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In this video lecture,
we will be talking about stationarity.

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Objectives is the following.

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We would like to get some intuition
about weak stationary time series.

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So stationary time series is what we're
going to be building our modules on.

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And what we want in a time series,
is to be stationary.

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What it means is the following.

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We do not want any systematic
change in the properties and

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the behavior of the time series.

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For example, we do not want to have any
systematic change in the mean, right?

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So no systematic change in the mean.

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In other words, we do not want to see
a trend in a stationary time series.

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We do not want to see a systematic
change in variation, right?

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So in one of the datasets we looked
at on the Johnson & Johnson,

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we saw that there was a change
even in the variation.

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Now for a stationary time series,

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we don't want any systematic
change in the variation.

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And we do not want any
periodic fluctuations as well.

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So basically, the properties of one
section of a data in a time series

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are much like the properties of
the other sections of the data.

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To be honest,
usually stationarity's a property of

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a stochastic process of a model,
not a time series.

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But we say stationary time series
if you think that it can be modeled

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with stationary models,
stationary stochastic process.

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If we have a non-stationary time series,
which we usually have.

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What we do,
we basically do some transformations and

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we get the stationary time series
after the transformations.

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Once we have a stationary time series,
we model it and

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then we go back and
we model our non-stationary time series.

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So we use the transformations
as a middle step.

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So what have you learned in this lecture?

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You have learned that in
a weak stationary time series,

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there is no systematic change in the mean.

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In other words, there is no trend.

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There is no systematic change in variance
and there is no periodic variations.