# Introduction

The fancy name for a moving average is called ARIMA, or auto-regressive integrated moving average. In statistics, any time you use history to forecast the future, it is called “auto-regressive”. A typical method used by JDA allocation, a moving average is a basic forecasting method that uses a user-defined time period, or a rolling time period of history, averages the values together, and uses it to estimate the future. The equation is simple:

Example:  Say we have 3 sales periods, 100, 120, and 230.  The average would be these three values divided by 3, or 150.  Now let’s say the next period sales is 40.  A moving average will take the last three periods, or 120, 230, and 40, or 130.

If sales are relatively flat from period to period, without any seasonal trend then a moving average is a good bet. In retail apparel this is not a particularly helpful method unless the time period you average is from a year ago for the same time period you’re trying to forecast. In statistics, this is called the ARIMA model. The moving average also is challenged by trend effects, especially if the time period being used for the average is from a year ago.

### Example:

We’ll create a retailer with February as their first fiscal month. Let’s try to forecast our retailer’s February sales of the new fiscal year for 2016 using a moving average. Say we have the following sales by month for 2014 and 2015. One way we can forecast is to take a rolling average (non-seasonal). The other is to take an average of the same time period from both years (seasonal).

Here are the monthly sales (click to enlarge).  We will be using a standard 4-5-4 NRF calendar.

The seasonal moving average, means we take the sales from February 2014 and February 2015 and average them together to predict 2016, or (379,762 + 373,141) / 2 = 376,452.

To obtain a regular moving average let’s take the last three months.  But first we’ll need to convert the monthly sales into average weekly sales so we can compare months which have different numbers of weeks.  Click to enlarge.

So, if we take November 2015, December 2015, and January 2015, average them together we get (162,319 + 156,690 + 64,895) / 3 = 127,968.  Now we convert it back to monthly figure by multiplying this value times 4 since February is a 4 week month and we get 127,968 X 4 = 511,872.  With just a minimal amount of analysis we can see this forecast is going to be unreasonable.  Non-Seasonal moving averages on seasonal data is generally not a good idea and now you can see why.

The actual sales for February 2016 is 326,181 as shown in this bar chart.

Part I:  Moving Averages
Part II: Exponential Smoothing
Part III: Sales Profiles
Part IV: Variable Response Smoothing