Autocorrelation (ACF)

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status="ready" · a year of storefront orders. Nothing about lag 1 is interesting — it is lags 7, 14, 21 and 28, at 0.74, 0.75, 0.71 and 0.70, that carry the signal, with the troughs two days either side of each peak. 12 of 28 lags leave the ±0.10 band where about 1.4 would by chance, and the verdict names the weekly period rather than leaving it to be counted off the axis. Hover a stem, or tab into the plot and use the arrow keys; Enter picks one.

Daily orders · autocorrelation

364 days · lags 1–28, weekly period marked

ACF PACF inside the band ±0.10 = ±1.96/√364

12 ACF and 10 PACF of 28 lags outside the band — about 1.4 would be there by chance alone. Lag 0 is 1 by definition and is never plotted.

Lags 7, 14, 21 are outside the band — multiples of the 7 it repeats on, so the structure here is seasonal rather than a short memory. 12 of 28 lags leave the band in all: read the rest against that cycle rather than one at a time.

Daily orders · autocorrelation: 28 lags estimated from 364 readings. Significance band: ±0.10 = ±1.96/√364. 12 ACF and 10 PACF of 28 lags outside the band — about 1.4 would be there by chance alone. Outside the band: 12 lags — 2, 5, 7, 9, 12, 14, 16, 19 and 4 more. Lags 7, 14, 21 are outside the band — multiples of the 7 it repeats on, so the structure here is seasonal rather than a short memory. 12 of 28 lags leave the band in all: read the rest against that cycle rather than one at a time.
Lag	ACF	ACF band	PACF	PACF band
1	+0.06	±0.10 — inside	+0.06	±0.10 — inside
2	-0.40	±0.10 — outside	-0.41	±0.10 — outside
3	+0.06	±0.10 — inside	+0.14	±0.10 — outside
4	+0.03	±0.10 — inside	-0.20	±0.10 — outside
5	-0.42	±0.10 — outside	-0.40	±0.10 — outside
6	0.00	±0.10 — inside	+0.05	±0.10 — inside
7	+0.74	±0.10 — outside	+0.61	±0.10 — outside
8	0.00	±0.10 — inside	-0.23	±0.10 — outside
9	-0.39	±0.10 — outside	-0.04	±0.10 — inside
10	+0.08	±0.10 — inside	-0.03	±0.10 — inside
11	+0.08	±0.10 — inside	+0.09	±0.10 — inside
12	-0.39	±0.10 — outside	-0.08	±0.10 — inside
13	0.00	±0.10 — inside	+0.07	±0.10 — inside
14	+0.75	±0.10 — outside	+0.40	±0.10 — outside
15	+0.03	±0.10 — inside	-0.01	±0.10 — inside
16	-0.38	±0.10 — outside	-0.02	±0.10 — inside
17	+0.07	±0.10 — inside	-0.03	±0.10 — inside
18	+0.05	±0.10 — inside	-0.02	±0.10 — inside
19	-0.41	±0.10 — outside	0.00	±0.10 — inside
20	0.00	±0.10 — inside	+0.04	±0.10 — inside
21	+0.71	±0.10 — outside	+0.17	±0.10 — outside
22	+0.01	±0.10 — inside	-0.07	±0.10 — inside
23	-0.37	±0.10 — outside	+0.01	±0.10 — inside
24	+0.06	±0.10 — inside	-0.11	±0.10 — outside
25	+0.04	±0.10 — inside	-0.01	±0.10 — inside
26	-0.38	±0.10 — outside	+0.02	±0.10 — inside
27	-0.01	±0.10 — inside	-0.02	±0.10 — inside
28	+0.70	±0.10 — outside	+0.13	±0.10 — outside

onLagSelect → nothing picked

status="empty" · a valid payload carrying no readings at all — a different sentence from "loading" and from a fetch that failed.

Daily orders · autocorrelation

364 days · lags 1–28, weekly period marked

No series yet

Autocorrelations and their significance band appear here once the series arrives.

status="loading" · a decaying stem row around a baseline — the silhouette the plot itself has — so nothing jumps when the numbers land. aria-hidden, no timers, and no pulsing under reduced motion.

Daily orders · autocorrelation

364 days · lags 1–28, weekly period marked

status="error" · the fetch failed. "Try again" only exists when onRetry is passed; clicking it flips this card to ready and moves focus to the card, so focus never lands on <body> when the button unmounts.

Daily orders · autocorrelation

364 days · lags 1–28, weekly period marked

Couldn't load this series

The data source didn't respond.

An AR(1) queue · 240 minutes of p95 latency where each minute keeps 0.7 of the last one. This is the pair of panels the toggle exists for: the ACF decays geometrically across 7 lags because every lag inherits lag 1's shadow, while the PACF — which regresses those intervening lags out — shows exactly one spike at 0.67 and nothing after it. One picture says 'sticky', two say 'AR(1)'.

p95 checkout latency · autocorrelation

240 minutes · AR(1) with φ ≈ 0.7

ACF PACF inside the band ±0.13 = ±1.96/√240

7 ACF and 1 PACF of 24 lags outside the band — about 1.2 would be there by chance alone. Lag 0 is 1 by definition and is never plotted.

