Level 4 · Month over month and year over year

Growth against what?

“Up 93%” means nothing until you say compared with what. The two comparisons every analyst uses:

• Period over period (month over month, MoM): this month against the month before. Good for spotting sudden changes.
• Year over year (YoY): this month against the same month last year. The fair test for a seasonal business, because November is compared with another November.

shift and pct_change

shift(n) moves a series down by n rows, so each row sits next to the value from n rows earlier. Growth is then plain arithmetic:

monthly = orders.set_index("order_date").resample("MS").size()
growth = (monthly / monthly.shift(1) - 1) * 100

pct_change(n) is the shortcut for exactly that: monthly.pct_change() is the change on the previous row, and monthly.pct_change(12) on the row 12 places back. On a monthly series with no missing months, 12 rows back is the same month last year. That’s one more reason to build monthly series with resample: it never skips a month, so row offsets always match calendar offsets.

Note that pct_change returns a fraction (0.137), so multiply by 100 for a percentage (13.7).

The first row has nothing before it, so its MoM change is NaN. The first 12 rows have no year-ago row, so their YoY change is NaN. That’s correct: don’t fill them with 0, which would claim “no change”.

A worked example

Computed on the full series, the 2025 rows read:

#  order_date  n_orders  mom_pct  yoy_pct
#  2025-01-01       296    -57.6     26.0
#  2025-10-01       371      7.5     14.2
#  2025-11-01       715     92.7     13.7
#  2025-12-01       777      8.7     11.3

November 2025 nearly doubled on October (+92.7%), which sounds like a breakthrough. Year over year it’s +13.7%, in line with the rest of the year. January looks like a collapse month over month (−57.6%) because December is the peak; year over year it grew 26%. Seasonality makes MoM swing wildly at exactly the moments people pay most attention to.

Compute first, filter last

As with rolling windows, the comparison needs history. If you select 2025 first, January has no December before it and nothing has a year-ago row. Build the columns on all 36 months, then select with table.loc["2025"]: on a DatetimeIndex, a year string selects the whole year.

Common mistakes

• Filtering to one year before pct_change, which turns the comparisons into NaN.
• Forgetting * 100 and reporting 0.137 as “0.1%”.
• Using pct_change(12) on a series with missing months, so 12 rows is no longer 12 months.
• Calling seasonal MoM jumps “growth” without the YoY figure next to it.