Displays the autocorrelation function (ACF) and partial autocorrelation function (PACF) of a time series as vertical stem/bar plots arranged in two vertically stacked subplots. Each lag is represented by a vertical line from zero to the correlation value, with horizontal dashed lines indicating 95% confidence bounds. These plots are essential for identifying the order of AR and MA components in ARIMA modeling and for diagnosing residual independence.
// anyplot.ai
// acf-pacf: Autocorrelation and Partial Autocorrelation (ACF/PACF) Plot
// Library: highcharts 12.6.0 | JavaScript 22.22.3
// Quality: 90/100 | Created: 2026-06-10
//# anyplot-orientation: landscape
const t = window.ANYPLOT_TOKENS;
// Reproducible RNG: LCG seed=42 + Box-Muller transform
function makeLCG(seed) {
let s = seed >>> 0;
return () => { s = (Math.imul(1664525, s) + 1013904223) >>> 0; return s / 4294967296; };
}
function makeNormal(lcg) {
return () => {
const u1 = lcg() + 1e-10, u2 = lcg();
return Math.sqrt(-2 * Math.log(u1)) * Math.cos(2 * Math.PI * u2);
};
}
// AR(2) time series: X_t = 0.7 X_{t-1} − 0.2 X_{t-2} + ε_t (N=300)
// PACF cutoff after lag 2 reveals the AR(2) order clearly
const N = 300;
const randn = makeNormal(makeLCG(42));
const tsSeries = new Array(N).fill(0);
for (let i = 2; i < N; i++) {
tsSeries[i] = 0.7 * tsSeries[i - 1] - 0.2 * tsSeries[i - 2] + randn();
}
// ACF: sample autocorrelation for lags 0..maxLag
function computeACF(x, maxLag) {
const n = x.length;
const mu = x.reduce((a, b) => a + b, 0) / n;
const v = x.reduce((s, xi) => s + (xi - mu) ** 2, 0) / n;
const r = [1.0];
for (let h = 1; h <= maxLag; h++) {
let c = 0;
for (let i = 0; i < n - h; i++) c += (x[i] - mu) * (x[i + h] - mu);
r.push(c / (n * v));
}
return r;
}
// PACF: Durbin–Levinson recursion, returns values for lags 1..maxLag
function computePACF(rho, maxLag) {
const p = [];
let phi = [rho[1]];
p.push(rho[1]);
for (let k = 2; k <= maxLag; k++) {
let num = rho[k], den = 1;
for (let j = 0; j < k - 1; j++) {
num -= phi[j] * rho[k - 1 - j];
den -= phi[j] * rho[j + 1];
}
const phikk = num / den;
p.push(phikk);
const np = new Array(k);
np[k - 1] = phikk;
for (let j = 0; j < k - 1; j++) np[j] = phi[j] - phikk * phi[k - 2 - j];
phi = np;
}
return p;
}
const MAX_LAG = 35;
const acfVals = computeACF(tsSeries, MAX_LAG); // lags 0..35
const pacfVals = computePACF(acfVals, MAX_LAG); // lags 1..35
const ci = 1.96 / Math.sqrt(N); // 95% confidence bound ≈ 0.113
Highcharts.chart("container", {
chart: {
backgroundColor: "transparent",
animation: false,
style: { fontFamily: "inherit" },
marginTop: 85,
marginBottom: 75,
marginLeft: 78,
marginRight: 50
},
credits: { enabled: false },
colors: t.palette,
title: {
text: "acf-pacf · javascript · highcharts · anyplot.ai",
style: { color: t.ink, fontSize: "22px", fontWeight: "600" }
},
subtitle: {
text: "AR(2) process · N = 300 observations · dashed lines show 95% confidence bounds",
style: { color: t.inkSoft, fontSize: "13px" }
},
xAxis: {
min: 0,
max: MAX_LAG,
tickInterval: 5,
lineColor: t.inkSoft,
tickColor: t.inkSoft,