The ACF decays across 7 lags while the PACF cuts off after 1 lag — the classic autoregressive signature, so AR(1) is the order to try first.

p95 checkout latency · autocorrelation: 24 lags estimated from 240 readings. Significance band: ±0.13 = ±1.96/√240. 7 ACF and 1 PACF of 24 lags outside the band — about 1.2 would be there by chance alone. Outside the band: 7 lags — 1, 2, 3, 4, 5, 6, 7. The ACF decays across 7 lags while the PACF cuts off after 1 lag — the classic autoregressive signature, so AR(1) is the order to try first.
Lag	ACF	ACF band	PACF	PACF band
1	+0.67	±0.13 — outside	+0.67	±0.13 — outside
2	+0.47	±0.13 — outside	+0.04	±0.13 — inside
3	+0.34	±0.13 — outside	+0.02	±0.13 — inside
4	+0.28	±0.13 — outside	+0.07	±0.13 — inside
5	+0.22	±0.13 — outside	-0.02	±0.13 — inside
6	+0.18	±0.13 — outside	+0.02	±0.13 — inside
7	+0.14	±0.13 — outside	-0.01	±0.13 — inside
8	+0.10	±0.13 — inside	-0.01	±0.13 — inside
9	+0.03	±0.13 — inside	-0.08	±0.13 — inside
10	+0.05	±0.13 — inside	+0.09	±0.13 — inside
11	+0.03	±0.13 — inside	-0.05	±0.13 — inside
12	-0.02	±0.13 — inside	-0.06	±0.13 — inside
13	-0.01	±0.13 — inside	+0.06	±0.13 — inside
14	-0.03	±0.13 — inside	-0.07	±0.13 — inside
15	-0.05	±0.13 — inside	-0.01	±0.13 — inside
16	-0.06	±0.13 — inside	-0.01	±0.13 — inside
17	-0.05	±0.13 — inside	+0.01	±0.13 — inside
18	-0.06	±0.13 — inside	-0.05	±0.13 — inside
19	-0.03	±0.13 — inside	+0.08	±0.13 — inside
20	+0.03	±0.13 — inside	+0.07	±0.13 — inside
21	+0.08	±0.13 — inside	+0.03	±0.13 — inside
22	+0.06	±0.13 — inside	-0.01	±0.13 — inside
23	+0.07	±0.13 — inside	+0.01	±0.13 — inside
24	+0.07	±0.13 — inside	0.00	±0.13 — inside

The same series against a Bartlett band · band='bartlett' widens the band with the correlations already found, so it asks 'does lag k add anything beyond the lags before it' instead of 'is the whole series white noise'. Seven significant lags become five, and the two that drop out were never independent evidence — they were lag 1 being counted again.

p95 checkout latency · autocorrelation

240 minutes · AR(1) with φ ≈ 0.7

ACF PACF inside the band Bartlett band, widening with the correlations already found (±0.13 at lag 1)

5 ACF and 1 PACF of 24 lags outside the band — about 1.2 would be there by chance alone. Lag 0 is 1 by definition and is never plotted.

The ACF decays across 5 lags while the PACF cuts off after 1 lag — the classic autoregressive signature, so AR(1) is the order to try first.

p95 checkout latency · autocorrelation: 24 lags estimated from 240 readings. Significance band: Bartlett band, widening with the correlations already found (±0.13 at lag 1). 5 ACF and 1 PACF of 24 lags outside the band — about 1.2 would be there by chance alone. Outside the band: 5 lags — 1, 2, 3, 4, 5. The ACF decays across 5 lags while the PACF cuts off after 1 lag — the classic autoregressive signature, so AR(1) is the order to try first.
Lag	ACF	ACF band	PACF	PACF band
1	+0.67	±0.13 — outside	+0.67	±0.13 — outside
2	+0.47	±0.17 — outside	+0.04	±0.13 — inside
3	+0.34	±0.19 — outside	+0.02	±0.13 — inside
4	+0.28	±0.20 — outside	+0.07	±0.13 — inside
5	+0.22	±0.21 — outside	-0.02	±0.13 — inside
6	+0.18	±0.21 — inside	+0.02	±0.13 — inside
7	+0.14	±0.21 — inside	-0.01	±0.13 — inside
8	+0.10	±0.22 — inside	-0.01	±0.13 — inside
9	+0.03	±0.22 — inside	-0.08	±0.13 — inside
10	+0.05	±0.22 — inside	+0.09	±0.13 — inside
11	+0.03	±0.22 — inside	-0.05	±0.13 — inside
12	-0.02	±0.22 — inside	-0.06	±0.13 — inside
13	-0.01	±0.22 — inside	+0.06	±0.13 — inside
14	-0.03	±0.22 — inside	-0.07	±0.13 — inside
15	-0.05	±0.22 — inside	-0.01	±0.13 — inside
16	-0.06	±0.22 — inside	-0.01	±0.13 — inside
17	-0.05	±0.22 — inside	+0.01	±0.13 — inside
18	-0.06	±0.22 — inside	-0.05	±0.13 — inside
19	-0.03	±0.22 — inside	+0.08	±0.13 — inside
20	+0.03	±0.22 — inside	+0.07	±0.13 — inside
21	+0.08	±0.22 — inside	+0.03	±0.13 — inside
22	+0.06	±0.22 — inside	-0.01	±0.13 — inside
23	+0.07	±0.22 — inside	+0.01	±0.13 — inside
24	+0.07	±0.22 — inside	0.00	±0.13 — inside

