shocks

Definition

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:

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

where:

$\map {z_d} t$ 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.

Sources

• 1927: G. Udny Yule: 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)

• 1994: George E.P. Box, Gwilym M. Jenkins and Gregory C. Reinsel: Time Series Analysis: Forecasting and Control (3rd ed.) ... (previous) ... (next):

$1$: Introduction:

$1.2$ Stochastic and Deterministic Dynamic Mathematical Models

$1.2.1$ Stationary and Nonstationary Stochastic Models for Forecasting and Control: Linear filter model