feat(makie): implement acf-pacf

plots/acf-pacf/implementations/julia/makie.jl

@@ -0,0 +1,170 @@
+# anyplot.ai
+# acf-pacf: Autocorrelation and Partial Autocorrelation (ACF/PACF) Plot
+# Library: makie 0.22.10 | Julia 1.11.9
+# Quality: 86/100 | Created: 2026-06-10
+
+using CairoMakie
+using Colors
+using Random
+using Statistics
+
+Random.seed!(42)
+
+# Theme tokens
+const THEME     = get(ENV, "ANYPLOT_THEME", "light")
+const PAGE_BG   = THEME == "light" ? colorant"#FAF8F1" : colorant"#1A1A17"
+const INK       = THEME == "light" ? colorant"#1A1A17" : colorant"#F0EFE8"
+const INK_SOFT  = THEME == "light" ? colorant"#4A4A44" : colorant"#B8B7B0"
+const IMPRINT_PALETTE = [
+    colorant"#009E73", colorant"#C475FD", colorant"#4467A3", colorant"#BD8233",
+    colorant"#AE3030", colorant"#2ABCCD", colorant"#954477", colorant"#99B314",
+]
+
+# Data: AR(2) time series — monthly economic indicator
+# x[t] = 0.7*x[t-1] + 0.2*x[t-2] + noise  (φ₁=0.7, φ₂=0.2)
+# PACF cuts off at lag 2; ACF decays as a mixture of exponentials
+n_obs = 300
+series = zeros(n_obs)
+series[1] = randn()
+series[2] = 0.7 * series[1] + randn()
+for t in 3:n_obs
+    series[t] = 0.7 * series[t-1] + 0.2 * series[t-2] + randn()
+end
+
+# ACF (lags 0 through max_lag)
+max_lag = 35
+s_mean = mean(series)
+s_var  = sum((v - s_mean)^2 for v in series) / n_obs
+acf_vals = [sum((series[i] - s_mean) * (series[i-k] - s_mean) for i in (k+1):n_obs) / (n_obs * s_var)
+            for k in 0:max_lag]
+
+# PACF via Levinson-Durbin recursion
+phi       = zeros(max_lag, max_lag)
+phi[1, 1] = acf_vals[2]
+pacf_vals = zeros(max_lag)
+pacf_vals[1] = phi[1, 1]
+for k in 2:max_lag
+    numer = acf_vals[k + 1]
+    denom = 1.0
+    for j in 1:(k - 1)
+        numer -= phi[k-1, j] * acf_vals[k - j + 1]
+        denom -= phi[k-1, j] * acf_vals[j + 1]
+    end
+    phi[k, k] = numer / denom
+    for j in 1:(k - 1)
+        phi[k, j] = phi[k-1, j] - phi[k, k] * phi[k-1, k-j]
+    end
+    pacf_vals[k] = phi[k, k]
+end
+
+conf_bound = 1.96 / sqrt(n_obs)
+acf_lags   = Float64.(0:max_lag)
+
+# Build linesegments! data for ACF: interleaved [x_base, x_tip, ...] pairs per segment
+acf_seg_x = vcat([[lag, lag] for lag in acf_lags]...)
+acf_seg_y = vcat([[0.0, v]   for v   in acf_vals]...)
+
+# PACF: split lags into significant (|r| > conf_bound) vs. within-bound for visual hierarchy
+pacf_sig_idx = findall(v -> abs(v) > conf_bound, pacf_vals)
+pacf_ns_idx  = findall(v -> abs(v) <= conf_bound, pacf_vals)
+
+# Muted variant for non-significant PACF lags (same hue, lower opacity)
+GREEN_FULL  = IMPRINT_PALETTE[1]
+GREEN_MUTED = RGBAf(GREEN_FULL.r, GREEN_FULL.g, GREEN_FULL.b, 0.38f0)
+
+function make_segs(idx, vals)
+    xs = vcat([[Float64(i), Float64(i)] for i in idx]...)
+    ys = vcat([[0.0, vals[i]] for i in idx]...)