A random walk · inventory on hand is a level, not a rate, so every day starts from yesterday's number. All 24 lags clear the band and lag 10 is still at 0.81: the ACF decays far too slowly to be a short memory. The card says to difference it first, because every model fitted to this picture would be fitting the trend.

Units in stock · autocorrelation

220 days · a level, not a rate

ACF PACF inside the band ±0.13 = ±1.96/√220

24 ACF and 1 PACF of 24 lags outside the band — about 1.2 would be there by chance alone. Lag 0 is 1 by definition and is never plotted.

The first 24 lags are all positive and outside the band, and lag 10 is still at 0.81 — the ACF decays far too slowly to be a short memory, which is the signature of a trend or a random walk. Difference the series once and read this chart again before fitting anything.

Units in stock · autocorrelation: 24 lags estimated from 220 readings. Significance band: ±0.13 = ±1.96/√220. 24 ACF and 1 PACF of 24 lags outside the band — about 1.2 would be there by chance alone. Outside the band: 24 lags — 1, 2, 3, 4, 5, 6, 7, 8 and 16 more. The first 24 lags are all positive and outside the band, and lag 10 is still at 0.81 — the ACF decays far too slowly to be a short memory, which is the signature of a trend or a random walk. Difference the series once and read this chart again before fitting anything.
Lag	ACF	ACF band	PACF	PACF band
1	+0.98	±0.13 — outside	+0.98	±0.13 — outside
2	+0.96	±0.13 — outside	-0.01	±0.13 — inside
3	+0.94	±0.13 — outside	-0.06	±0.13 — inside
4	+0.92	±0.13 — outside	-0.03	±0.13 — inside
5	+0.89	±0.13 — outside	+0.02	±0.13 — inside
6	+0.87	±0.13 — outside	+0.01	±0.13 — inside
7	+0.86	±0.13 — outside	+0.07	±0.13 — inside
8	+0.84	±0.13 — outside	+0.09	±0.13 — inside
9	+0.83	±0.13 — outside	-0.07	±0.13 — inside
10	+0.81	±0.13 — outside	-0.09	±0.13 — inside
11	+0.79	±0.13 — outside	-0.03	±0.13 — inside
12	+0.77	±0.13 — outside	-0.02	±0.13 — inside
13	+0.75	±0.13 — outside	-0.11	±0.13 — inside
14	+0.72	±0.13 — outside	+0.01	±0.13 — inside
15	+0.70	±0.13 — outside	-0.06	±0.13 — inside
16	+0.67	±0.13 — outside	+0.05	±0.13 — inside
17	+0.65	±0.13 — outside	-0.07	±0.13 — inside
18	+0.62	±0.13 — outside	+0.03	±0.13 — inside
19	+0.60	±0.13 — outside	+0.03	±0.13 — inside
20	+0.58	±0.13 — outside	-0.07	±0.13 — inside
21	+0.56	±0.13 — outside	+0.01	±0.13 — inside
22	+0.54	±0.13 — outside	+0.06	±0.13 — inside
23	+0.52	±0.13 — outside	-0.01	±0.13 — inside
24	+0.50	±0.13 — outside	-0.07	±0.13 — inside

Forecast residuals · 280 days after the model took the structure out. One lag of 24 pokes past the ±0.12 band where about 1.2 would by chance alone, and the verdict says so rather than reporting a significant lag 20: at 95% coverage, one stem in twenty leaves the band on a perfect sample. This is the case a card without an expected count turns into a false alarm.

Forecast residuals · autocorrelation

280 days · forecast residuals

ACF PACF inside the band ±0.12 = ±1.96/√280

1 ACF and 0 PACF of 24 lags outside the band — about 1.2 would be there by chance alone. Lag 0 is 1 by definition and is never plotted.

1 of 24 lags leaves the ±0.12 band where about 1.2 would by chance alone — this still reads as white noise, and what is outside is the band doing its job rather than a finding.

