Creating a Simple Moving
Average in 3 Steps in Excel
(Click On Image To See a Larger Version)
This is one of the following three articles on Time Series Analysis in Excel
Forecasting With Exponential Smoothing in Excel
Forecasting With the Weighted Moving Average in Excel
Forecasting With the Simple Moving Average in Excel
Overview of the Moving Average
The moving average is a statistical technique used to smooth out shortterm fluctuations in a series of data in order to more easily recognize longerterm trends or cycles. The moving average is sometimes referred to as a rolling average or a running average. A moving average is a series of numbers, each of which represents the average of an interval of specified number of previous periods. The larger the interval, the more smoothing occurs. The smaller the interval, the more that the moving average resembles the actual data series.
Moving averages perform the following three functions:

Smoothing the data, which means to improve the fit of the data to a line.

Reducing the effect of temporary variation and random noise.

Highlighting outliers above or below the trend.
The moving average is one of the most widely used statistical techniques in industry to identify data trends. For example, sales managers commonly view threemonth moving averages of sales data. The article will compare a twomonth, threemonth, and sixmonth simple moving averages of the same sale data. The moving average is used quite often in technical analysis of financial data such as stock returns and in economics to locate trends in macroeconomic time series such as employment.
There are a number of variations of the moving average. The mostcommonly employed are the simple moving average, the weighted moving average, and the exponential moving average. Performing each of these techniques in Excel will be covered in detail in separate articles in this blog. Here is a brief overview of each of these three techniques.
Simple Moving Average
Every point in a simple moving average is the average of a specified number of previous periods. This blog article will provide a detailed explanation of the implementation of this technique in Excel.
Weighted Moving Average
Points in the weighted moving average also represent an average of a specified number of previous periods. The weighted moving average applies different weighting to certain previous periods; quite often the more recent periods are given greater weight. A link to another article in this blog which provides a detailed explanation of the implementation of this technique in Excel is as follows:
http://blog.excelmasterseries.com/2010/11/weightedmovingaverageaccuratesimple.html
Exponential Moving Average
Points in the exponential moving average also represent an average of a specified number of previous periods. Exponential smoothing applies weighting factors to previous periods that decrease exponentially, never reaching zero. As a result exponential smoothing takes into account all previous periods instead of a designated number of previous periods that the weighted moving average does. A link to another article in this blog which provides a detailed explanation of the implementation of this technique in Excel is as follows:
http://blog.excelmasterseries.com/2010/11/excelmarketingforecastingtechnique3.html
The following describes the 3step process of creating a simple moving average of timeseries data in Excel;
Step 1 – Graph the Original Data in a TimeSeries Plot
The line chart is the most commonlyused Excel chart to graph timeseries data. An example of such an Excel chart used to plot 13 periods of sales data is shown as follows:
(Click On Image To See a Larger Version)
Step 2 – Create the Moving Average in Excel
Excel provides the Moving Average tool within the Data Analysis menu. The Moving Average tool creates a simple moving average from a data series.
(Click On Image To See a Larger Version)
The Moving Average dialogue box should be filled out as follows in order to create a moving average of the previous 2 periods of data for each data point.
(Click On Image To See a Larger Version)
The output of the 2period moving average is shown as follows, along with the formulas that were used to calculate the value of each point in the moving average.
(Click On Image To See a Larger Version)
Step 3 – Add the Moving Average Series to the Chart
This data should now be added to the chart containing the original time line of sales data. The data will simply be added as one more data series in the chart. To do that, rightclick anywhere on the chart and a menu will pop up. Hit Select Data to add the new series of data. The moving average series will be added by completing the Edit Series dialogue box as follows:
(Click On Image To See a Larger Version)
(Click On Image To See a Larger Version)
The chart containing the original data series and that data’s 2interval simple moving average is shown as follows. Note that the moving average line is quite a bit smoother and raw data’s deviations above and below the trend line are much more apparent. The overall trend is now much more apparent as well.
