{ "cells": [ { "cell_type": "markdown", "id": "3a812a09", "metadata": {}, "source": [ "# Bootstrapping with exogenous regressors (ARX / VARX / ARIMAX)\n", "\n", "Many series are driven partly by an external covariate you observe but do not want to resample: a policy rate, a price index, a control input. `tsbootstrap` handles this with one extra keyword, `bootstrap(..., exog=z)`. The exogenous series is held fixed across every replicate, while only the model innovations are resampled. Three model shapes accept `exog`:\n", "\n", "- ARX: a univariate AR with a covariate, `y_t = c + sum_j phi_j y_{t-j} + beta . z_t + e_t`.\n", "- VARX: a vector AR with a covariate, `Y_t = c + sum_j A_j Y_{t-j} + B z_t + e_t`.\n", "- ARIMAX: an integrated ARMA where the covariate enters at the level.\n", "\n", "Every data-generating process here has a known coefficient, so we can check that the bootstrap distribution recovers the truth instead of taking the library's word for it." ] }, { "cell_type": "code", "execution_count": 1, "id": "98e053cc", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:14:46.682692Z", "iopub.status.busy": "2026-06-22T16:14:46.682477Z", "iopub.status.idle": "2026-06-22T16:14:47.589057Z", "shell.execute_reply": "2026-06-22T16:14:47.587185Z" } }, "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": "786d8360", "metadata": {}, "source": [ "## What accepts `exog`, and what does not\n", "\n", "The `exog` keyword is routed only to the model-based methods: `ResidualBootstrap` (with an `AR`, `VAR`, or `ARIMA` model) and `SieveAR`. The block methods and `IID` resample observations directly; they have no model to attach a covariate to, so passing `exog` to them raises immediately rather than silently ignoring it. The last section deliberately triggers that error to show what it looks like.\n", "\n", "There is one alignment rule. For ARX and VARX the recursion steps through time, so the covariate value at each step has to line up with the step being generated. That requires `initial=\"fixed\"` (start from the observed initial block, not a random one) and `burn_in=0` (there is no covariate value to feed the discarded burn-in steps). ARIMAX has no such constraint: the covariate enters at the level after inverse-differencing, not inside the step recursion, so the default settings are fine." ] }, { "cell_type": "code", "execution_count": 2, "id": "6188886d", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:14:47.594060Z", "iopub.status.busy": "2026-06-22T16:14:47.593755Z", "iopub.status.idle": "2026-06-22T16:14:47.877412Z", "shell.execute_reply": "2026-06-22T16:14:47.876104Z" } }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "from tsbootstrap import AR, ARIMA, VAR, MovingBlock, ResidualBootstrap, bootstrap\n", "from tsbootstrap.model.fit import fit_ar, fit_var\n", "\n", "\n", "# A single re-fit helper: estimate the exog coefficient(s) on any series given the\n", "# same fixed covariate. This is how we read the bootstrap distribution of beta.\n", "def refit_ar_beta(series, exog, order=1):\n", " return fit_ar(np.asarray(series), order, exog).exog_coefs\n", "\n", "\n", "def refit_var_beta(series, exog, order=1):\n", " return fit_var(np.asarray(series), order, exog).exog_coefs" ] }, { "cell_type": "markdown", "id": "987d4c68", "metadata": {}, "source": [ "## ARX: recover a known covariate effect\n", "\n", "We generate a stationary AR(1) with a known covariate effect:\n", "\n", "`y_t = phi * y_{t-1} + beta * z_t + e_t`, with `phi = 0.6`, `beta = 2.0`, and standard-normal noise.