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Stationary time series

Stationary time series

Stationary time series:

A time series x(t); t=1,... is called to be stationary if its statistical properties do not depend on time t . A time series may be stationary in respect to one characteristic, e.g. the mean, but not stationary in respect to another, e.g. the variance:


M(x(t)) = const - the mean does not depend on time t;


Var(x(t)) = v(t) - the variance depends on time t;


where M(·) is the mean, Var(·) is the variance.


If joint probability distributions does not depend on time itself but only on the difference of time moments,



P(x(t)) = p(x);
P(x(t1), x(t2)) = p(t2 - t1);
P(x(t1), x(t2), x(t3)) = p(t2 - t1, t3 - t2);
...


then the time series x(t) is stationary in respect to any statistical characteristic.

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Courses Using This Term

Forecasting Analytics
This course will teach you how to choose an appropriate time series model: fit the model, conduct diagnostics, and use the model for forecasting.
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