How do moving holidays like Easter distort the seasonal indices of a monthly retail series?

## Why a month-of-year index is a strong assumption The classical seasonal step averages the detrended values for each position in the season across all cycles: all Januaries together, all Februaries together, and so on. The output is one number per calendar month, reused every year. That is only correct if everything the calendar does to the series is a function of *which month it is*. Three common effects break that assumption. ## Moving holidays Easter is determined by a lunar rule and can fall anywhere from March 22 to April 25. Retail responds strongly to the run-up, not to the day itself, so the surge lands in March in some years and in April in others. Now consider what the seasonal step does. In a history where Easter is in April two years out of three, the April index is an average of two large values and one small one, and the March index of one large and two small. Neither index describes any actual year. In an April-Easter year, the March index over-predicts March and the April index under-predicts April; in a March-Easter year the errors reverse. The signature in the remainder is unmistakable once you look for it: a large March residual paired with an opposite-signed April residual, flipping sign from year to year in step with the holiday date. Chinese New Year is the same problem in January and February, again lunar-determined and again with an effect that runs for days or weeks before the date. Ramadan drifts across the solar calendar entirely, moving about eleven days earlier each year, so its effect walks slowly through every month of the year over a few decades. ## Trading-day and month-length effects Even with no holidays, months are not comparable units. A month contains 28 to 31 days, so a February is short by roughly ten percent relative to a January for any quantity that accrues daily. Part of what a naive February index measures is simply that February is short, which is not a behavioural fact about February at all, and leap years make it inconsistent from year to year. The composition of weekdays varies too. A 31-day month contains five of some weekdays and four of others, and which ones depends on the day the month starts. For a weekend-heavy retail business the difference between a March with five full weekends and a March with four is easily a few percent of the month's sales, with no change whatever in underlying demand. This is calendar variation, not seasonality, and a month-of-year index has no way to represent it because it differs between two instances of the same month. ## Handling it **Adjust for the calendar before decomposing.** The standard approach in official statistics is a pre-adjustment step: estimate how much of each observation is attributable to the moving holiday, to the number of trading days, and to the length of the month, remove that, and decompose the adjusted series. The seasonal step then only has to explain genuinely month-of-year behaviour, and the estimated indices become interpretable again. The holiday effect is usually modelled as a window of elevated activity spanning several days before the date, with the window's contribution to each month computed from how many of those days actually fell in that month. **Or change the time unit.** Two reframings help. Normalising by days in the month removes the length effect directly for daily-accrual quantities. Aligning the series relative to the holiday, so that the index is weeks-before or weeks-after the holiday rather than a calendar month, turns a moving effect into a stationary one, at the cost of a series that is harder to reconcile with monthly reporting. Retail organisations often use 4-4-5 style periods, which fix the number of weekends per period, precisely to avoid trading-day noise in period-over-period comparisons. **Or move to weekly data**, where the holiday sits in one identifiable week and its effect is easier to isolate, then aggregate for reporting. ## Diagnosing a decomposition you were handed You will often inherit a decomposition rather than build one. Three checks find these problems quickly: 1. Plot the remainder by calendar month across years. A moving holiday shows as a paired, opposite-signed March-April pattern that alternates with the holiday date, not as scatter. 2. Check whether February's index looks unusually low in a way that tracks days in the month rather than any story about February demand. 3. For a weekend-sensitive series, count the weekends in each month and see whether the remainder correlates with that count. If it does, you have a trading-day effect sitting in the residual. ## The framing that reads as senior The point is not that these effects are exotic; it is that they are *systematic errors misfiled as noise*. Each one produces a remainder that looks larger and more erratic than the series really is, which then makes every downstream judgment about the series less sharp. Naming the mechanism, saying which calendar effect you would remove first, and showing you know to check the remainder by month is the whole answer.