(Click On Image To See a Larger Version)
A 3interval moving average can be created and placed on the chart using the same procedure as follows:
(Click On Image To See a Larger Version)
(Click On Image To See a Larger Version)
It is interesting to note that the 2interval simple moving average creates a smoother graph than the3interval simple moving average. In this case the 2interval simple moving average might be the more desirable than the 3interval moving average.
(Click On Image To See a Larger Version)
For comparison, a 6interval simple moving average will be calculated and added to the chart in the same way as follows:
(Click On Image To See a Larger Version)
(Click On Image To See a Larger Version)
(Click On Image To See a Larger Version)
As expected,the 6interval simple moving average is significantly smoother than the 2 or 3interval simple moving averages. A smoother graph more closely fits a straight line.
Analyzing Forecast Accuracy
Accuracy can be described as goodness of fit. The two components of forecast accuracy are the following:
Forecast Bias – The tendency of a forecast to be consistently higher or lower than actual values of a time series. Forecast bias is the sum of all error divided by the number of periods as follows:
Bias = ∑E_{t}/n = ∑(Y_{tact} – Y_{test})/n
A positive bias indicates a tendency to underforecast. A negative bias indicates a tendency to overforecast. Bias does not measure accuracy because positive and negative error cancel each other out.
Forecast Error – The difference between actual values of a time series and the predicted values of the forecast. The most common measures of forecast error are the following:
MAD – Mean Absolute Deviation
MAD calculates the average absolute value of the error and is computed with the following formula:
MAD = ∑ E_{t} / n = ∑ (Y_{tact} – Y_{test}) / n
Averaging the absolute values of the errors eliminates the canceling effect of positive and negative errors. The smaller the MAD, the better the model is.
MSE – Mean Squared Error
MSE is a popular measure of error that eliminates the cancelling effect of positive and negative errors by summing the squares of the error with the following formula:
MSE = ∑ E_{t}^{2} / n = ∑ (Y_{tact} – Y_{test})^{2} / n
Large error terms tend to exaggerate MSE because the error terms are all squared. RMSE (Root Square Mean) reduces this problem by taking the square root of MSE.
MAPE – Mean Absolute Percent Error
MAPE also eliminates the cancelling effect of positive and negative errors by summing the absolute values of the error terms. MAPE calculates the sum of the percent error terms with the following formula:
MAPE = ∑ ( E_{t} / Y_{tact} ) * 100% / n = ∑ ( (Y_{tact} – Y_{test}) / Y_{tact} ) * 100% / n
By summing percent error terms, MAPE can be used to compare forecasting models that use different scales of measurement.
Calculating Bias, MAD, MSE, RMSE, and MAPE in Excel For the Simple Moving Average
Bias, MAD, MSE, RMSE, and MAPE will be calculated in Excel to evaluate the 2interval, 3interval, and 6interval simple moving average forecast obtained in this article and shown as follows:
(Click On Image To See a Larger Version)
The first step is to calculate E_{t}, E_{t}^{2}, E_{t}, E_{t} / Y_{tact} , and then sum them as follows:
(Click On Image To See a Larger Version)
Bias, MAD, MSE, MAPE and RMSE can be calculated as follows:
(Click On Image To See a Larger Version)
The same calculations are now performed to calculate Bias, MAD, MSE, MAPE and RMSE for the 3interval simple moving average.
(Click On Image To See a Larger Version)
(Click On Image To See a Larger Version)
The same calculations are now performed to calculate Bias, MAD, MSE, MAPE and RMSE for the 6interval simple moving average.
(Click On Image To See a Larger Version)
(Click On Image To See a Larger Version)
Bias, MAD, MSE, MAPE and RMSE are summarized for the 2interval, 3interval, and 6interval simple moving averages as follows. The 3interval simple moving average is the model that most closely fits that actual data.
