Temporal granularity decides which periodicities become visible

What it is

Which cycles a time-series chart can develop depends on the aggregation granularity: daily granularity cannot see intra-day rhythm (rush hours averaged away); hourly granularity loses weekly detail in the thicket of points; monthly granularity kills both daily and weekly cycles at once. Granularity is a filter on periodicity — and not a neutral one: cycles shorter than the granularity average out, cycles near it distort into aliasing artifacts, cycles far below it cannot fit on the page. Choosing granularity is therefore deciding "what readers will find," not settling a technical detail.

Why it happens

Aggregation is a low-pass filter: rolling hours into days cancels intra-day variance into the mean, and structure shorter than the granularity vanishes mathematically. Aliasing is more treacherous: when the sampling granularity approaches but misses a true cycle (hourly sampling of an oscillation with a 40-minute period), the polyline reveals a slow wave that does not exist — the false cycle looks as credible as a true one on the chart. The rendering layer filters a second time: 500 pixels showing a year of hourly data (8,760 points) drowns sub-pixel detail — weekly and monthly waves visible, daily waves mush — so screen resolution is itself a granularity. Multi-scale structure (real business with intra-day + weekly + seasonal components stacked) inevitably loses somewhere under any single granularity.

Where it stops holding

No universal granularity exists — only alignment with the question: intra-day rhythm takes hours or minutes, weekday effects take days with weekly windows, seasonality takes weeks or months. Aliasing risk peaks when granularity nears the true cycle; the working rule is sampling at least five times finer than the target period (an engineering weakening of the sampling theorem). The right tools for multi-scale exploration are hierarchical aggregation switches (interactive day/week/month toggles) or calendar/nested hour-day-week layouts, letting each cycle develop at its fitting granularity. Static reports must declare granularity and name the cycles filtered out.

Applying it

• List the target cycles first (daily/weekly/monthly/quarterly) and pick for each question the coarsest granularity that renders that cycle faithfully; "finer than one-fifth of the period" as the floor.
• Interactive charts get a granularity switcher with the caption declaring the current level and the invisible ones; static reports with coexisting cycles use nested layouts (hourly facets arranged by week).
• Verification: plot the same data at two granularities and ask readers what cycles they see; differing visible cycles across versions demonstrate the filtering effect directly.

Related

• Same group: U3.06.1 Uneven sampling plotted at even spacing distorts rates of change · U3.06.2 Gaps in a series should appear as gaps on the axis, not be skipped over · U3.06.3 Months have unequal lengths; equal-width monthly bars are not directly comparable · U3.06.4 Time zones and DST create duplicated or missing hours on the axis
• Nearby: U2.08.1 Histogram bin width changes the conclusion · U6.03.1 Zooming and panning the time range
• Search terms: temporal aggregation · periodicity · aliasing · multi-scale time series