{ "cells": [ { "cell_type": "markdown", "id": "2de5d765", "metadata": {}, "source": [ "# Multivariate bootstrap: keeping series in step\n", "\n", "Real macro and financial data come as several series at once: output and\n", "consumption, two interest rates, a basket of asset returns. What makes them\n", "multivariate is that the columns move together, not merely that there are several\n", "of them. A bootstrap of multivariate data is only useful if it keeps that joint\n", "structure intact.\n", "\n", "In `tsbootstrap`, multivariate input is an array of shape `(n, d)`: `n`\n", "time steps, `d` series. Two ideas preserve the cross-series structure:\n", "\n", "1. Row-resampling methods (the block family, and IID) resample whole rows, so\n", " the contemporaneous relationship between columns at a given time is carried\n", " along untouched.\n", "2. `ResidualBootstrap(model=VAR(order=...))` fits a vector autoregression, which\n", " models how each series depends on the recent past of every series, then\n", " simulates new paths forward. This captures the dynamic, lead-lag structure\n", " that row-resampling within a single time step cannot.\n", "\n", "We work both ideas through on a synthetic VAR(1) with known structure and on a real\n", "macro subset, and pin down where the simple methods fall short." ] }, { "cell_type": "code", "execution_count": 1, "id": "28ad38a8", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:15:00.077365Z", "iopub.status.busy": "2026-06-22T16:15:00.077118Z", "iopub.status.idle": "2026-06-22T16:15:00.861147Z", "shell.execute_reply": "2026-06-22T16:15:00.860335Z" } }, "outputs": [], "source": [ "# On Colab or Binder, install tsbootstrap first (skipped if already present):\n", "try:\n", " import tsbootstrap # noqa: F401\n", "except ImportError:\n", " %pip install -q \"tsbootstrap[examples]\"" ] }, { "cell_type": "markdown", "id": "9db6485c", "metadata": {}, "source": [ "## A synthetic bivariate VAR(1) with known structure\n", "\n", "We generate a two-series VAR(1), `X[t] = A @ X[t-1] + e[t]`, where the\n", "coefficient matrix `A` and the innovation covariance are ours to choose, so every\n", "correlation we measure later has a ground truth. Two channels carry the joint\n", "structure:\n", "\n", "- contemporaneous: the innovations `e[t]` are correlated across the two series\n", " (off-diagonal of the covariance), so the columns co-move at the same instant;\n", "- dynamic: `A` is not diagonal, so each series depends on the recent past of the\n", " other. Here series 1 feeds into series 0, a lead-lag relationship." ] }, { "cell_type": "code", "execution_count": 2, "id": "604d913d", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:15:00.865197Z", "iopub.status.busy": "2026-06-22T16:15:00.864936Z", "iopub.status.idle": "2026-06-22T16:15:01.383393Z", "shell.execute_reply": "2026-06-22T16:15:01.382329Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "X shape: (200, 2) (n time steps, d series)\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "rng = np.random.default_rng(0)\n", "n = 200\n", "\n", "# Coefficient matrix: x0 picks up the lagged value of x1 (x1 leads x0).\n", "A = np.array([[0.5, 0.3], [0.0, 0.5]])\n", "\n", "# Innovation covariance: positive contemporaneous correlation between the series.