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.