Building a shared workbook for calendar seasonality tests

Three views of one calendar history

Editorial view: treat a seasonal idea as unfinished until the same calendar history is built three ways and each view is forced through one shared-test-stack. A month-based candidate becomes a keep, size, or refuse decision only after level, year-relative, and month-to-month-change representations can be tested as a single procedure inside a regime-aware book.

The archive workflow starts from a calendar-matrix, a rectangular history whose columns are calendar months and whose rows are successive years or comparable periods.

Level summaries on the first calendar-matrix

The first data matrix is summarized with row averages, row standard deviations, and row observation counts, plus matching column summaries and a single matrix-wide average, standard deviation, and count. Those rows are the level view of the same calendar history that the later restatements will reuse.

How the column test is built

Each column-t-statistic is a two-sample comparison of one month's mean with the whole-matrix mean. It is the absolute gap between that column's average and the matrix average, divided by the square root of the sum of each variance divided by its own count.

Approximate-p-values are produced from those T statistics with a stored six-coefficient polynomial that approximates a normal curve rather than a native statistical function. The six stored coefficients are 0.7070735, 0.1411281, 0.08864028, 0.02743349, -0.00039446, and 0.00328975.

The approximate-p-value expression halves the reciprocal of one plus a fifth-degree polynomial in the T statistic plus the first coefficient, with that entire denominator then squared.

Year-relative months and month-to-month changes

A second matrix restates each monthly price as a year-relative month: 100 times that month divided by the same year's row average, so seasonal shape is separated from the year's level. Column summaries, column-t-statistics, and approximate-p-values are then repeated.

A third matrix restates each observation as a month-to-month change, the percentage move from the prior month's observation. The opening cell is specified to use a December 1960 index level as that predecessor.

The T and p construction defined on the first matrix is reused without a new formula on both the year-relative matrix and the month-to-month-change matrix. That reuse is the shared-test-stack: the same average, dispersion, count, T, and p rows applied unchanged to raw levels, year-relative months, and month-to-month changes.