Forecast residuals · autocorrelation: 24 lags estimated from 280 readings. Significance band: ±0.12 = ±1.96/√280. 1 ACF and 0 PACF of 24 lags outside the band — about 1.2 would be there by chance alone. Outside the band: 1 lag — 20. 1 of 24 lags leaves the ±0.12 band where about 1.2 would by chance alone — this still reads as white noise, and what is outside is the band doing its job rather than a finding.
Lag	ACF	ACF band	PACF	PACF band
1	+0.09	±0.12 — inside	+0.09	±0.12 — inside
2	+0.09	±0.12 — inside	+0.08	±0.12 — inside
3	0.00	±0.12 — inside	-0.02	±0.12 — inside
4	+0.09	±0.12 — inside	+0.09	±0.12 — inside
5	-0.09	±0.12 — inside	-0.10	±0.12 — inside
6	+0.06	±0.12 — inside	+0.07	±0.12 — inside
7	+0.07	±0.12 — inside	+0.08	±0.12 — inside
8	+0.02	±0.12 — inside	-0.01	±0.12 — inside
9	+0.02	±0.12 — inside	+0.03	±0.12 — inside
10	+0.01	±0.12 — inside	-0.01	±0.12 — inside
11	-0.03	±0.12 — inside	-0.04	±0.12 — inside
12	-0.09	±0.12 — inside	-0.08	±0.12 — inside
13	-0.05	±0.12 — inside	-0.05	±0.12 — inside
14	-0.06	±0.12 — inside	-0.04	±0.12 — inside
15	+0.02	±0.12 — inside	+0.04	±0.12 — inside
16	-0.07	±0.12 — inside	-0.06	±0.12 — inside
17	-0.07	±0.12 — inside	-0.07	±0.12 — inside
18	-0.07	±0.12 — inside	-0.04	±0.12 — inside
19	-0.05	±0.12 — inside	-0.03	±0.12 — inside
20	-0.13	±0.12 — outside	-0.09	±0.12 — inside
21	-0.05	±0.12 — inside	-0.02	±0.12 — inside
22	-0.03	±0.12 — inside	-0.01	±0.12 — inside
23	-0.03	±0.12 — inside	-0.02	±0.12 — inside
24	-0.03	±0.12 — inside	-0.01	±0.12 — inside

The other contract path · a warehouse job computed the correlations and sent lags plus the sampleSize they came from, with no PACF — which is what most reporting APIs return. The PACF and Both options are disabled and the card says which field would enable them, instead of offering a view that would draw an empty panel. Monthly revenue, period 12: lags 12 and 24 are the finding.

Monthly revenue · ACF from the warehouse

monthly revenue · correlations computed upstream

ACF inside the band ±0.17 = ±1.96/√132

20 of 24 lags outside the band — about 1.2 would be there by chance alone. Lag 0 is 1 by definition and is never plotted.

Lags 12, 24 are outside the band — multiples of the 12 it repeats on, so the structure here is seasonal rather than a short memory. 20 of 24 lags leave the band in all: read the rest against that cycle rather than one at a time.

No partial autocorrelations available, so the PACF views are off: supply a raw series, or a pacf on every lag.

Monthly revenue · ACF from the warehouse: 24 lags estimated from 132 readings, supplied precomputed. Significance band: ±0.17 = ±1.96/√132. 20 of 24 lags outside the band — about 1.2 would be there by chance alone. Outside the band: 20 lags — 1, 2, 4, 5, 6, 7, 8, 10 and 12 more. Lags 12, 24 are outside the band — multiples of the 12 it repeats on, so the structure here is seasonal rather than a short memory. 20 of 24 lags leave the band in all: read the rest against that cycle rather than one at a time.
Lag	ACF	ACF band	PACF	PACF band
1	+0.64	±0.17 — outside	not supplied	no band
2	+0.37	±0.17 — outside	not supplied	no band
3	+0.01	±0.17 — inside	not supplied	no band
4	-0.40	±0.17 — outside	not supplied	no band
5	-0.61	±0.17 — outside	not supplied	no band
6	-0.73	±0.17 — outside	not supplied	no band
7	-0.63	±0.17 — outside	not supplied	no band
8	-0.34	±0.17 — outside	not supplied	no band
9	-0.03	±0.17 — inside	not supplied	no band
10	+0.31	±0.17 — outside	not supplied	no band
11	+0.58	±0.17 — outside	not supplied	no band
12	+0.70	±0.17 — outside	not supplied	no band
13	+0.58	±0.17 — outside	not supplied	no band
14	+0.36	±0.17 — outside	not supplied	no band
15	+0.04	±0.17 — inside	not supplied	no band
16	-0.31	±0.17 — outside	not supplied	no band
17	-0.59	±0.17 — outside	not supplied	no band
18	-0.62	±0.17 — outside	not supplied	no band
19	-0.55	±0.17 — outside	not supplied	no band
20	-0.31	±0.17 — outside	not supplied	no band
21	-0.02	±0.17 — inside	not supplied	no band
22	+0.25	±0.17 — outside	not supplied	no band
23	+0.51	±0.17 — outside	not supplied	no band
24	+0.61	±0.17 — outside	not supplied	no band

A stubbed sensor · 60 readings, every one of them 21.5. Every correlation would be 0/0, and a row of stems flat on the baseline would read as a clean white-noise verdict — so the card refuses and names the reason instead of drawing that lie.

