Try the new Google Books
Check out the new look and enjoy easier access to your favorite features
Try the new Google Books
Check out the new look and enjoy easier access to your favorite features
This method calculates a trend, a seasonal index, and an exponentially smoothed average from the sales order history. The system then applies a projection of the trend to the forecast and adjusts for the seasonal index.
This method requires the number of periods best fit plus two years of sales data, and is useful for items that have both trend and seasonality in the forecast. You can enter the alpha and beta factor, or have the system calculate them. Alpha and beta factors are the smoothing constant that the system uses to calculate the smoothed average for the general level or magnitude of sales (alpha) and the trend component of the forecast (beta).
This method is similar to Method 11, Exponential Smoothing, in that a smoothed average is calculated. However, Method 12 also includes a term in the forecasting equation to calculate a smoothed trend. The forecast is composed of a smoothed average that is adjusted for a linear trend. When specified in the processing option, the forecast is also adjusted for seasonality.
Forecast specifications:
-
Alpha equals the smoothing constant that is used in calculating the smoothed average for the general level or magnitude of sales.
Values for alpha range from 0 to 1.
-
Beta equals the smoothing constant that is used in calculating the smoothed average for the trend component of the forecast.
Values for beta range from 0 to 1.
-
Whether a seasonal index is applied to the forecast.
Minimum required sales history: One year plus the number of time periods that are required to evaluate the forecast performance (periods of best fit). When two or more years of historical data is available, the system uses two years of data in the calculations.
Method 12 uses two Exponential Smoothing equations and one simple average to calculate a smoothed average, a smoothed trend, and a simple average seasonal index.
An exponentially smoothed average:
At = α (Dt/St-L) + (1 - α)(At-1 + Tt-1)
An exponentially smoothed trend:
Tt = β (At - At-1) + (1 - β)Tt-1
A simple average seasonal index:
The forecast is then calculated by using the results of the three equations:
Ft+m = (At + Ttm)St-L+m
where:
-
L is the length of seasonality (L equals 12 months or 52 weeks).
-
t is the current time period.
-
m is the number of time periods into the future of the forecast.
-
S is the multiplicative seasonal adjustment factor that is indexed to the appropriate time period.
This table lists history used in the forecast calculation:
Calculation of Linear and Seasonal Exponential Smoothing, given alpha = 0.3, beta = 0.4
Initializing the Process:
January of past year 1 Seasonal Index, S1 =
S1 = (125 + 128 / 1534 + 1514) × 12 = 0.083005 × 12 = 0.9961
January of past year 1 Smoothed Average*, A1 =
A1 = (January of past year 1 Actual) / (January Seasonal Index)
A1 = 128 / 0.9960
A1 = 128.51
January of past year 1 Smoothed Trend*, T1 =
T1 = 0 insufficient information to calculate first smoothed trend
February of past year 1 Seasonal Index, S2 =
S2 = (123 + 117 / 1534 + 1514) × 12 = 0.07874 × 12 = 0.9449
February of past year 1 Smoothed Average, A2 =
A2 = α(D2 / S2) + (1 – α) (A1 + T1)
A2 = 0.3(117 / 0.9449) + (1 – 0.3) (128.51 + 0) = 127.10
February of past year 1 Smoothed Trend, T2 =
T2 = β(A2 - A1) + (1 - β)T1
T2=0.4 (127.10 – 128.51) + (1 – 0.4) × 0 = –0.56
March of past year 1 Seasonal Index, S3 =
S3 = (115 + 115 / 1534 + 1514) × 12 = 0.07546 × 12 = 0.9055
March of past year 1 Smoothed Average, A3 =
A3 = α(D3/S3) + (1 – α)(A2 + T2)
A3 = 0.3 (115 / 0.9055) + (1 – 0.3)(127.10 – 0.56) = 126.68
March of past year 1 Smoothed Trend, T3 =
T3 = β(A3 –A2) + (1 – β)T2
T3 = 0.4(126.68 – 127.10) + (1 – 0.4) x – 0.56 = – 0.50
(Continue through December of past year 1)
December of past year 1 Seasonal Index, S12 =
S12 = (133 + 137 / 1534 + 1514) × 12 = 0.08858 × 12 = 1.0630
December of past year 1 Smoothed Average, A12 =
A12 = α (D12/S12)+ (1 – α)( A11 + T11)
A12 = 0.3 (137/1.0630 ) + ( 1 – 0.3)( 124.64 – 1.121 ) = 125.13
December of past year 1 Smoothed Trend, T12 =
T12 = β (A12 – A11) + (1 – β)T11
T12 = 0.4 (125.13 – 124.64)+ ( 1 – 0.4) x – 1.121 = – 0.477
Calculation of linear and seasonal exponentially smoothed forecast is calculated as follows:
F t + m = (At +Tt m )St – L + m
* Calculations for Exponential Smoothing with Trend and Seasonality are initialized by setting the first smoothed average equal to the deseasonalized first actual sales data. The trend is initialized at zero for the first iteration. For subsequent calculations, alpha and beta are set to the values that are specified in the processing options.
