Posts Tagged ‘calendar effects’

Forecast Friday Topic: Calendar Effects in Forecasting

December 16, 2010

(Thirty-third in a series)

It is a common practice to compare a particular point in time to its equivalent one or two years ago. Companies often report their earnings and revenues for the first quarter of this year with respect to the first quarter of last year to see if there’s been any improvement or deterioration since then. Retailers want to know if December 2010 sales were higher or lower than December 2009 and even December 2008 sales. Sometimes, businesses want to see how sales compared for October, November, and December. While these approaches seem straightforward, the way the calendar falls can create misleading comparisons and faulty forecasts.

Every four years, February has 29 days instead of the usual 28. That extra day can cause problems in forecasting February sales. In some years, Easter falls in April, and other years March. This can cause forecasting nightmares for confectioners, greeting cards manufacturers, and retailers alike. In some years, a given month might have five Fridays and/or Saturdays, and just four in other years. If your business’ sales are much higher on the weekend, these can generate significant forecast error.

Adjusting for Month Length

Some months have as many as 31 days, others 30, while February 28 or 29. Because the variation in the calendar can cause variation in the time series, it is necessary to make adjustments. If you do not adjust for variation in the length of the month, the effects can show up as a seasonal effect, which may not cause serious forecast errors, but will certainly make it difficult to interpret any seasonal patterns. You can easily adjust for month length:

Where Wt is the weighted value of your dependent variable for that month. Hence, if you had sales of $100,000 in February and $110,000 in March, you would first start with the numerator. There’s 365.25 days in a (non-leap) year. Divide that by 12. That means the numerator will be 30.44. Divide that by the number of days in each of those months to get adjustment factors for each month. So, for February, you’d divide 30.44 by 28 and get an adjustment factor of 1.09; for March, you would divide by 31 and get an adjustment factor of .98. Then you would multiply those factors by their respective months. Hence, your weighted sales for February would be $109,000, and for March approximately $108,000. Although sales appear to be higher in March than in February, once you adjust for month length, you find that the two months actually were about the same in terms of volume.

Adjusting for Trading Days

As described earlier, months can have four or five occurrences of the same day. As a result, a month may have more trading days in one year than they do in the next. This can cause problems in retail sales and banking. If a month has five Sundays in it, and Sunday is a non-trading day (as is the case in banking) you must account for it. Unlike month-length adjustments, where differences in length from one month to the next are obvious, trading day adjustments aren’t always precise, as their variance is not as predictable.

In the simplest cases, your approach can be similar to that of the formula above, only you’re dividing the number of trading days in an average month by the number of trading days in a given month. However, that can be misleading.

Many analysts also rely on other approaches to adjust for trading days in regression analysis: seasonal dummy variables (which we discussed earlier this year); creating independent variables that denote the number of times each day of the week occurred in that month; and a dummy variable for Easter (having a value of 1 in either March or April, depending on when it fell, and 0 in the non-Easter month).

Adjusting for calendar and trading day effects is crucial to effective forecasting and discernment of seasonal patterns.

Forecast Friday Resumes January 6, 2011

Forecast Friday will not be published on December 23 and December 30, in observance of Christmas and New Year’s, but will resume on January 6, 2011. When we resume on that day, we will begin a six-week miniseries on autoregressive integrated moving average (ARIMA) models in forecasting. This six-week series will round out all of our discussions on quantitative forecasting techniques, after which we will begin discussing judgmental forecasts for five weeks, followed by a four week capstone tying together everything we’ve discussed. There’s much to look forward to in the New Year.

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