In this video, we're going to discuss about autocorrelation and partial autocorrelation.
Earlier, we had discussed auto regression model where we tried to find the relationship between the
decent value of the variable and the historical values of the variable.
But did we also had a question that how do we know how many land values or historical values should
we use?
This is where autocorrelation and passell autocorrelation will help us.
Correlation between two variables is basically a relationship or a connection between two numbers.
It is measured by Pearsons correlation coefficient, which ranges between minus one to one.
If the value of this number is one, this means that the relationship between the two variables is positive.
Positive means that if X increases, Y also increases.
And if X decreases, Y also decreases.
On the other extreme.
Is if the value is minus one.
It means that if X increases via decreases and if X decreases, Y increases, that both will move in
the opposite direction.
Both are still correlated.
There is a relationship between the two, but correlation is negative.
But when the correlation coefficient is zero, this means that there is no relationship between these
two variables.
So we cannot say that if X increases, what will happen, the way it may increase or it may decrease.
So this is what correlation is between two variables.
But when it comes to Time series, we are trying to find the correlation of the variable with its own
lag values, which is why, like auto regression, this correlation is called auto correlation.
That is correlation with itself, its own lag values.
Now, how do we use it?
To use it, we first find Decorrelation with all the flag values.
Suppose this is our data.
The number of bullets per day in the first table.
We have the flag when values.
We find the correlation between these two regional values and the lag when values.
This correlation is called autocorrelation of lag one.
This is coming out to point eight.
Then we find love to lose.
This is the additional column, what, like two values?
And then we find the autocorrelation of original values with like two values.
And that is the autocorrelation of like two.
And so on as far as we can go.
So you find autocorrelation values for all the flag values.
Then we plot all of these autocorrelation values against the corresponding lag values.
This is what we get when we plot all of these autocorrelation values.
This is called auto correlation function plot.
So it is HCF plot in this graph.
The lag values are on the x axis.
So this first line is at zero.
That is it is for lag zero.
The second line is for lag one and so on.
On the Y axis, we have correlation coefficient value.
So with lag's zero value, that is with itself.
The correlation coefficient is plus one, which is obvious with lag one value.
It is nearly point eight.
We'd like to.
It is nearly point six and so on.
The colored corn at the bottom, this colored corn.
This is called 95 percent confidence interval corn.
Basically, a point outside this corn means that we are more than 95 percent confident that there is
a correlation between these variables.
And this coalition is not just any ran down statistical fluctuation.
So till that time, these venues are outside this cone.
We can take those many, like values into consideration.
This works well for the moving average better.
Well, we have to find the relationship between lag's of residuals.
So ECF works well, the.
But when we are looking at auto regression, there is some ambiguity in the HCF plot.
For example, when we find out lag one autocorrelation, it is zero point eight.
Now, when we see the lag to autocorrelation lag to already has some impact on the lag one variable.
So the impact of lag, too variable was already accommodated to some extent when we saw lag one autocorrelation.
Ideally, to find the correlation between this series and its lag, two values, we should remove these
direct and indirect impacts of large quantities on the original cities.
Similarly, when we are finding correlation between original series and laggardly values, we should
remove the effect of lag one and like two values.
When we remove these effects of intervening observations, then the correlation coefficient is called
partial autocorrelation coefficient.
And to calculate this also, we do not need to know the maths behind it.
Our software finds only partial autocorrelation coefficient values for all the lag values.
We can also applaud this on a graph to visualize them.
The plot of Passell Autocorrelation Values is called up BATF plot, that is partial autocorrelation
function plot.
PCM gives a much clearer view of Gey.
That is the number of lag values we should use in auto regression.
So when we are trying to find out the number of lagged values which we should use in order regression
model, we have to look at the partial autocorrelation function with Wendy.
The a value goes below the 95 percent confidence interval gone.
That is the point to which we will use the lagged values for auto regression model.
But when we are trying to find out day lag values of the day, as it was for moving average, we will
use the AC a function.
We will see the point where the ACL function value goes beyond goes below the 95 percent confidence
interval level.
And that point will be used as the number of lag values for moving average model.
So that's all.
This is how HCF and PSC of plots are used.