Cold-room temperature · autocorrelation

60 readings from a sensor that never moved

Nothing to correlate

every reading is the same value, so the series has no variation to correlate — every lag would be 0/0.

A feed nobody validated · 22 weeks arrive, 2 of them carrying NaN out of an empty column. Those are dropped and counted on the card, not interpolated — an invented reading would be paired with real ones at every lag. What is left is 20 readings, where the band is ±0.44: the card estimates the lags, prints the n/4 rule-of-thumb breach, and withholds any verdict, because at that width almost nothing real can clear it.

Weekly signups · autocorrelation

22 weeks reported, 2 of them empty

ACF PACF inside the band ±0.44 = ±1.96/√20

0 ACF and 0 PACF of 10 lags outside the band — about 0.5 would be there by chance alone. Lag 0 is 1 by definition and is never plotted.

Only 20 readings: the band is ±0.44, wide enough to swallow most real structure, so no shape is called from this sample.

Feed notes: 2 readings dropped — not a finite number, so no pair could include it · 10 lags on 20 readings is past the n/4 rule of thumb — the far lags average few pairs and shrink toward zero.

Weekly signups · autocorrelation: 10 lags estimated from 20 readings. Significance band: ±0.44 = ±1.96/√20. 0 ACF and 0 PACF of 10 lags outside the band — about 0.5 would be there by chance alone. Only 20 readings: the band is ±0.44, wide enough to swallow most real structure, so no shape is called from this sample.
Lag	ACF	ACF band	PACF	PACF band
1	-0.10	±0.44 — inside	-0.10	±0.44 — inside
2	-0.33	±0.44 — inside	-0.34	±0.44 — inside
3	-0.13	±0.44 — inside	-0.24	±0.44 — inside
4	-0.07	±0.44 — inside	-0.29	±0.44 — inside
5	+0.24	±0.44 — inside	+0.04	±0.44 — inside
6	-0.07	±0.44 — inside	-0.20	±0.44 — inside
7	-0.15	±0.44 — inside	-0.19	±0.44 — inside
8	+0.06	±0.44 — inside	-0.10	±0.44 — inside
9	+0.32	±0.44 — inside	+0.29	±0.44 — inside
10	-0.14	±0.44 — inside	-0.15	±0.44 — inside

level={0.99} view='acf' height={200} · a stricter band for evidence rather than triage, one panel because the PACF is not the question here, and a taller box so the weekly peaks have room. The band widens from ±0.10 to ±0.14 and all twelve lags stay outside it — the expected count drops from 1.4 to 0.3 and is printed beside the actual one, so the comparison moves with the level instead of going stale.

Daily orders · autocorrelation

364 days · lags 1–28, weekly period marked

ACF inside the band ±0.14 = ±2.576/√364

12 of 28 lags outside the band — about 0.3 would be there by chance alone. Lag 0 is 1 by definition and is never plotted.

Daily orders · autocorrelation: 28 lags estimated from 364 readings. Significance band: ±0.14 = ±2.576/√364. 12 of 28 lags outside the band — about 0.3 would be there by chance alone. Outside the band: 12 lags — 2, 5, 7, 9, 12, 14, 16, 19 and 4 more. Lags 7, 14, 21 are outside the band — multiples of the 7 it repeats on, so the structure here is seasonal rather than a short memory. 12 of 28 lags leave the band in all: read the rest against that cycle rather than one at a time.
Lag	ACF	ACF band	PACF	PACF band
1	+0.06	±0.14 — inside	+0.06	±0.14 — inside
2	-0.40	±0.14 — outside	-0.41	±0.14 — outside
3	+0.06	±0.14 — inside	+0.14	±0.14 — outside
4	+0.03	±0.14 — inside	-0.20	±0.14 — outside
5	-0.42	±0.14 — outside	-0.40	±0.14 — outside
6	0.00	±0.14 — inside	+0.05	±0.14 — inside
7	+0.74	±0.14 — outside	+0.61	±0.14 — outside
8	0.00	±0.14 — inside	-0.23	±0.14 — outside
9	-0.39	±0.14 — outside	-0.04	±0.14 — inside
10	+0.08	±0.14 — inside	-0.03	±0.14 — inside
11	+0.08	±0.14 — inside	+0.09	±0.14 — inside
12	-0.39	±0.14 — outside	-0.08	±0.14 — inside
13	0.00	±0.14 — inside	+0.07	±0.14 — inside
14	+0.75	±0.14 — outside	+0.40	±0.14 — outside
15	+0.03	±0.14 — inside	-0.01	±0.14 — inside
16	-0.38	±0.14 — outside	-0.02	±0.14 — inside
17	+0.07	±0.14 — inside	-0.03	±0.14 — inside
18	+0.05	±0.14 — inside	-0.02	±0.14 — inside
19	-0.41	±0.14 — outside	0.00	±0.14 — inside
20	0.00	±0.14 — inside	+0.04	±0.14 — inside
21	+0.71	±0.14 — outside	+0.17	±0.14 — outside
22	+0.01	±0.14 — inside	-0.07	±0.14 — inside
23	-0.37	±0.14 — outside	+0.01	±0.14 — inside
24	+0.06	±0.14 — inside	-0.11	±0.14 — inside
25	+0.04	±0.14 — inside	-0.01	±0.14 — inside
26	-0.38	±0.14 — outside	+0.02	±0.14 — inside
27	-0.01	±0.14 — inside	-0.02	±0.14 — inside
28	+0.70	±0.14 — outside	+0.13	±0.14 — inside