\n", "cov = np.array([[1.0, 0.5], [0.5, 1.0]])\n", "chol = np.linalg.cholesky(cov)\n", "\n", "X = np.zeros((n, 2))\n", "for t in range(1, n):\n", " X[t] = A @ X[t - 1] + chol @ rng.standard_normal(2)\n", "\n", "print(\"X shape:\", X.shape, \" (n time steps, d series)\")\n", "\n", "fig, ax = plt.subplots(figsize=(9, 3.5), constrained_layout=True)\n", "ax.plot(X[:, 0], color=\"tab:blue\", lw=1.4, label=\"series 0 (lags series 1)\")\n", "ax.plot(X[:, 1], color=\"tab:orange\", lw=1.4, label=\"series 1 (leads series 0)\")\n", "ax.set_title(\"Synthetic bivariate VAR(1) with contemporaneous and lead-lag structure\")\n", "ax.set_xlabel(\"time step\")\n", "ax.set_ylabel(\"value\")\n", "ax.grid(True, alpha=0.3)\n", "ax.legend(loc=\"upper right\", framealpha=0.9)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "3c19eaf2", "metadata": {}, "source": [ "## Two kinds of cross-correlation\n", "\n", "We will track two summaries of the joint structure throughout:\n", "\n", "- contemporaneous cross-correlation, `corr(x0[t], x1[t])`, the off-diagonal of\n", " the correlation matrix of the columns;\n", "- lag-1 cross-correlation, `corr(x0[t], x1[t-1])`, which is non-zero precisely\n", " because series 1 leads series 0 through the coefficient matrix.\n", "\n", "A faithful multivariate bootstrap should reproduce both." ] }, { "cell_type": "code", "execution_count": 3, "id": "3f395e72", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:15:01.387407Z", "iopub.status.busy": "2026-06-22T16:15:01.387079Z", "iopub.status.idle": "2026-06-22T16:15:01.393596Z", "shell.execute_reply": "2026-06-22T16:15:01.392517Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "original contemporaneous cross-corr corr(x0_t, x1_t) : 0.604\n", "original lag-1 cross-corr corr(x0_t, x1_(t-1)) : 0.528\n" ] } ], "source": [ "def contemp_cross_corr(series):\n", " \"\"\"Off-diagonal of the column correlation matrix: corr(x0[t], x1[t]).\"\"\"\n", " return float(np.corrcoef(np.asarray(series).T)[0, 1])\n", "\n", "\n", "def lag1_cross_corr(series):\n", " \"\"\"corr(x0[t], x1[t-1]): the lead of series 1 into series 0.\"\"\"\n", " s = np.asarray(series, dtype=float)\n", " a, b = s[1:, 0], s[:-1, 1]\n", " a = a - a.mean()\n", " b = b - b.mean()\n", " return float(np.dot(a, b) / np.sqrt(np.dot(a, a) * np.dot(b, b)))\n", "\n", "\n", "orig_contemp = contemp_cross_corr(X)\n", "orig_lag1 = lag1_cross_corr(X)\n", "print(f\"original contemporaneous cross-corr corr(x0_t, x1_t) : {orig_contemp:.3f}\")\n", "print(f\"original lag-1 cross-corr corr(x0_t, x1_(t-1)) : {orig_lag1:.3f}\")" ] }, { "cell_type": "markdown", "id": "9ee404bf", "metadata": {}, "source": [ "## VAR residual bootstrap\n", "\n", "`ResidualBootstrap(model=VAR(order=1))` fits the vector autoregression once, then\n", "regenerates each replicate by resampling the fitted residuals and running the VAR\n", "recursion forward. Because the fitted `A` encodes the lead-lag structure and the\n", "residuals carry the contemporaneous innovation correlation, both kinds of\n", "cross-correlation should survive into the replicates.\n", "\n", "The replicates have the same `(n, d)` shape as the input, stacked into a\n", "`(n_bootstraps, n, d)` array by `result.values()`. VAR requires `d >= 2`\n", "series." ] }, { "cell_type": "code", "execution_count": 4, "id": "a2171a61", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:15:01.396474Z", "iopub.status.busy": "2026-06-22T16:15:01.396352Z", "iopub.status.idle": "2026-06-22T16:15:01.672429Z", "shell.execute_reply": "2026-06-22T16:15:01.670448Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "replicate array shape: (500, 200, 2) (n_bootstraps, n, d)\n", "metadata n_series: 2\n", "\n", " original VAR mean\n", "contemporaneous corr 0.604 0.595\n", "lag-1 corr 0.528 0.515\n" ] } ], "source": [ "from tsbootstrap import VAR, ResidualBootstrap, bootstrap\n", "\n", "var_res = bootstrap(\n", " X, method=ResidualBootstrap(model=VAR(order=1)), n_bootstraps=500, random_state=0\n", ")\n", "var_vals = var_res.values()\n", "print(\"replicate array shape:\", var_vals.shape, \" (n_bootstraps, n, d)\")\n", "print(\"metadata n_series:\", var_res.metadata.n_series)\n", "\n", "var_contemp = np.array([contemp_cross_corr(v) for v in