+    xs, ys
+end
+
+# Figure
+fig = Figure(
+    size            = (1600, 900),
+    fontsize        = 14,
+    backgroundcolor = PAGE_BG,
+)
+
+# ACF axis (top)
+ax_acf = Axis(
+    fig[1, 1];
+    title             = "AR(2) Process · acf-pacf · julia · makie · anyplot.ai",
+    titlesize         = 20,
+    titlecolor        = INK,
+    ylabel            = "ACF",
+    ylabelsize        = 14,
+    ylabelcolor       = INK,
+    xticklabelsize    = 12,
+    yticklabelsize    = 12,
+    xticklabelcolor   = INK_SOFT,
+    yticklabelcolor   = INK_SOFT,
+    xtickcolor        = INK_SOFT,
+    ytickcolor        = INK_SOFT,
+    backgroundcolor   = PAGE_BG,
+    topspinevisible   = false,
+    rightspinevisible = false,
+    leftspinecolor    = INK_SOFT,
+    bottomspinecolor  = INK_SOFT,
+    xgridvisible      = false,
+    ygridvisible      = true,
+    ygridcolor        = RGBAf(INK.r, INK.g, INK.b, 0.12f0),
+)
+
+# PACF axis (bottom)
+ax_pacf = Axis(
+    fig[2, 1];
+    xlabel            = "Lag",
+    ylabel            = "PACF",
+    xlabelsize        = 14,
+    ylabelsize        = 14,
+    xlabelcolor       = INK,
+    ylabelcolor       = INK,
+    xticklabelsize    = 12,
+    yticklabelsize    = 12,
+    xticklabelcolor   = INK_SOFT,
+    yticklabelcolor   = INK_SOFT,
+    xtickcolor        = INK_SOFT,
+    ytickcolor        = INK_SOFT,
+    backgroundcolor   = PAGE_BG,
+    topspinevisible   = false,
+    rightspinevisible = false,
+    leftspinecolor    = INK_SOFT,
+    bottomspinecolor  = INK_SOFT,
+    xgridvisible      = false,
+    ygridvisible      = true,
+    ygridcolor        = RGBAf(INK.r, INK.g, INK.b, 0.12f0),
+)
+
+linkxaxes!(ax_acf, ax_pacf)
+ax_acf.xticklabelsvisible = false
+ax_acf.xlabelvisible      = false
+
+# ACF stems, tips, and reference lines
+linesegments!(ax_acf, acf_seg_x, acf_seg_y;
+    color = GREEN_FULL, linewidth = 2.0)
+scatter!(ax_acf, acf_lags, acf_vals;
+    color = GREEN_FULL, markersize = 8, strokewidth = 0)
+hlines!(ax_acf, [0.0]; color = INK_SOFT, linewidth = 1.0)
+hlines!(ax_acf, [conf_bound, -conf_bound];
+    color = INK_SOFT, linestyle = :dash, linewidth = 1.5)
+
+# PACF: within-bound lags (muted) drawn first, then significant lags on top
+if !isempty(pacf_ns_idx)
+    ns_sx, ns_sy = make_segs(pacf_ns_idx, pacf_vals)
+    linesegments!(ax_pacf, ns_sx, ns_sy; color = GREEN_MUTED, linewidth = 1.5)
+    scatter!(ax_pacf, Float64.(pacf_ns_idx), pacf_vals[pacf_ns_idx];
+        color = GREEN_MUTED, markersize = 7, strokewidth = 0)
+end
+if !isempty(pacf_sig_idx)
+    sig_sx, sig_sy = make_segs(pacf_sig_idx, pacf_vals)
+    linesegments!(ax_pacf, sig_sx, sig_sy; color = GREEN_FULL, linewidth = 2.5)
+    scatter!(ax_pacf, Float64.(pacf_sig_idx), pacf_vals[pacf_sig_idx];
+        color = GREEN_FULL, markersize = 9, strokewidth = 0)
+end
+hlines!(ax_pacf, [0.0]; color = INK_SOFT, linewidth = 1.0)
+hlines!(ax_pacf, [conf_bound, -conf_bound];
+    color = INK_SOFT, linestyle = :dash, linewidth = 1.5)
+
+rowgap!(fig.layout, 1, 20)
+
+save("plot-$(THEME).png", fig; px_per_unit = 2)