This table indicates the Exponential Smoothing with Trend and Seasonality forecast for next year, where alpha = 0.3, beta = 0.4:
- Career development
- Rolling Averages: What They Are and How To Calculate Them
By Indeed Editorial Team
Published August 4, 2021
Rolling average = sum of data over time / time period
Tracking a company's trends can help executives understand whether the business is successful. Rolling averages can give those executives the data they need to assess those trends. Understanding what a rolling average is and how to calculate one gives you the tools you need to figure out how your business changes over time. In this article, we define rolling averages, give you the formula for calculating it and offer a step-by-step guide on how to complete the formula to help you determine business trends over any period you choose.
Related: Business Metrics: Definition, Examples and Formulas
What is a rolling average?
A rolling average, sometimes referred to as a moving average, is a metric that calculates trends over short periods of time using a set of data. Specifically, it helps calculate trends when they might otherwise be difficult to detect. For instance, if your data set includes many points where the numbers shift up and down drastically, you might not see whether it trends up or down over time.
To discover the trend, a rolling average uses smaller parts of the data. For instance, you might use the numbers collected over the last 30 days and find out their average. Then, the average rolls or moves for each new period. Making these calculations for every 30 day period allows professionals to discover the way the average changes as time moves forward.
Related: Helpful Metrics to Measure Success
Why are rolling averages useful?
Rolling averages are useful for finding long-term trends otherwise disguised by occasional fluctuations. For instance, if your company sells ice, you might notice a fluctuation upwards on hot days. If the temperature in your area fluctuates often, your data might become difficult to track. Calculating a rolling average can help you determine your ice sales trends for each period. While you might notice your ice sales go down in cooler months, your business might trend up over the entire year.
Rolling averages can also help you determine the factors that cause your trends. This can help you prepare and make decisions for the future of your business. If weather makes your ice sales fluctuate on hot days, you might notice an upward trend during the summer months. This can help you set strategic goals and determine how much ice to produce during those months based on previous data.
Related: Complete Guide To Setting Strategic Goals (With Examples)
How do you calculate a rolling average?
Professionals use a formula to calculate rolling averages. This involves collecting data over time and inserting it into the formula. The formula looks like this: rolling average = sum of data over time / time period. These steps help you figure out which numbers to include in the formula, then how to solve the equation:
1. Determine your time period
Figuring out the time period for your rolling average depends on your goal in calculating it. For instance, if you hope to determine how much each month's sales affect your trends, you might choose a rolling 12-month period. When you want to know which day of the week affects the trend, you could decide to average a rolling seven-day period.
Related: 4 Examples of Key Performance Metrics to Track
2. Collect the data
Next, you need the data based on the time you chose. It's helpful to collect data over a longer period than you chose. For example, if you tracked how monthly sales trends over the year, you might collect data from the past 18 months or the past year. Having more data can help you determine the way trends change.
3. Add your earliest totals
To track your trends, it's helpful to start with the earliest totals you have available. If you have sales totals from July 2019 to December 2020, a good practice is to begin with the 12-month period from July 2019 to June 2020 and add them all together. For example, these might be your totals for those months:
July 2019: $48,904
August 2019: $49,615
September 2019: $47,546
October 2019: $51,600
December 2019: $50,455
January 2020: $50, 690
February 2020: $51,900
March 2020: $52,420
April 2020: $51,981
May 2020: $53,315
June 2020: $54,100
Total: $526,526
4. Divide the total by your time period
Dividing the total by your time period gives you your average for each unit. If you're calculating your average for a 30-day period, divide by 30. If you're calculative over a 12-month period, divide by 12. To continue our example, for your total of $526,526 over 12 months, it might look like this:
$526,526 / 12 = $46,877.17
This means your business averaged $46,877.17 per month from July 2019 to June 2020.
5. Calculate the average for your next rolling period
Calculating your next rolling period involves leaving off your earliest unit and adding in your next unit. In the monthly example, this means leaving off the sales from July 2019 and adding in your sales from July 2020. This helps you calculate your average for the 12-month period from August 2019 to July 2020. If your sales total $55,000 in June 2020, your new total would be $532,622. Again, since it's a 12-month period, dividing by 12 can give you your monthly average.
$532,622 / 12 = $44,385.17
6. Continue the formula for each rolling period
As you continue, the rolling period keeps moving. As you continue, removing the earliest month's sales and adding in the next and completing the formula gives you each 12-month period's average. Your next 3 month's sales might look like this:
August 2020: $54,200
September 2020: $55,600
October 2020: $56,100
This helps you continue to calculate your rolling period averages. When placing them into the formula, your averages look like this:
September 2019 to August 2020: $537,207 / 12 = $44,767.25
October 2019 to September 2020: $545,261 / 12 = $45,438.42
November 2019 to October 2020: $549,761 / 12 = $45,813
With these calculations, you can determine that for each rolling period, your sales typically trend upward.
7. Complete the formula regularly
As you continue to run your business, you can continue to complete the formula as you collect new data. This way, you can regularly determine your rolling average so you can continue to track your trends. Then, you can better understand the health of your business, report it to executives and shareholders and make decisions that prepare you for the future of your company.