band='none' · stems and a baseline, nothing else. Nothing is then called significant — no filled dots, no emphasised lag numbers, no verdict about shape — and the card states that instead of leaving every stem looking ordinary. It is the right mode when the correlations feed a model rather than a decision.

p95 checkout latency · autocorrelation

240 minutes · AR(1) with φ ≈ 0.7

ACF PACF

No band is drawn, so nothing here is marked significant. Lag 0 is 1 by definition and is never plotted.

p95 checkout latency · autocorrelation: 24 lags estimated from 240 readings. No band is drawn, so nothing here is marked significant.
Lag	ACF	ACF band	PACF	PACF band
1	+0.67	no band	+0.67	no band
2	+0.47	no band	+0.04	no band
3	+0.34	no band	+0.02	no band
4	+0.28	no band	+0.07	no band
5	+0.22	no band	-0.02	no band
6	+0.18	no band	+0.02	no band
7	+0.14	no band	-0.01	no band
8	+0.10	no band	-0.01	no band
9	+0.03	no band	-0.08	no band
10	+0.05	no band	+0.09	no band
11	+0.03	no band	-0.05	no band
12	-0.02	no band	-0.06	no band
13	-0.01	no band	+0.06	no band
14	-0.03	no band	-0.07	no band
15	-0.05	no band	-0.01	no band
16	-0.06	no band	-0.01	no band
17	-0.05	no band	+0.01	no band
18	-0.06	no band	-0.05	no band
19	-0.03	no band	+0.08	no band
20	+0.03	no band	+0.07	no band
21	+0.08	no band	+0.03	no band
22	+0.06	no band	-0.01	no band
23	+0.07	no band	+0.01	no band
24	+0.07	no band	0.00	no band

Loading preview…

"use client"

import * as React from "react"

import { cn } from "@/lib/utils"
import {
  type AutocorrelationRow,
  type ChartAutocorrelationBand,
  type ChartAutocorrelationData,
  type ChartAutocorrelationLevel,
  buildAutocorrelationModel,
  describeCorrelogram,
  pickLagTicks,
  symmetricScale,

Installation

npx shadcn@latest add https://ui.zyeon.ai/r/chart-autocorrelation.json

Prompt

Build a React + TypeScript + Tailwind "ChartAutocorrelation" card in plain SVG
with zod. Recharts has no stem primitive, and the geometry is not the hard part
anyway: the x axis is a lag index rather than a measured quantity, the band is a
function of the sample size, and both series on the card are DERIVED from the
raw readings. The maths lives in small pure functions beside the schema and
there is no statistics dependency.

Contract
- One zod schema is the source of truth:
  { status: "loading" | "empty" | "error" | "ready"; title: string;
    caption?: string; series?: number[];
    lags?: { lag >= 1; acf in [-1,1]; pacf? in [-1,1] }[];
    maxLag?: int >= 1; sampleSize?: int >= 2; period?: int >= 2 }.
- TWO input paths, one model. `series` is the raw readings in time order and is
  preferred: the correlations and the band both depend on n, so a card that
  receives the series can guarantee they were computed from the same sample.
  `lags` is for correlations someone else computed, and then `sampleSize` is
  REQUIRED — without n there is no band, and a stem plot with no band is a
  picture of noise.
- superRefine: a ready card needs one or the other; precomputed lags need
  sampleSize; lag numbers unique (a repeat collides as a React key). Guard every
  access — sibling refinements all run, so a ragged payload must produce an
  issue rather than a TypeError out of safeParse.
- Props = z.infer of the schema plus view ("acf" | "pacf" | "both", controlled),
  defaultView (uncontrolled, "both"), onViewChange, band ("white-noise" |
  "bartlett" | "none", default "white-noise"), level (0.9 | 0.95 | 0.99, default
  0.95), height (one panel, 150, clamped 90-320), onRetry, onLagSelect,
  className and the div's native props; forwardRef to the card.
- Export the maths beside the schema: prepareSeries(), resolveMaxLag(),
  computeAcf(), computePacf(), acfBandHalfWidths(), criticalValue(),
  buildAutocorrelationModel(), describeCorrelogram(), symmetricScale(),
  pickLagTicks().