(Click On Image To See a Larger Version)
Excel Master Series Blog Directory
Statistical Topics and Articles In Each Topic
 Histograms in Excel
 Bar Chart in Excel
 Combinations & Permutations in Excel
 Normal Distribution in Excel
 Overview of the Normal Distribution
 Normal Distribution’s PDF (Probability Density Function) in Excel 2010 and Excel 2013
 Normal Distribution’s CDF (Cumulative Distribution Function) in Excel 2010 and Excel 2013
 Solving Normal Distribution Problems in Excel 2010 and Excel 2013
 Overview of the Standard Normal Distribution in Excel 2010 and Excel 2013
 An Important Difference Between the t and Normal Distribution Graphs
 The Empirical Rule and Chebyshev’s Theorem in Excel – Calculating How Much Data Is a Certain Distance From the Mean
 Demonstrating the Central Limit Theorem In Excel 2010 and Excel 2013 In An EasyToUnderstand Way
 tDistribution in Excel
 Binomial Distribution in Excel
 zTests in Excel
 Overview of Hypothesis Tests Using the Normal Distribution in Excel 2010 and Excel 2013
 OneSample zTest in 4 Steps in Excel 2010 and Excel 2013
 2Sample Unpooled zTest in 4 Steps in Excel 2010 and Excel 2013
 Overview of the Paired (TwoDependentSample) zTest in 4 Steps in Excel 2010 and Excel 2013
 tTests in Excel
 Overview of tTests: Hypothesis Tests that Use the tDistribution
 1Sample tTests in Excel
 1Sample tTest in 4 Steps in Excel 2010 and Excel 2013
 Excel Normality Testing For the 1Sample tTest in Excel 2010 and Excel 2013
 1Sample tTest – Effect Size in Excel 2010 and Excel 2013
 1Sample tTest Power With G*Power Utility
 Wilcoxon SignedRank Test in 8 Steps As a 1Sample tTest Alternative in Excel 2010 and Excel 2013
 Sign Test As a 1Sample tTest Alternative in Excel 2010 and Excel 2013
 2IndependentSample Pooled tTests in Excel
 2IndependentSample Pooled tTest in 4 Steps in Excel 2010 and Excel 2013
 Excel Variance Tests: Levene’s, BrownForsythe, and F Test For 2Sample Pooled tTest in Excel 2010 and Excel 2013
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 2 Sample Pooled tTest – Effect Size in Excel 2010 and Excel 2013
 2Sample Pooled tTest Power With G*Power Utility
 MannWhitney U Test in 12 Steps in Excel as 2Sample Pooled tTest Nonparametric Alternative in Excel 2010 and Excel 2013
 2 Sample Pooled tTest = SingleFactor ANOVA With 2 Sample Groups
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 Excel Normality Tests KolmogorovSmirnov, AndersonDarling, and ShapiroWilk For 2Sample Unpooled tTest
 2Sample Unpooled tTest Excel Calculations, Formulas, and Tools
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 Test Power of a 2Independent Sample Unpooled tTest With GPower Utility
 Paired (2Sample Dependent) tTests in Excel
 Paired tTest in 4 Steps in Excel 2010 and Excel 2013
 Excel Normality Testing of Paired tTest Data
 Paired tTest Excel Calculations, Formulas, and Tools
 Paired tTest – Effect Size in Excel 2010, and Excel 2013
 Paired tTest – Test Power With GPower Utility
 Wilcoxon SignedRank Test in 8 Steps As a Paired tTest Alternative
 Sign Test in Excel As A Paired tTest Alternative
 Hypothesis Tests of Proportion in Excel
 Hypothesis Tests of Proportion Overview (Hypothesis Testing On Binomial Data)
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 Confidence Intervals in Excel
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 tBased Confidence Intervals of a Population Mean in 2 Steps in Excel 2010 and Excel 2013
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 Min Sample Size of Confidence Interval of Proportion in Excel 2010 and Excel 2013
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 Complete Simple Linear Regression Example in 7 Steps in Excel 2010 and Excel 2013
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 Basics of Multiple Regression in Excel 2010 and Excel 2013
 Complete Multiple Linear Regression Example in 6 Steps in Excel 2010 and Excel 2013
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 Logistic Regression Overview
 Logistic Regression in 6 Steps in Excel 2010 and Excel 2013
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 ShapiroWilk Normality Test in Excel For Each SingleFactor ANOVA Sample Group
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 ANOVA Effect Size Calculation Eta Squared in Excel 2010 and Excel 2013
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