\n", "\n", "The covariate `z` is just white noise here; what matters is that its true coefficient is `beta = 2.0`. We fit the ARX once, bootstrap with `exog=z` (innovations resampled, `z` held fixed), refit `beta` on every replicate, and look at the resulting distribution." ] }, { "cell_type": "code", "execution_count": 3, "id": "66e317ed", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:14:47.881236Z", "iopub.status.busy": "2026-06-22T16:14:47.880972Z", "iopub.status.idle": "2026-06-22T16:14:47.886843Z", "shell.execute_reply": "2026-06-22T16:14:47.885961Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "observed phi hat = 0.6056 (true 0.6)\n", "observed beta hat = 2.0871 (true 2.0)\n" ] } ], "source": [ "rng = np.random.default_rng(0)\n", "n_arx = 400\n", "PHI, BETA = 0.6, 2.0\n", "\n", "z = rng.standard_normal(n_arx)\n", "e = rng.standard_normal(n_arx)\n", "y = np.zeros(n_arx)\n", "for t in range(1, n_arx):\n", " y[t] = PHI * y[t - 1] + BETA * z[t] + e[t]\n", "\n", "# Point estimate on the observed data.\n", "fit = fit_ar(y, 1, z)\n", "print(f\"observed phi hat = {fit.ar_coefs[0]:.4f} (true {PHI})\")\n", "print(f\"observed beta hat = {fit.exog_coefs[0]:.4f} (true {BETA})\")" ] }, { "cell_type": "markdown", "id": "82054466", "metadata": {}, "source": [ "ARX requires `initial=\"fixed\"` and `burn_in=0`. The `AR` spec already defaults to those, but we set them explicitly to make the contract visible." ] }, { "cell_type": "code", "execution_count": 4, "id": "38c54b0b", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:14:47.891027Z", "iopub.status.busy": "2026-06-22T16:14:47.890885Z", "iopub.status.idle": "2026-06-22T16:14:48.189030Z", "shell.execute_reply": "2026-06-22T16:14:48.187094Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "bootstrap beta mean = 2.0876 (true 2.0)\n", "bootstrap beta std = 0.0498\n", "95% bootstrap interval = [1.9899, 2.1824] contains true beta: True\n" ] } ], "source": [ "arx_spec = ResidualBootstrap(model=AR(order=1, initial=\"fixed\", burn_in=0))\n", "arx_res = bootstrap(y, method=arx_spec, n_bootstraps=600, random_state=1, exog=z)\n", "\n", "beta_draws = np.array([refit_ar_beta(v, z)[0] for v in arx_res.values()])\n", "lo, hi = np.quantile(beta_draws, [0.025, 0.975])\n", "print(f\"bootstrap beta mean = {beta_draws.mean():.4f} (true {BETA})\")\n", "print(f\"bootstrap beta std = {beta_draws.std():.4f}\")\n", "print(f\"95% bootstrap interval = [{lo:.4f}, {hi:.4f}] contains true beta: {lo <= BETA <= hi}\")" ] }, { "cell_type": "code", "execution_count": 5, "id": "15838fac", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:14:48.192071Z", "iopub.status.busy": "2026-06-22T16:14:48.191811Z", "iopub.status.idle": "2026-06-22T16:14:48.573322Z", "shell.execute_reply": "2026-06-22T16:14:48.571347Z" }, "nbsphinx-thumbnail": { "output-index": 0 } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 4.5), constrained_layout=True)\n", "ax.hist(beta_draws, bins=35, color=\"tab:blue\", alpha=0.75, edgecolor=\"white\", linewidth=0.4)\n", "ax.axvspan(\n", " lo, hi, color=\"tab:orange\", alpha=0.15, label=f\"95% bootstrap interval [{lo:.3f}, {hi:.3f}]\"\n", ")\n", "ax.axvline(BETA, color=\"black\", lw=2.5, label=f\"true beta = {BETA}\")\n", "ax.axvline(\n", " beta_draws.mean(),\n", " color=\"tab:red\",\n", " lw=2,\n", " ls=\"--\",\n", " label=f\"bootstrap mean = {beta_draws.mean():.3f}\",\n", ")\n", "ax.set_xlabel(r\"re-estimated covariate coefficient $\\beta$\")\n", "ax.set_ylabel(\"frequency (count of replicates)\")\n", "ax.set_title(\"ARX bootstrap distribution of the covariate coefficient\")\n", "ax.legend(loc=\"upper right\", framealpha=0.9)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "id": "b5a58016", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:14:48.577580Z", "iopub.status.busy": "2026-06-22T16:14:48.577346Z", "iopub.status.idle": "2026-06-22T16:14:48.846001Z", "shell.execute_reply": "2026-06-22T16:14:48.844821Z" } }, "outputs": [ { "data": { "text/html": [ "
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beta2.02.08760.04981.98992.1824True
\n", "