var_vals])\n", "var_lag1 = np.array([lag1_cross_corr(v) for v in var_vals])\n", "\n", "print()\n", "print(f\"{'':22s} {'original':>10s} {'VAR mean':>10s}\")\n", "print(f\"{'contemporaneous corr':22s} {orig_contemp:10.3f} {var_contemp.mean():10.3f}\")\n", "print(f\"{'lag-1 corr':22s} {orig_lag1:10.3f} {var_lag1.mean():10.3f}\")" ] }, { "cell_type": "markdown", "id": "b8788343", "metadata": {}, "source": [ "The VAR replicates recover both summaries. The contemporaneous correlation is\n", "inherited from the resampled residuals, and the lag-1 correlation comes back\n", "because the recursion replays the fitted coefficient matrix. Modelling the joint\n", "dynamics is what buys the second number; resampling the columns in isolation\n", "would not." ] }, { "cell_type": "markdown", "id": "a569de80", "metadata": {}, "source": [ "## Block methods on multivariate input\n", "\n", "The block family also accepts `(n, d)` input directly. A block bootstrap copies\n", "contiguous blocks of *rows*, so the columns inside each block stay locked\n", "together. That keeps the contemporaneous correlation exactly, and it keeps the\n", "within-block dynamics, which is enough to reproduce short-lag cross-correlation\n", "too. No model is fitted, so this is the robust choice when you do not want to\n", "commit to a VAR." ] }, { "cell_type": "code", "execution_count": 5, "id": "d6c8276e", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:15:01.677263Z", "iopub.status.busy": "2026-06-22T16:15:01.676749Z", "iopub.status.idle": "2026-06-22T16:15:01.788644Z", "shell.execute_reply": "2026-06-22T16:15:01.787339Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "method shape contemp lag-1\n", "--------------------------------------------------------\n", "original 0.604 0.528\n", "MovingBlock (500, 200, 2) 0.598 0.458\n", "StationaryBlock (500, 200, 2) 0.595 0.442\n" ] } ], "source": [ "from tsbootstrap import MovingBlock, StationaryBlock\n", "\n", "block_specs = {\n", " \"MovingBlock\": MovingBlock(block_length=\"auto\"),\n", " \"StationaryBlock\": StationaryBlock(avg_block_length=\"auto\"),\n", "}\n", "\n", "print(f\"{'method':18s} {'shape':>18s} {'contemp':>9s} {'lag-1':>9s}\")\n", "print(\"-\" * 56)\n", "print(f\"{'original':18s} {'':>18s} {orig_contemp:9.3f} {orig_lag1:9.3f}\")\n", "for name, spec in block_specs.items():\n", " res = bootstrap(X, method=spec, n_bootstraps=500, random_state=0)\n", " vals = res.values()\n", " contemp = np.mean([contemp_cross_corr(v) for v in vals])\n", " lag1 = np.mean([lag1_cross_corr(v) for v in vals])\n", " print(f\"{name:18s} {str(vals.shape):>18s} {contemp:9.3f} {lag1:9.3f}\")" ] }, { "cell_type": "markdown", "id": "ae67a192", "metadata": {}, "source": [ "Both block methods return `(n_bootstraps, n, d)` arrays and reproduce the\n", "contemporaneous and lag-1 cross-correlations. Resampling whole rows is what\n", "preserves the joint structure." ] }, { "cell_type": "markdown", "id": "669a04da", "metadata": {}, "source": [ "## Where the naive choice fails\n", "\n", "It is tempting to conclude that any row-resampler is fine for multivariate data.\n", "For the *contemporaneous* correlation that holds: even plain IID resampling keeps\n", "it, because it never splits a row. But IID shuffles rows independently, so it\n", "destroys every relationship that spans more than one time step, including the\n", "lead-lag cross-correlation. That gap is the reason to reach for a time-series\n", "method on multivariate data instead of a plain resampler." ] }, { "cell_type": "code", "execution_count": 6, "id": "7cb301e2", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:15:01.792452Z", "iopub.status.busy": "2026-06-22T16:15:01.792143Z", "iopub.status.idle": "2026-06-22T16:15:02.400309Z", "shell.execute_reply": "2026-06-22T16:15:02.399181Z" }, "nbsphinx-thumbnail": { "output-index": 