If you are looking for ways to calculate Autocorrelation in Excel, then you will find this article useful. Autocorrelation or serial correlation is helpful to determine the relationship between a data series over time with its lagged version by different amounts.
So, let’s dive into the main article to know more about this issue.
Related Articles
Download Workbook
2 Ways to Calculate Autocorrelation in Excel
Here, we have the following dataset containing the sales records over different months of a company. We will try to determine the autocorrelation for different lags in these records between these time ranges using the following 2 ways.
We have used Microsoft Excel 365 version here, you can use any other versions according to your convenience.
Method-1: Using SUMPRODUCT, OFFSET, AVERAGE, and DEVSQ Functions to Calculate Autocorrelation
Here, we will use the combination of the SUMPRODUCT, OFFSET, AVERAGE, and DEVSQ functions to calculate the autocorrelation of the sales values for a range of lags between 1 to 5.
Steps:
Firstly, we need to calculate the total number of months for determining the time series of the sales values.
➤ Type the following function in cell D13.
=COUNTA(B4:B12)COUNTA will determine the total months in the range B4:B12.
➤ After pressing ENTER, you will get the total number of months; 9.
Now, we will determine the autocorrelations for the Sales Series between the lags 1 to 5.
➤ Write down the following formula in cell G4.
=SUMPRODUCT(OFFSET($D$4:$D$12,0,0,$D$13-F4)-AVERAGE($D$4:$D$12),OFFSET($D$4:$D$12,F4,0,$D$13-F4)-AVERAGE($D$4:$D$12))/DEVSQ($D$4:$D$12)Here, $D$4:$D$12 is the Sales range, $D$13 is the total number of months, and F4 is the lag value.
$D$13-F4becomes9-1 → 8
OFFSET($D$4:$D$12,0,0,$D$13-F4)becomesOFFSET($D$4:$D$12,0,0,8) →extracts a range with a height of8rows from the reference cell$D$4.Output →{4996; 4137; 3203; 3403; 4831; 4931; 4753; 4381}
AVERAGE($D$4:$D$12) →determines the average value of this rangeOutput →4367.555
OFFSET($D$4:$D$12,0,0,$D$13-F4)-AVERAGE($D$4:$D$12)becomes{4996; 4137; 3203; 3403; 4831; 4931; 4753; 4381}-4367.555Output →{628.444; -230.556; -1164.556; -964.556; 463.444; 563.444; 385.444; 13.444}
OFFSET($D$4:$D$12,F4,0,$D$13-F4)becomesOFFSET($D$4:$D$12,1,0,8) →the starting cell reference moves1cell downwards from$D$4and then extracts a range with a height of8rows from the reference cell$D$5Output →{4137; 3203; 3403; 4831; 4931; 4753; 4381; 4673}
OFFSET($D$4:$D$12,F4,0,$D$13-F4)-AVERAGE($D$4:$D$12)becomes{4137; 3203; 3403; 4831; 4931; 4753; 4381; 4673}-4367.555Output →{ -230.556; -1164.556; -964.556; 463.444; 563.444; 385.444; 13.444; 305.444}
SUMPRODUCT(OFFSET($D$4:$D$12,0,0,$D$13-F4)-AVERAGE($D$4:$D$12),OFFSET($D$4:$D$12,F4,0,$D$13-F4)-AVERAGE($D$4:$D$12))becomesSUMPRODUCT({628.444; -230.556; -1164.556; -964.556; 463.444; 563.444; 385.444; 13.444},{ -230.556; -1164.556; -964.556; 463.444; 563.444; 385.444; 13.444; 305.444})Output →1287454.358
DEVSQ($D$4:$D$12) →returns the sum of squares of the deviations of the data range from their mean.Output →3508950.222
SUMPRODUCT(OFFSET($D$4:$D$12,0,0,$D$13-F4)-AVERAGE($D$4:$D$12),OFFSET($D$4:$D$12,F4,0,$D$13-F4)-AVERAGE($D$4:$D$12))/DEVSQ($D$4:$D$12)becomes1287454.358/3508950.222Output →0.366905848
➤ Press ENTER and drag down the Fill Handle tool.