" ], "text/plain": [ " true bootstrap mean bootstrap std 95% lower 95% upper covers true\n", "beta 2.0 2.0876 0.0498 1.9899 2.1824 True" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "\n", "# Recovered-vs-true summary for the ARX covariate coefficient.\n", "arx_table = pd.DataFrame(\n", " {\n", " \"true\": [BETA],\n", " \"bootstrap mean\": [beta_draws.mean()],\n", " \"bootstrap std\": [beta_draws.std()],\n", " \"95% lower\": [lo],\n", " \"95% upper\": [hi],\n", " \"covers true\": [bool(lo <= BETA <= hi)],\n", " },\n", " index=[\"beta\"],\n", ").round(4)\n", "arx_table" ] }, { "cell_type": "markdown", "id": "06b41f07", "metadata": {}, "source": [ "The distribution is centered on the true `beta = 2.0` and the 95% bootstrap interval brackets it. The covariate was held fixed across replicates, so this spread reflects only the innovation resampling, which is the uncertainty in `beta` given the observed `z`." ] }, { "cell_type": "markdown", "id": "dde9cb3c", "metadata": {}, "source": [ "## VARX: a multivariate covariate effect\n", "\n", "The same idea extends to a vector AR. We generate a bivariate VAR(1) driven by a single scalar covariate `z` with a known loading vector `B = [1.5, -0.8]`:\n", "\n", "`Y_t = A Y_{t-1} + B z_t + e_t`.\n", "\n", "We bootstrap with `exog=z` and refit the covariate loading on each replicate, one number per output series." ] }, { "cell_type": "code", "execution_count": 7, "id": "55637802", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:14:48.850757Z", "iopub.status.busy": "2026-06-22T16:14:48.850333Z", "iopub.status.idle": "2026-06-22T16:14:48.857458Z", "shell.execute_reply": "2026-06-22T16:14:48.856328Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "observed B hat: [ 1.464 -0.8921] (true [ 1.5 -0.8] )\n" ] } ], "source": [ "rng = np.random.default_rng(2)\n", "n_varx = 400\n", "A_true = np.array([[0.5, 0.1], [0.0, 0.4]])\n", "B_true = np.array([1.5, -0.8])\n", "\n", "zv = rng.standard_normal(n_varx)\n", "ev = rng.standard_normal((n_varx, 2))\n", "Y = np.zeros((n_varx, 2))\n", "for t in range(1, n_varx):\n", " Y[t] = A_true @ Y[t - 1] + B_true * zv[t] + ev[t]\n", "\n", "fit_v = fit_var(Y, 1, zv)\n", "print(\"observed B hat:\", np.round(fit_v.exog_coefs.ravel(), 4), \" (true\", B_true, \")\")" ] }, { "cell_type": "code", "execution_count": 8, "id": "7c7d2910", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:14:48.861501Z", "iopub.status.busy": "2026-06-22T16:14:48.861359Z", "iopub.status.idle": "2026-06-22T16:14:48.924185Z", "shell.execute_reply": "2026-06-22T16:14:48.921726Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "series 0: boot mean +1.4631 true +1.5 95% [+1.3693, +1.5646]\n", "series 1: boot mean -0.8916 true -0.8 95% [-0.9920, -0.7998]\n" ] } ], "source": [ "varx_spec = ResidualBootstrap(model=VAR(order=1, initial=\"fixed\", burn_in=0))\n", "varx_res = bootstrap(Y, method=varx_spec, n_bootstraps=500, random_state=3, exog=zv)\n", "\n", "# exog_coefs has shape (k, d) = (1, 2); ravel to the two per-series loadings.\n", "B_draws = np.array([refit_var_beta(v, zv).ravel() for v in varx_res.values()])\n", "for j in range(2):\n", " lo_j, hi_j = np.quantile(B_draws[:, j], [0.025, 0.975])\n", " print(\n", " f\"series {j}: boot mean {B_draws[:, j].mean():+.4f} true {B_true[j]:+.1f} \"\n", " f\"95% [{lo_j:+.4f}, {hi_j:+.4f}]\"\n", " )" ] }, { "cell_type": "code", "execution_count": 9, "id": "0fefd2b6", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:14:48.928499Z", "iopub.status.busy": "2026-06-22T16:14:48.927918Z", "iopub.status.idle": "2026-06-22T16:14:49.240073Z", "shell.execute_reply": "2026-06-22T16:14:49.238657Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Each loading sits at a different level (+1.5 vs -0.8), so center each panel on its\n", "# own coefficient but give both panels the SAME x-axis WIDTH, so the recovered spreads\n", "# are read on one comparable scale.