## A Conceptual Vocalubary of Time Series Analysis

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## S |
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## stationarityIn time series analysis context,
if the time series is one for which the probabilistic behavior of every
collection of values $$ \{x_{t_1},x_{t{_2},...,x_{t_k}}\} $$is identical
to that of the time shifted
series$$\{x_{t_{1+h}},x_{t_{2+h}},...,x_{t_{k+h}}\}$$for all \(
k=1,2,... \), all time points \(t_1,t_2,...,t_k\) and all time shifts \(
h=0, \pm1, \pm2,... \), time series is said to be a It
is difficult to assess strict stationarity from data. Rather than
imposing conditions on all possible distributions of a time series, a
milder version called Stationarity
requires regularity in the mean and autocorrelation functions so that
these quantities (at least) may be estimated by averaging. It should be
clear that a strictly stationary, finite variance, time series is also
stationary. The converse is not true in general. One important case
where stationarity implies strict stationarity is if the time series is
Gaussian [meaning all finite collections of the series are Gaussian]. |