0 } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "method contemp mean lag-1 mean\n", "VAR(order=1) 0.595 0.515\n", "MovingBlock 0.598 0.458\n", "IID 0.601 -0.009\n", "original 0.604 0.528\n" ] } ], "source": [ "from tsbootstrap import IID\n", "\n", "methods = {\n", " \"VAR(order=1)\": ResidualBootstrap(model=VAR(order=1)),\n", " \"MovingBlock\": MovingBlock(block_length=\"auto\"),\n", " \"IID\": IID(),\n", "}\n", "\n", "contemp_by_method, lag1_by_method = {}, {}\n", "for name, spec in methods.items():\n", " vals = bootstrap(X, method=spec, n_bootstraps=500, random_state=0).values()\n", " contemp_by_method[name] = np.array([contemp_cross_corr(v) for v in vals])\n", " lag1_by_method[name] = np.array([lag1_cross_corr(v) for v in vals])\n", "\n", "names = list(methods)\n", "# Colorblind-friendly per-method colors (Okabe-Ito subset).\n", "method_colors = {\"VAR(order=1)\": \"#0072B2\", \"MovingBlock\": \"#009E73\", \"IID\": \"#D55E00\"}\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(11, 4.5), constrained_layout=True)\n", "for ax, data, orig, title in [\n", " (axes[0], contemp_by_method, orig_contemp, \"Contemporaneous corr($x_{0,t}$, $x_{1,t}$)\"),\n", " (axes[1], lag1_by_method, orig_lag1, \"Lag-1 corr($x_{0,t}$, $x_{1,t-1}$)\"),\n", "]:\n", " bp = ax.boxplot(\n", " [data[k] for k in names],\n", " tick_labels=names,\n", " showfliers=False,\n", " patch_artist=True,\n", " medianprops={\"color\": \"black\", \"lw\": 1.5},\n", " )\n", " for patch, name in zip(bp[\"boxes\"], names):\n", " patch.set_facecolor(method_colors[name])\n", " patch.set_alpha(0.65)\n", " ax.axhline(orig, color=\"black\", lw=2, ls=\"--\", label=f\"original = {orig:.2f}\")\n", " ax.set_title(title)\n", " ax.set_xlabel(\"bootstrap method\")\n", " ax.set_ylabel(\"cross-correlation across replicates\")\n", " ax.grid(True, axis=\"y\", alpha=0.3)\n", " ax.legend(loc=\"lower left\", fontsize=9, framealpha=0.9)\n", "fig.suptitle(\n", " \"Row-resampling keeps contemporaneous corr; only VAR and block keep the lead-lag\",\n", " fontsize=12,\n", ")\n", "plt.show()\n", "\n", "print(f\"{'method':14s} {'contemp mean':>13s} {'lag-1 mean':>11s}\")\n", "for name in names:\n", " print(f\"{name:14s} {contemp_by_method[name].mean():13.3f} {lag1_by_method[name].mean():11.3f}\")\n", "print(f\"original {orig_contemp:13.3f} {orig_lag1:11.3f}\")" ] }, { "cell_type": "markdown", "id": "1a6dd72d", "metadata": {}, "source": [ "The left panel is flat: all three methods land on the original\n", "contemporaneous correlation, because none of them splits a row. The right panel\n", "separates them. VAR and the moving block sit on the dashed lead-lag truth; IID\n", "collapses to zero. IID has thrown away the dynamic cross-dependence while keeping\n", "the static one, the kind of silent failure to watch for." ] }, { "cell_type": "markdown", "id": "01150079", "metadata": {}, "source": [ "## A real macro example\n", "\n", "We repeat the check on a small macro subset from `statsmodels`: real GDP, real\n", "consumption, and the CPI (quarterly US data). The levels trend upward and are\n", "non-stationary, so we work with quarterly log growth rates, which a VAR can fit\n", "sensibly. The truth is no longer known, but we can still confirm that the\n", "replicate cross-correlations track the observed ones." ] }, { "cell_type": "code", "execution_count": 7, "id": "4f815573", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:15:02.402902Z", "iopub.status.busy": "2026-06-22T16:15:02.402566Z", "iopub.status.idle": "2026-06-22T16:15:02.727918Z", "shell.execute_reply": "2026-06-22T16:15:02.727071Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "growth shape: (202, 3) (n, d)\n", "original cross-correlation matrix:\n" ] }, { "data": { "text/html": [ "