\n", "half_width = 0.5 * max(np.ptp(B_draws[:, j]) for j in range(2)) + 0.15\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(11, 4.5), sharey=True, constrained_layout=True)\n", "for j, ax in enumerate(axes):\n", " lo_j, hi_j = np.quantile(B_draws[:, j], [0.025, 0.975])\n", " center = B_draws[:, j].mean()\n", " ax.hist(B_draws[:, j], bins=30, color=\"tab:green\", alpha=0.7, edgecolor=\"white\", linewidth=0.4)\n", " ax.axvspan(\n", " lo_j, hi_j, color=\"tab:orange\", alpha=0.15, label=f\"95% interval [{lo_j:+.3f}, {hi_j:+.3f}]\"\n", " )\n", " ax.axvline(B_true[j], color=\"black\", lw=2.5, label=f\"true = {B_true[j]:+.1f}\")\n", " ax.axvline(center, color=\"tab:red\", lw=2, ls=\"--\", label=f\"bootstrap mean = {center:+.3f}\")\n", " ax.set_title(f\"covariate loading on output series {j}\")\n", " ax.set_xlabel(r\"re-estimated loading $B_j$\")\n", " ax.set_xlim(center - half_width, center + half_width)\n", " ax.legend(fontsize=8, loc=\"upper left\", framealpha=0.9)\n", "axes[0].set_ylabel(\"frequency (count of replicates)\")\n", "fig.suptitle(\n", " \"VARX bootstrap distributions of both loading-vector components (panels share one x-axis width)\"\n", ")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 10, "id": "3fda4850", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:14:49.244861Z", "iopub.status.busy": "2026-06-22T16:14:49.244673Z", "iopub.status.idle": "2026-06-22T16:14:49.255937Z", "shell.execute_reply": "2026-06-22T16:14:49.254627Z" } }, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
truebootstrap meanbootstrap std95% lower95% uppercovers true
B[0]1.51.46310.04971.36931.5646True
B[1]-0.8-0.89160.0481-0.9920-0.7998True
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" ], "text/plain": [ " true bootstrap mean bootstrap std 95% lower 95% upper covers true\n", "B[0] 1.5 1.4631 0.0497 1.3693 1.5646 True\n", "B[1] -0.8 -0.8916 0.0481 -0.9920 -0.7998 True" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Recovered-vs-true summary for both components of the loading vector B.\n", "_rows = []\n", "for j in range(2):\n", " lo_j, hi_j = np.quantile(B_draws[:, j], [0.025, 0.975])\n", " _rows.append(\n", " {\n", " \"true\": B_true[j],\n", " \"bootstrap mean\": B_draws[:, j].mean(),\n", " \"bootstrap std\": B_draws[:, j].std(),\n", " \"95% lower\": lo_j,\n", " \"95% upper\": hi_j,\n", " \"covers true\": bool(lo_j <= B_true[j] <= hi_j),\n", " }\n", " )\n", "varx_table = pd.DataFrame(_rows, index=[\"B[0]\", \"B[1]\"]).round(4)\n", "varx_table" ] }, { "cell_type": "markdown", "id": "c71610a5", "metadata": {}, "source": [ "Both components of `B` are recovered: the positive loading on series 0 and the negative loading on series 1. The covariate enters the vector recursion at each step, which is why VARX inherits the same `initial=\"fixed\"`, `burn_in=0` requirement as ARX." ] }, { "cell_type": "markdown", "id": "cad00b8b", "metadata": {}, "source": [ "## ARIMAX: a covariate on a trending series\n", "\n", "Real macro series usually trend, so a stationary AR is the wrong model. ARIMAX differences the series to stationarity, fits an ARMA to the differenced part, and lets the covariate enter at the level. We use the statsmodels `macrodata` set: real GDP (a strongly trending series) as the target, and the consumer price index as the covariate.\n", "\n", "This path needs statsmodels for the MA / MLE fit, which ships in the `[models]` extra (`pip install \"tsbootstrap[models]\"`). The `[examples]` extra used by the install cell already includes it." ] }, { "cell_type": "code", "execution_count": 11, "id": "d547696e", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:14:49.261159Z", "iopub.status.busy": "2026-06-22T16:14:49.260975Z", "iopub.status.idle": "2026-06-22T16:14:49.284479Z", "shell.execute_reply": "2026-06-22T16:14:49.282766Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "realgdp: 203 quarters, ranges 2710 to 13415 (clearly trending)\n", "cpi : ranges 29.0 to 218.6\n" ] } ], "source": [ "from statsmodels.datasets import macrodata\n", "\n", "macro = macrodata.load_pandas().data\n", "gdp = macro[\"realgdp\"].to_numpy()\n", "cpi = macro[\"cpi\"].to_numpy()\n", "print(f\"realgdp: {len(gdp)} quarters, ranges {gdp.min():.0f} to {gdp.max():.0f} (clearly