We also have uncorrelated time series.

In the case of uncorrelated time series,

we don't have a strong relationship one way or the other.

So basically, it may be that in these two case,

we might see if a variable is increasing,

the other one is also increasing.

But you might also see the opposite.

We might see that basically,

between these two series,

when one of the variable is increasing,

the value of the other variable is decreasing.

So, these are essentially basic uncorrelated time series,

time series where when one of them have a high value,

we cannot necessarily predict whether the other one will have a high value or low value.

Uncorrelated time series. So, essentially,

this shows us that when we are comparing time series,

we have different ways to quantify their similarity or difference.

The way we're going to select whether

which one or the other one to use depends on the application.

In the case of Euclidean distance,

we measure how close the two time series

are to each other but we don't necessarily basically see whether if one is increasing,

the other one is decreasing or vice versa.

We cannot tell that. We can only say,

these two time series are similar to each

other in terms of their amplitudes or they are far apart from each other.

This the only thing that we can say.

If you look at the correlation, however,

correlation can tell us if one of them is

increasing whether the other one is decreasing or not.

So, we can actually get some more information about

the sort of overall patterns but in that case,

you may not be able to say in absolute terms whether they are close to each other or not.

So, to decide basically one or the other,

we need to look at the application and we need to say are we comparing them in

terms of their absolute values or are we trying to understand whether when is decreasing,

the other was increasing or not.

So we need to basically ask ourselves,

what is the application and we need to decide about

the distance or similarity function based on the application that is given to us.