Here it is strong and positive,

here it's strong and negative.

What this tells me is that indeed I have a cyclic behavior

with a half period of 12 units.

The full period is indeed

24 unit and it confirms that the half period of this is 12 units.

So, because half period,

I expect that basically the time series is going to switch

over and indeed this is exactly it's showing me.

The autocorrelation function it's showing me that,

it's showing me a 24-unit period and 12th unit half period.

Now, it turns out that basically you can use the PACF to confirm that.

You can use PACF to confirm that.

So, in this case, if I take a look at the PACF,

I will see if you look at that,

that the value is getting close to zero,

it has basically there's non-zero.

First positive then negative values but non-zero values up to

10 to 12 unit range.

So as anything below that,

I essentially need to- for statistical reasons,

I need to basically treat as non-zeros.

In this case, essentially what's happening is that my partial autocorrelation function,

essentially indicates or confirms that there is a cyclic pattern with a half lag,

half period which is around 10, 12 units.

Not that I am not exactly getting 12 because I have some random components,

because I have some random components

that might basically somehow draw off perfect results.

The reason basically here I'm not getting perfect zeros for example,

is because of the random component that I have.

Another reason is that this is finite series,

so I don't basically extend this infinitely as I have finite series with only one,

two, three, four, five, six cycles,

which essentially means that basically I'm learning

about the statistical properties of the cycles using only six cycle samples.

If I had 60, if I had 600 of these,

I might basically be able to get a more accurate results,

a more predictive results and it could be at these the bounds could have been tighter.

But even now, even if I am basically have a small sample,

as of small observations,

small number of observations.

So, what's happening is that

the autocorrelation function and

the partial autocorrelation function is telling me a lot of things.

It is telling me that, "Hey, Shadrack,

you might be looking at a cyclic data with a period of 24 units and

the half period of somewhere close to 12 units rather it's telling me that,

that it's very strong very strong.

But, of course, I mean, you will tell me that basically in the real world

the data is not- is almost never perfectly cyclic,

almost never perfect trend,

almost never perfect autoregressive,

it's almost never perfect moving average,

you have complex complex models.

What do we do then?

How do we deal with this complex models?

Well, what we do is, what we can do is basically we again plot the

auto-correlation and partial auto-correlation plots and see what it tells us.

So, in this case, if I take the complex model and if I basically plot,

it's the autocorrelation function first, let's start from there.

What we are seeing is that it decays-