# Definition:Independent Shocks

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## 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:
*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

- $1.2$ Stochastic and Deterministic Dynamic Mathematical Models

- $1$: Introduction: