In this video lecture, we will be talking about stationarity.
Objectives is the following.
We would like to get some intuition about weak stationary time series.
So stationary time series is what we're going to be building our modules on.
And what we want in a time series, is to be stationary.
What it means is the following.
We do not want any systematic change in the properties and
the behavior of the time series.
For example, we do not want to have any systematic change in the mean, right?
So no systematic change in the mean.
In other words, we do not want to see a trend in a stationary time series.
We do not want to see a systematic change in variation, right?
So in one of the datasets we looked at on the Johnson & Johnson,
we saw that there was a change even in the variation.
Now for a stationary time series,
we don't want any systematic change in the variation.
And we do not want any periodic fluctuations as well.
So basically, the properties of one section of a data in a time series
are much like the properties of the other sections of the data.
To be honest, usually stationarity's a property of
a stochastic process of a model, not a time series.
But we say stationary time series if you think that it can be modeled
with stationary models, stationary stochastic process.
If we have a non-stationary time series, which we usually have.
What we do, we basically do some transformations and
we get the stationary time series after the transformations.
Once we have a stationary time series, we model it and
then we go back and we model our non-stationary time series.
So we use the transformations as a middle step.
So what have you learned in this lecture?
You have learned that in a weak stationary time series,
there is no systematic change in the mean.
In other words, there is no trend.
There is no systematic change in variance and there is no periodic variations.