In statistical analysis, calculating cross-correlation is a common task. It may be quite tricky and time-consuming if you try to find it in the traditional mathematical way. But in Excel, you can do it brilliantly and fast. So you will learn 2 quick ways to calculate cross-correlation in Excel from this article with proper illustrations.
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What Is Cross Correlation?
Cross-correlation is a statistical term. It defines the relationship between two or more variables in terms of time. It tracks how one or more variables change with the change of another variable. We can also use multiple time series to track the amount of variation. From different time scales, we will find out the maximum similarity or dissimilarity.
The amount of correlation coefficient ranges from +1 to -1.
+1 means the variable is identical and -1 means opposite one another. And when this is 0 means, there is no relationship between the variables.
The mathematical formula for calculating the cross-correlation is given below:
r = Cross-correlation coefficient
n = Number of data available
xy =Sum, and product of the data of the first and second variables.
x = Sum of the first variable
y = Sum of the second variable
x2 =Square sum of each data of the first variable
y2 =Square sum of each data of the second variable
In simple words, we can explain the cross-correlation. We consider we have a dataset containing columns X, Y, and Z. Here, X is independent and Y and Z are dependent. If X and Y are positively correlated, then when X increases Y will also increase.
Again, if X and Z are the same positively co-related, Z will increase as X increases. So, Y and Z are said to be cross-correlated, as both of them show the same behavior concerning X.
2 Ways to Calculate Cross Correlation in Excel
In this article, we will show 2 examples to calculate cross-correlation in Excel. Those examples are based on the CORREL function and Add-Ins of Excel. Those examples are based on the CORREL function and Add-Ins of Excel. We will consider the following dataset.
We will calculate the cross-correlation of Production and Revenue based on the Investment.
1. Calculate Cross Correlation Without Time Lag
We can calculate cross-correlation without time lag in 2 ways- the CORREL function and the Data Analysis tool.
i. Using Excel CORREL Function
Here, we will use the CORREL function to calculate cross-correlation without time lag. As we will not consider time lag, we will consider the whole dataset for calculation.
- We add new rows in the dataset to find the correlation efficiency.
- First, we will calculate the correlation coefficient between Investment, Production, and Investment, Revenue by applying the following formulas.
On Cell D16:
On Cell D17:
We can see both cases correlation coefficient is close to 1. This means Production and Revenue are both positively co-related with Investment. Now, we will find out the cross-correlation coefficient between Production and Revenue.
- Put the following formula on Cell D18.
This result is also close to 1. So, Production and Revenue will show similar behavior. If Production increases, Revenue will also increase.
We can also plot the following dataset in a line chart.
This chart clearly indicates that the other two variables Production and Revenue are positively related to the Investment.
ii. Using the Data Analysis Tool of Analysis-ToolPak
Here, we will use default Add-ins of Excel to calculate the cross-correlation.
- Go to File >> Options >> Add-ins.
- After that, select Add-ins and then the Go button.
- The Add-ins window appears.
- Choose Analysis Toolpak add-in from the list.
- Then, press OK.
This add-is has been attached to the main tab of Excel.
- Now, click on the Data Analysis option in the Data tab.
- Select the Correlation option from the Data Analysis window.
- Finally, press the OK button.
- The Correlation window appears.
- Choose the Input Range from the dataset. We choose Investment, Production, and Revenue columns.
- Tick the Labels in first row option.
- After that, select a cell as the Output Range.
- Then, click on the OK button.
We can see the correlation coefficients are shown here.
2. Calculate Cross Correlation with Time Lag Using CORREL Function
Here, we will consider time lag to calculate the correlative coefficient. It is assumed that investment in the company will not reflect immediately. It may be seen that after a particular time period investment dominate production and revenue.
- First, we calculate the correlative coefficient considering different lags in the Range H5:I9 using the CORREL function.
We can see for lag 3, we get the maximum coefficient value.
- Now, use lag 3 for calculating the cross-correlative coefficient using the following formula.
We calculated the cross-correlation for lag 3.
Here is a graph for cross-correlation with time lag 3.
In this article, we showed 2 ways to calculate the cross-correlation in Excel with proper explanation. I hope this will satisfy your needs. Please have a look at our website ExcelDemy and give your suggestions in the comment box.
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