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cpi-0.059-0.1711.000
\n", "
" ], "text/plain": [ " realgdp realcons cpi\n", "realgdp 1.000 0.658 -0.059\n", "realcons 0.658 1.000 -0.171\n", "cpi -0.059 -0.171 1.000" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "import statsmodels.api as sm\n", "\n", "macro = sm.datasets.macrodata.load_pandas().data\n", "levels = macro[[\"realgdp\", \"realcons\", \"cpi\"]].to_numpy()\n", "labels = [\"realgdp\", \"realcons\", \"cpi\"]\n", "\n", "# Quarterly log growth (in percent): a stationary multivariate series.\n", "growth = np.diff(np.log(levels), axis=0) * 100.0\n", "print(\"growth shape:\", growth.shape, \" (n, d)\")\n", "\n", "orig_corr = np.corrcoef(growth.T)\n", "print(\"original cross-correlation matrix:\")\n", "pd.DataFrame(orig_corr, index=labels, columns=labels).round(3)" ] }, { "cell_type": "markdown", "id": "1dbf3d9b", "metadata": {}, "source": [ "We fit a VAR(2) on the growth rates, average the replicate correlation matrices,\n", "and compare them against the original. The two matrices appear side by side as\n", "heatmaps, with the off-diagonal pairs collected into a table below." ] }, { "cell_type": "code", "execution_count": 8, "id": "b06f69df", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:15:02.730493Z", "iopub.status.busy": "2026-06-22T16:15:02.730352Z", "iopub.status.idle": "2026-06-22T16:15:03.034556Z", "shell.execute_reply": "2026-06-22T16:15:03.033385Z" } }, "outputs": [ { "data": { "image/png": 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", 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2realcons / cpi-0.171-0.1490.022
\n", "
" ], "text/plain": [ " pair original VAR(2) replicate mean difference\n", "0 realgdp / realcons 0.658 0.652 -0.006\n", "1 realgdp / cpi -0.059 -0.041 0.018\n", "2 realcons / cpi -0.171 -0.149 0.022" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "\n", "macro_res = bootstrap(\n", " growth,\n", " method=ResidualBootstrap(model=VAR(order=2)),\n", " n_bootstraps=500,\n", " random_state=0,\n", ")\n", "macro_corr = np.mean([np.corrcoef(v.T) for v in macro_res.values()], axis=0)\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(11, 4.6), constrained_layout=True)\n", "for ax, mat, title in [\n", " (axes[0], orig_corr, \"Original growth rates\"),\n", " (axes[1], macro_corr, \"VAR(2) replicate mean\"),\n", "]:\n", " im = ax.imshow(mat, vmin=-1, vmax=1, cmap=\"coolwarm\")\n", " ax.set_xticks(range(len(labels)))\n", " ax.set_xticklabels(labels, rotation=45, ha=\"right\")\n", " ax.set_yticks(range(len(labels)))\n", " ax.set_yticklabels(labels)\n", " ax.set_title(title)\n", " # Annotate each cell; pick black or white text for contrast against the fill.\n", " for i in range(len(labels)):\n", " for j in range(len(labels)):\n", " val = mat[i, j]\n", " ax.text(\n", " j,\n", " i,\n", " f\"{val:.2f}\",\n", " ha=\"center\",\n", " va=\"center\",\n", " fontsize=10,\n", " color=\"white\" if abs(val) > 0.6 else \"black\",\n", " )\n", "cbar = fig.colorbar(im, ax=axes, shrink=0.85, pad=0.02)\n", "cbar.set_label(\"Pearson correlation\")\n", "cbar.set_ticks([-1.0, -0.5, 0.0, 0.5, 1.0])\n", "fig.suptitle(\n", " \"Cross-correlation is preserved across GDP / consumption / CPI growth\",\n", " fontsize=12,\n", ")\n", "plt.show()\n", "\n", "# Off-diagonal pairs side by side: original vs replicate mean.\n", "pairs = [(0, 1), (0, 2), (1, 2)]\n", "comparison = pd.DataFrame(\n", " {\n", " \"pair\": [f\"{labels[i]} / {labels[j]}\" for i, j in pairs],\n", " \"original\": [orig_corr[i, j] for i, j in pairs],\n", " \"VAR(2) replicate mean\": [macro_corr[i, j] for i, j in pairs],\n", " }\n", ")\n", "comparison[\"difference\"] = comparison[\"VAR(2) replicate mean\"] - comparison[\"original\"]\n", "comparison.round(3)" ] }, { "cell_type": "markdown", "id": "5b9cba04", "metadata": {}, "source": [ "The two heatmaps match: the strong GDP-consumption co-movement and the weak,\n", "slightly negative links to CPI growth all carry over into the VAR replicates.