actually, let me take it the other way.

If the PACF does not shut off,

shut off meaning having zero values beyond.

If the PACF does not shut off,

at a fixed lag,

but moves to zero slowly,

but moves the case towards zero slowly, right?

It does not shut off but moves towards zero,

then that might indicate that we are looking at a moving average series.

So, essentially PACF may tell me whether I'm looking at the moving average series,

or whether I'm looking at the auto-regressive series

based on the shape of the PACF.

So, if I can do that, that's great because I can differentiate

between these two major type of time series.

Let's see whether it is correct or not, can we use that?

Okay. Here, once again,

I have a series on the left,

and in this case,

the partial auto-correlation function plots,

PACF plot on the on the right.

Let's take a look at the PACF plot in this case.

Note that the PACF plot in this case doesn't shut off, rather it doesn't shut off.

I have non-zero values here and there.

Here and there I have non-zero values.

It doesn't really shut off.

It starts high, it gets lowered,

but it doesn't shut off.

Right? Usually, as I mentioned before,

usually we discount the values in this range.

This is the area where it is anything in this range,

I can treat that with zero values,

because they are not significant.

So, they are almost zero,

but essentially what we are seeing with this parameter called the PACF,

we see that it starts high,

it has some large values,

and then it basically gets closer to zero.

It starts basically taking values very close to zero.

So, this tells us that maybe we are looking at a moving average time series.

Indeed, if you take a look at the model of the time series, in its sense,

the function that are used to create this time series,

you will see that it's auto-regressive. All right.

It depends on the random input,

random errors, in the previous time instance.

We called this, if you remember, a MA(1) models.

So this is an MA(1) model.

It's a moving average time series,

and the partial auto-correlation function,

the part of the partial auto-correlation function is telling me that.

It's telling me that, ''Hey, Celtrick,

you are looking at a moving average time series."

Because the plot doesn't shut off,

immediately the plot starts getting smaller and smaller values. Right? That's great.

I have another tool that tells me if I'm looking at a moving average time series,

or if I'm looking at the auto-regressive time series.

Let's see another example.

Right? So, this is another time series I have on the left,

and I have another partial auto-correlation function on the right.

Indeed, again, if you take a look at that,

the values that this is taking doesn't shut off immediately.

In fact, basically, it goes

beyond this red area that I plot which is not significant, but it doesn't shut off.

I mean, it takes non-zero values,

beyond immediate small lags.

So, this again tells me that I might be looking at the moving average time series.

Again, if I take a look at the formula that I used to create this time series,

it is a auto-regressive time series.

Sorry, I apologize, I take it back.

It is a moving average time series.

It has two moving average terms.

In fact, the lag in this case is three,

the maximum lag that I'm using is three.

So, what I know,

if I now look at the closed form formula,

is that this is an MA(3) model,

moving average three model,

but what the partial auto-correlation plot tells me is that,

I am looking at the moving average model.

So, great. So now,

I can tell if I'm looking at a trend,

I can tell if I'm looking at a auto-regressive function,

and I can tell if I'm looking at moving average function

by looking at ACF and PACF plots.

This is strong. So this is really good

because before that I had no idea when I look at the time series.

I couldn't tell what I'm looking at.

Now, I can actually tell that this is really good.

Right? What else though?

I mean, can I do anything else?

Can I be adequate to learn more about the time series

by maybe studying these PACF and ACF more closely?

But it turns out that actually I can if I am looking at a moving average time series,

say if confirmed by the PACF,

then if I look at the ACF,

then I look at the ACF,

maybe I can actually learn more about my moving average time series.

So, it turns out that the ACF plot has non-zero values,