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In this video, we're going to discuss about autocorrelation and partial autocorrelation.

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Earlier, we had discussed auto regression model where we tried to find the relationship between the

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decent value of the variable and the historical values of the variable.

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But did we also had a question that how do we know how many land values or historical values should

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we use?

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This is where autocorrelation and passell autocorrelation will help us.

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Correlation between two variables is basically a relationship or a connection between two numbers.

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It is measured by Pearsons correlation coefficient, which ranges between minus one to one.

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If the value of this number is one, this means that the relationship between the two variables is positive.

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Positive means that if X increases, Y also increases.

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And if X decreases, Y also decreases.

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On the other extreme.

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Is if the value is minus one.

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It means that if X increases via decreases and if X decreases, Y increases, that both will move in

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the opposite direction.

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Both are still correlated.

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There is a relationship between the two, but correlation is negative.

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But when the correlation coefficient is zero, this means that there is no relationship between these

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two variables.

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So we cannot say that if X increases, what will happen, the way it may increase or it may decrease.

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So this is what correlation is between two variables.

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But when it comes to Time series, we are trying to find the correlation of the variable with its own

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lag values, which is why, like auto regression, this correlation is called auto correlation.

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That is correlation with itself, its own lag values.

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Now, how do we use it?

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To use it, we first find Decorrelation with all the flag values.

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Suppose this is our data.

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The number of bullets per day in the first table.

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We have the flag when values.

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We find the correlation between these two regional values and the lag when values.

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This correlation is called autocorrelation of lag one.

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This is coming out to point eight.

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Then we find love to lose.

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This is the additional column, what, like two values?

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And then we find the autocorrelation of original values with like two values.

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And that is the autocorrelation of like two.

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And so on as far as we can go.

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So you find autocorrelation values for all the flag values.

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Then we plot all of these autocorrelation values against the corresponding lag values.

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This is what we get when we plot all of these autocorrelation values.

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This is called auto correlation function plot.

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So it is HCF plot in this graph.

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The lag values are on the x axis.

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So this first line is at zero.

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That is it is for lag zero.

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The second line is for lag one and so on.

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On the Y axis, we have correlation coefficient value.

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So with lag's zero value, that is with itself.

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The correlation coefficient is plus one, which is obvious with lag one value.

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It is nearly point eight.

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We'd like to.

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It is nearly point six and so on.

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The colored corn at the bottom, this colored corn.

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This is called 95 percent confidence interval corn.

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Basically, a point outside this corn means that we are more than 95 percent confident that there is

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a correlation between these variables.

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And this coalition is not just any ran down statistical fluctuation.

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So till that time, these venues are outside this cone.

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We can take those many, like values into consideration.

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This works well for the moving average better.

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Well, we have to find the relationship between lag's of residuals.

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So ECF works well, the.

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But when we are looking at auto regression, there is some ambiguity in the HCF plot.

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For example, when we find out lag one autocorrelation, it is zero point eight.

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Now, when we see the lag to autocorrelation lag to already has some impact on the lag one variable.

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So the impact of lag, too variable was already accommodated to some extent when we saw lag one autocorrelation.

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Ideally, to find the correlation between this series and its lag, two values, we should remove these

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direct and indirect impacts of large quantities on the original cities.

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Similarly, when we are finding correlation between original series and laggardly values, we should

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remove the effect of lag one and like two values.

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When we remove these effects of intervening observations, then the correlation coefficient is called

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partial autocorrelation coefficient.

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And to calculate this also, we do not need to know the maths behind it.

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Our software finds only partial autocorrelation coefficient values for all the lag values.

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We can also applaud this on a graph to visualize them.

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The plot of Passell Autocorrelation Values is called up BATF plot, that is partial autocorrelation

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function plot.

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PCM gives a much clearer view of Gey.

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That is the number of lag values we should use in auto regression.

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So when we are trying to find out the number of lagged values which we should use in order regression

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model, we have to look at the partial autocorrelation function with Wendy.

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The a value goes below the 95 percent confidence interval gone.

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That is the point to which we will use the lagged values for auto regression model.

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But when we are trying to find out day lag values of the day, as it was for moving average, we will

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use the AC a function.

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We will see the point where the ACL function value goes beyond goes below the 95 percent confidence

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interval level.

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And that point will be used as the number of lag values for moving average model.

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So that's all.

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This is how HCF and PSC of plots are used.