title: { text: "Lag", style: { color: t.inkSoft, fontSize: "16px" } },
labels: { style: { color: t.inkSoft, fontSize: "13px" } }
},
yAxis: [
{
top: "8%",
height: "40%",
max: 1.15,
title: { text: "ACF", style: { color: t.inkSoft, fontSize: "16px" } },
labels: {
style: { color: t.inkSoft, fontSize: "12px" },
format: "{value:.2f}"
},
gridLineColor: t.grid,
lineColor: t.inkSoft,
tickColor: t.inkSoft,
plotLines: [
{ value: 0, color: t.inkSoft, width: 1, zIndex: 2 },
{
value: ci,
color: t.amber,
dashStyle: "ShortDash",
width: 1.5,
zIndex: 3,
label: {
text: "95% CI",
align: "right",
x: -6,
style: { color: t.amber, fontSize: "11px" }
}
},
{ value: -ci, color: t.amber, dashStyle: "ShortDash", width: 1.5, zIndex: 3 }
]
},
{
top: "57%",
height: "38%",
offset: 0,
title: { text: "PACF", style: { color: t.inkSoft, fontSize: "16px" } },
labels: {
style: { color: t.inkSoft, fontSize: "12px" },
format: "{value:.2f}"
},
gridLineColor: t.grid,
lineColor: t.inkSoft,
tickColor: t.inkSoft,
plotLines: [
{ value: 0, color: t.inkSoft, width: 1, zIndex: 2 },
{ value: ci, color: t.amber, dashStyle: "ShortDash", width: 1.5, zIndex: 3 },
{ value: -ci, color: t.amber, dashStyle: "ShortDash", width: 1.5, zIndex: 3 }
]
}
],
plotOptions: {
series: { animation: false, enableMouseTracking: false },
column: { pointWidth: 2, borderWidth: 0, grouping: false, threshold: 0 },
scatter: { showInLegend: false }
},
legend: { enabled: false },
tooltip: { enabled: false },
series: [
{
name: "ACF",
type: "column",
data: acfVals.map((v, i) => ({ x: i, y: v })),
yAxis: 0,
color: t.palette[0]
},
{
name: "ACF dots",
type: "scatter",
data: acfVals.map((v, i) => ({ x: i, y: v })),
yAxis: 0,
color: t.palette[0],
marker: { radius: 4, symbol: "circle" }
},
{
name: "PACF",
type: "column",
data: pacfVals.map((v, i) => ({ x: i + 1, y: v })),
yAxis: 1,
color: t.palette[2]
},
{
name: "PACF dots",
type: "scatter",
data: pacfVals.map((v, i) => ({ x: i + 1, y: v })),
yAxis: 1,
color: t.palette[2],
marker: { radius: 4, symbol: "circle" }
}
]
});
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/acf-pacf/highcharts/code. Any spec id and library id listed in llms-full.txt fit the same URL shape; every URL below is complete and callable.
{
"spec_id": "acf-pacf",
"language": "javascript",
"library": "highcharts",
"page": "https://anyplot.ai/acf-pacf/javascript/highcharts",
"hub": "https://anyplot.ai/acf-pacf",
"code_json": "https://api.anyplot.ai/specs/acf-pacf/highcharts/code",
"spec_json": "https://api.anyplot.ai/specs/acf-pacf",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/acf-pacf/javascript/highcharts/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/acf-pacf/javascript/highcharts/plot-dark.png",
"interactive_light_html": "https://storage.googleapis.com/anyplot-images/plots/acf-pacf/javascript/highcharts/plot-light.html",
"interactive_dark_html": "https://storage.googleapis.com/anyplot-images/plots/acf-pacf/javascript/highcharts/plot-dark.html",
"quality_score": 90.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of Autocorrelation and Partial Autocorrelation (ACF/PACF) Plot on anyplot.ai.