Behavior
- THE MATHS IS THE COMPONENT.
  * r_k divides by the FULL sum of squares over all n readings at every lag —
    the "biased" estimator R's acf() and statsmodels both use. Dividing by the
    number of overlapping pairs instead looks fairer per lag and is not: it can
    produce a sequence that is not positive semi-definite, which makes the
    recursion below blow up and lets |r_k| exceed 1 out where the overlap is
    thinnest. The price is a known shrink toward zero at high lags, which is the
    honest direction to be wrong in.
  * The PACF comes from the ACF by Durbin-Levinson: the correlation between t
    and t-k once the k-1 lags between them are regressed out. That is the whole
    reason two panels exist — an AR(1) makes every lag correlate with lag 1's
    shadow, so the ACF decays geometrically while the PACF cuts off after the
    one lag that is real. Entries go null from the first non-invertible step
    onward; a value divided out of ~0 is numerical debris, not a correlation.
  * Band half-widths: "white-noise" is the flat z/sqrt(n) every textbook draws
    and it tests ONE null — the whole series is white noise. "bartlett" is
    sqrt((1 + 2*sum of r_j^2 for j<k)/n), which widens with the correlations
    already found and therefore tests whether lag k adds anything beyond the
    lags before it. A PACF is always read against the flat band (Quenouille), so
    the choice only ever changes the ACF panel.
- LAG 0 IS NEVER PLOTTED. It is 1 by definition; drawing it would own the y axis
  and say nothing. Print that on the card so its absence is a decision.
- maxLag defaults to min(24, floor(n/4)) and is clamped to n-2. Past the n/4
  rule of thumb the card keeps drawing but says the far lags average few pairs.
- THE VERDICT IS A SENTENCE, not a colour, and it is withheld when the sample
  cannot support one. Five shapes, checked in this order: at most as many lags
  outside as chance would put there (white noise — say the expected count out
  loud, since a 95% band leaves about one lag in twenty outside on a PERFECT
  sample); a long positive run still above 0.5 at lag 10 (trend or random walk —
  difference it first); significant lags landing on multiples of `period`
  (seasonal); ACF decaying while the PACF cuts off (AR(p)); ACF cutting off
  while the PACF trails (MA(q)). Under 30 readings no shape is called at all:
  the band is then ±0.36 and would swallow most real structure. With
  band="none" there is no verdict either, because every sentence is phrased in
  units of "outside the band".
- REFUSALS ARE SPECIFIC. A flat series (zero variance) makes every r_k 0/0 —
  refuse and say so, because a row of stems lying on the baseline reads as a
  clean white-noise result. Fewer than three readings: no lag exists yet.
  Precomputed lags with no sampleSize: no band, therefore no chart. Every
  reading non-finite: say THAT, not "no series arrived" — one did.
- NON-FINITE READINGS ARE HOLES, not deletions. They are COUNTED on the card and
  never interpolated (an invented reading would be paired with real ones at
  every lag), and they are dropped PAIRWISE — the reading keeps its position,
  every pair that touches it is skipped, r_k still divides by the sum of squares
  over the finite readings, which is what R's acf(na.action = na.pass) does.
  Compacting the array instead pulls everything after the hole one period
  earlier and files those pairs under the wrong lag, which invents spikes.
- INTERACTION. One column hit target per lag spanning both panels, so one
  pointer position reads the ACF and the PACF at the same lag. The plot is one
  role="listbox" with a roving tabindex: one tab stop, Left/Right steps a lag,
  Home/End jump to the ends, movement clamps and never wraps (lags run one way),
  Enter/Space fires onLagSelect with the computed row, Escape clears it. The
  view switch is a role="radiogroup" — three readings of one dataset, one drawn
  at a time — with arrows that move AND select, and the PACF options DISABLED
  when the feed carried no partial correlations, with the reason printed.
- CLEANUP: one ResizeObserver, disconnected on unmount and whenever the node
  changes. No timers, no rAF, nothing time-derived at render.

Rendering & styling
- Semantic tokens only: bg-card / text-card-foreground for the panel, border for
  the frame, gridlines and zero baseline, muted for the skeleton,
  muted-foreground for axis text and notes, ring for the keyboard cursor,
  var(--chart-1) for ACF stems, var(--chart-3) for PACF stems, var(--primary)
  for the band. The data is a chart hue and the MODEL is --primary on purpose:
  --chart-N is a five-hue ramp whose neighbours sit about 1.3:1 apart, so a band
  painted in it can land a step away from the stems it exists to be read
  against.
- COLOUR NEVER CARRIES SIGNIFICANCE ALONE. A lag outside the band is a thick
  stem with a FILLED dot and its number set in foreground weight on the axis;
  one inside is a hairline with a HOLLOW ring. Turn the palette to one hue and
  the chart still reads.
- Symmetric domain, always: a correlogram is read for sign as much as size, and
  an off-centre zero would make the negative stems look shorter than they are.
  The step ladder holds the axis at 5-7 gridlines whatever the extent. The
  domain clamps to ±1 only when the data stays inside it — a supplied
  correlation past ±1 is a broken feed and hiding it outside the frame would
  hide the bug.
- Axis labels: the thinned lag ticks first, then every significant lag, then the
  seasonal multiples, added only while there is room, so a 40-lag axis on a
  phone thins out instead of smearing. Panel names sit ABOVE each frame, never
  inside it — a lag-1 stem at 0.98 owns that corner.
- ACCESSIBILITY: do NOT put role="img" on the plot — that is
  children-presentational and would silence the focusable lags inside. Use
  role="group" named by the heading and described by a summary that states the
  finding in words: how many lags, from how many readings, the band and where it
  came from, how many are outside versus expected, which lags, and the verdict.
  Each lag is a role="option" whose accessible name reads both panels. Below the
  plot an sr-only WRAPPER DIV (never sr-only on the table itself: CSS width is
  only a lower bound for a table box, so a narrow viewport picks up real
  horizontal scroll) repeats every lag as a row. The visible readout is
  aria-hidden because focus already announces it; a polite live region carries
  only the pointer-driven readout.
- Motion: the only animation is the loading skeleton's pulse, carrying
  motion-reduce:animate-none. Nothing else moves, so nothing else has to stop.