After that, you will get the autocorrelations for the monthly sales series between a range of lags from 1 to 5.
Method-2: Using SUMPRODUCT, AVERAGE, VAR.P Functions to Calculate Autocorrelation in Excel
In this section, we are going to use the combination of SUMPRODUCT, AVERAGE, and VAR.P functions to have the autocorrelation for the monthly sales series with their lagged versions for lag values 1, 2, and 3.
Steps:
➤ Type the following function in cell D13 to determine the total number of rows in the data series.
=COUNTA(B4:B12)COUNTA will determine the total months in the range B4:B12.
➤ After pressing ENTER, you will get the total number of months; 9.
It’s time to determine the autocorrelations for the sales series between the lags 1 to 3.
➤ Type the following formula in cell G4.
=(SUMPRODUCT(D4:D11-AVERAGE(D4:D12),D5:D12-AVERAGE(D4:D12))/D13/VAR.P(D4:D12))Here, D4:D11 is the Sales range without the last cell value due to lag 1, similarly, D5:D12 is the Sales range without the first cell value due to lag 1, and D13 is the total number of months.
AVERAGE(D4:D12) →determines the average value of this rangeOutput →4367.555
D4:D11-AVERAGE(D4:D12)becomes{4996; 4137; 3203; 3403; 4831; 4931; 4753; 4381}-4367.555Output →{628.444; -230.556; -1164.556; -964.556; 463.444; 563.444; 385.444; 13.444}
D5:D12-AVERAGE(D4:D12)becomes{4137; 3203; 3403; 4831; 4931; 4753; 4381; 4673}-4367.555Output →{ -230.556; -1164.556; -964.556; 463.444; 563.444; 385.444; 13.444; 305.444}
SUMPRODUCT(D4:D11-AVERAGE(D4:D12),D5:D12-AVERAGE(D4:D12))becomesSUMPRODUCT({628.444; -230.556; -1164.556; -964.556; 463.444; 563.444; 385.444; 13.444},{ -230.556; -1164.556; -964.556; 463.444; 563.444; 385.444; 13.444; 305.444})Output →1287454.358
SUMPRODUCT(D4:D11-AVERAGE(D4:D12),D5:D12-AVERAGE(D4:D12))/D13becomes1287454.358/9Output →143050.484224966
P(D4:D12) →determines variance based on the entire range.Output →389883.358024691
(SUMPRODUCT(D4:D11-AVERAGE(D4:D12),D5:D12-AVERAGE(D4:D12))/D13/VAR.P(D4:D12))becomes(143050.484224966/389883.358024691)Output →0.366905848
➤ Press ENTER.
In this way, you will get the autocorrelation of the sales series with their one lagged version.
Similarly, to get the autocorrelation for lag=2 use the following formula.
=(SUMPRODUCT(D4:D10-AVERAGE(D4:D12),D6:D12-AVERAGE(D4:D12))/D13/VAR.P(D4:D12))D4:D10 represents the sales series without the last two values due to lag 2 and D6:D12 is the series without the first two values.
In the same way, you can have the autocorrelation for lag=3 by applying the following formula.
=(SUMPRODUCT(D4:D9-AVERAGE(D4:D12),D7:D12-AVERAGE(D4:D12))/D13/VAR.P(D4:D12))D4:D9 represents the sales series without the last three values due to lag 3 and D7:D12 is the series without the first three values.
Comparison of Results with Graphical Representation
As you can see, by using the above two formulas in two methods we are getting exactly the same autocorrelation values for their corresponding lags. Moreover, it can be concluded that with the increasing lagged values we are having a series of decreased autocorrelations.
For the lag value 1, we are having a positive value which represents a proportionate increase in this time interval. And, for the rest of the lag values, we are having negative autocorrelations defining a proportionate decrease in the time intervals.
Practice Section
For doing practice by yourself we have provided a Practice section like below in a sheet named Practice. Please do it by yourself.
Conclusion
In this article, we tried to cover the ways to Calculate Autocorrelation in Excel. Hope you will find it useful. If you have any suggestions or questions, feel free to share them in the comment section.
The post How to Calculate Autocorrelation in Excel (2 Ways) appeared first on ExcelDemy.