\n", "The bootstrap has preserved the joint structure of the real series, not just the\n", "marginals." ] }, { "cell_type": "markdown", "id": "1f9c4f7e", "metadata": {}, "source": [ "## `diagnose()` on multivariate input\n", "\n", "`diagnose()` inspects the series and recommends method specifications. When it\n", "sees more than one column it adds a VAR-based recommendation, because a VAR is\n", "the model-based way to capture cross-series dependence, while noting that block\n", "methods preserve it by resampling whole rows. We run it on both the\n", "non-stationary levels and the stationary growth rates." ] }, { "cell_type": "code", "execution_count": 9, "id": "a8e91605", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:15:03.036941Z", "iopub.status.busy": "2026-06-22T16:15:03.036769Z", "iopub.status.idle": "2026-06-22T16:15:03.060237Z", "shell.execute_reply": "2026-06-22T16:15:03.058650Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "macro levels (n_series=3):\n", " recommended: ('ResidualBootstrap(model=VAR(...))', 'ResidualBootstrap(model=ARIMA(...))', 'SieveAR')\n", " - Series looks non-stationary (unit root): difference it via ARIMA, or use the sieve.\n", " - Multivariate input: VAR captures cross-series dependence; block methods preserve it by resampling whole rows.\n", "\n", "macro growth (n_series=3):\n", " recommended: ('ResidualBootstrap(model=VAR(...))', 'StationaryBlock', 'MovingBlock', 'SieveAR')\n", " - Serial dependence present (lag-1 autocorrelation 0.64): use a block method or the sieve.\n", " - Multivariate input: VAR captures cross-series dependence; block methods preserve it by resampling whole rows.\n", " - Suggested automatic block length (Politis-White): 20.\n", "\n" ] } ], "source": [ "from tsbootstrap import diagnose\n", "\n", "for name, series in [(\"macro levels\", levels), (\"macro growth\", growth)]:\n", " d = diagnose(series)\n", " print(f\"{name} (n_series={d.n_series}):\")\n", " print(f\" recommended: {d.recommended_methods}\")\n", " for note in d.notes:\n", " print(f\" - {note}\")\n", " print()" ] }, { "cell_type": "markdown", "id": "f328cb11", "metadata": {}, "source": [ "For both the levels and the growth rates, `diagnose()` puts\n", "`ResidualBootstrap(model=VAR(...))` first, because the input is multivariate. The\n", "rest of the recommendation reflects what else it measured: an integrated model\n", "for the trending levels (a unit root), block methods and the sieve for the\n", "stationary growth rates. The multivariate signal is detected from the column\n", "count alone, so it fires regardless of the stationarity verdict.\n", "\n", "### Choosing for multivariate input\n", "\n", "Multivariate data is defined by how its series move together, so a bootstrap\n", "must preserve that joint structure. Row-resampling methods (the block family)\n", "keep it by copying whole rows of `(n, d)` input, which is robust and\n", "model-free. `ResidualBootstrap(model=VAR(...))` keeps it by fitting and replaying\n", "the vector dynamics, which additionally captures lead-lag relationships that a\n", "single-step resampler cannot. Plain IID keeps the contemporaneous correlation\n", "but discards the dynamics, so on data with real lead-lag structure a time-series\n", "method earns its keep. `diagnose()` flags the multivariate case for you and\n", "points at the VAR." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.13" } }, "nbformat": 4, "nbformat_minor": 5 }