Customization levers
- band: the most consequential knob. "white-noise" answers "is there anything
  here at all"; "bartlett" answers "does this lag add anything beyond the ones
  before it" and typically drops a decaying tail from 7 significant lags to 5;
  "none" is for a figure whose correlations feed a model rather than a decision.
- level: 0.95 by default. 0.99 for evidence, 0.90 for exploration — the expected
  count printed beside the actual one moves with it, so the comparison never
  goes stale.
- view + defaultView: ship "acf" for a compact dashboard tile, "both" when the
  card is being used to pick a model order. Controlled `view` lets a page-level
  segmented control drive several cards at once.
- maxLag + height: 24 lags at 150px per panel is a dashboard card; 40 lags at
  260px is an analysis page. Raising maxLag past n/4 is allowed and disclosed
  rather than blocked.
- period: pass 7 for daily data, 12 for monthly, 24 for hourly. It draws the
  guides, forces those lags onto the axis and lets the verdict name the cycle
  instead of describing it.
- Palette: re-point ACF_INK / PACF_INK / BAND_INK. Keep the band on --primary
  and keep significance carried by SHAPE, so a monochrome card loses nothing but
  decoration.
- Interaction: onLagSelect already carries the computed row (correlation, band
  half-width, verdict) — wire it to a lag input on a model form, or to a second
  chart that plots the series against itself at that lag.

Concepts

Correlation with its own past — the x axis is not time and not a category: it is how many periods back. Lag 7 at 0.74 means "a Tuesday looks like the Tuesday before it", which is a statement no plot of the series against time makes directly, however long you stare at it.
The band is the whole reading — a stem is only a finding relative to what noise alone would produce, so the half-width is z/√n and the card prints both the band and the count chance would put outside it. Without that comparison "lag 20 is significant" on 24 lags at 95% is arithmetic being read as a discovery.
Partial means "with the middle lags removed" — an AR(1) makes lag 2 correlate with lag 0 purely through lag 1. The PACF regresses those intervening lags out, which is why the pair of panels identifies an order that either panel alone cannot: ACF decaying plus PACF cutting off after one spike is AR(1), and the reverse is MA(1).
Slow decay is a different disease — an ACF still above 0.5 ten lags out is not a long memory, it is a series that never settles: a level rather than a rate. The card says to difference it first, because every model fitted to that picture is fitting the trend.
Refusal beats a drawn guess — a flat series would make every correlation 0/0 and a row of stems lying on the baseline reads as a clean white-noise result, so the card declines and names the reason. The same goes for precomputed lags with no sample size, and for a verdict under 30 readings.
One estimator, stated — dividing by the full sum of squares at every lag guarantees a sequence the PACF recursion can run on, at the cost of shrinking the far lags toward zero. Both choices are defensible; making it invisible is not, so it is written down where the numbers are.

Autocorrelation (ACF)

Daily orders · autocorrelation

Daily orders · autocorrelation

Daily orders · autocorrelation

Daily orders · autocorrelation

p95 checkout latency · autocorrelation

p95 checkout latency · autocorrelation

Units in stock · autocorrelation

Forecast residuals · autocorrelation

Monthly revenue · ACF from the warehouse

Cold-room temperature · autocorrelation

Weekly signups · autocorrelation

Daily orders · autocorrelation

p95 checkout latency · autocorrelation

Installation

Prompt

Concepts

On This Page

Daily orders · autocorrelation

Daily orders · autocorrelation

Daily orders · autocorrelation

Daily orders · autocorrelation

p95 checkout latency · autocorrelation

p95 checkout latency · autocorrelation

Units in stock · autocorrelation

Forecast residuals · autocorrelation

Monthly revenue · ACF from the warehouse

Cold-room temperature · autocorrelation

Weekly signups · autocorrelation

Daily orders · autocorrelation

p95 checkout latency · autocorrelation