Data Analysis: How to Track Aggregated Numbers in a Time Series

On a recent consulting assignment, I was discussing monthly sales numbers with the client when he made the following comment: “Oh, yes, sales for February are always somewhat lower—that’s an after effect of the Christmas peak.” Sales are always lower in February? How interesting.

Sure enough, if you plotted the monthly sales numbers for the last few years, there was a rather visible dip from the overall trend every February. But in contrast, there wasn’t much of a Christmas spike! (The client’s business was not particularly seasonal.) So why should there be a corresponding dip two months later?

By now I am sure you know the answer already: February is shorter than any of the other months. And it’s not a small effect, either: with 28 days, February is about three days shorter than the other months (which have 30–31 days). That’s about 10 percent—close to the size of the dip in the client’s sales numbers.

When monthly sales numbers were normalized by the number of days in the month, the February dip all but disappeared, and the adjusted February numbers were perfectly in line with the rest of the months. (The average number of days per month is 365/12 = 30.4.)

Whenever you are tracking aggregated numbers in a time series (such as weekly, monthly, or quarterly results), make sure that you have adjusted for possible variation in the aggregation time frame. Besides the numbers of days in the month, another likely candidate for hiccups is the number of business days in a month (for months with five weekends, you can expect a 20 percent drop for most business metrics). But the problem is, of course, much more general and can occur whenever you are reporting aggregate numbers rather than rates. (If the client had been reporting average sales per day for each month, then there would never have been an anomaly.)

This specific problem (i.e., nonadjusted variations in aggregation periods) is a particular concern for all business reports and dashboards. Keep an eye out for it!