trending)\")\n", "print(f\"cpi : ranges {cpi.min():.1f} to {cpi.max():.1f}\")" ] }, { "cell_type": "markdown", "id": "02dcc4a8", "metadata": {}, "source": [ "ARIMAX takes no `initial` or `burn_in` argument: it conditions on the observed initial differenced state, and integration would turn any burn-in transient into a permanent level shift, so those knobs would be incoherent. We just pass the order `(p, d, q)` and the covariate. With `d=1` the series is differenced once before the ARMA fit." ] }, { "cell_type": "code", "execution_count": 12, "id": "f1fd5b71", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:14:49.288654Z", "iopub.status.busy": "2026-06-22T16:14:49.288496Z", "iopub.status.idle": "2026-06-22T16:14:49.575385Z", "shell.execute_reply": "2026-06-22T16:14:49.574519Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "replicates shape: (300, 203) (n_bootstraps, n_quarters)\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "arimax_spec = ResidualBootstrap(model=ARIMA(order=(1, 1, 1)))\n", "arimax_res = bootstrap(gdp, method=arimax_spec, n_bootstraps=300, random_state=4, exog=cpi)\n", "\n", "samples = arimax_res.values()\n", "print(f\"replicates shape: {samples.shape} (n_bootstraps, n_quarters)\")\n", "\n", "band_lo, band_hi = np.quantile(samples, [0.05, 0.95], axis=0)\n", "fig, ax = plt.subplots(figsize=(9, 4.5))\n", "ax.fill_between(\n", " range(len(gdp)), band_lo, band_hi, color=\"tab:purple\", alpha=0.25, label=\"5-95% replicate band\"\n", ")\n", "for i in range(8):\n", " ax.plot(samples[i], color=\"tab:purple\", alpha=0.3, lw=0.7)\n", "ax.plot(gdp, color=\"black\", lw=1.8, label=\"observed realgdp\")\n", "ax.set_xlabel(\"quarter index\")\n", "ax.set_ylabel(\"real GDP\")\n", "ax.set_title(\"ARIMAX replicates track the trend (covariate cpi held fixed)\")\n", "ax.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "b8e4976f", "metadata": {}, "source": [ "The replicates follow the trend rather than collapsing to a stationary band, because the integration step rebuilds the level and the held-fixed covariate carries its part of the level back in. The covariate effect is estimated jointly with the ARMA part during the one-time fit and held fixed thereafter." ] }, { "cell_type": "markdown", "id": "cc2dc281", "metadata": {}, "source": [ "## When `exog` is rejected: a non-model method\n", "\n", "Passing `exog` to a block method or `IID` is a configuration error, not a silent no-op. `tsbootstrap` raises a structured `MethodConfigError` so the mistake surfaces immediately. Here is what that looks like." ] }, { "cell_type": "code", "execution_count": 13, "id": "2461064f", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:14:49.577630Z", "iopub.status.busy": "2026-06-22T16:14:49.577382Z", "iopub.status.idle": "2026-06-22T16:14:49.580688Z", "shell.execute_reply": "2026-06-22T16:14:49.580195Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "raised: MethodConfigError\n", "[TSB_UNSUPPORTED_EXOG] exogenous regressors are only supported for model-based methods (ResidualBootstrap, SieveAR)\n" ] } ], "source": [ "from tsbootstrap.errors import MethodConfigError\n", "\n", "try:\n", " bootstrap(gdp, method=MovingBlock(block_length=10), n_bootstraps=10, exog=cpi)\n", "except MethodConfigError as exc:\n", " print(\"raised:\", type(exc).__name__)\n", " print(exc)" ] }, { "cell_type": "markdown", "id": "3de08e0a", "metadata": {}, "source": [ "The error names which methods accept a covariate. The alignment constraints are enforced the same way: an ARX or VARX with `initial=\"random_block\"` or `burn_in > 0` and a covariate also raises a `MethodConfigError`, because a random initial block or burn-in steps would break the time alignment between the covariate and the generated path." ] }, { "cell_type": "code", "execution_count": 14, "id": "b177a8dd", "metadata": { "execution": { "iopub.execute_input": "2026-06-22T16:14:49.582607Z", "iopub.status.busy": "2026-06-22T16:14:49.582471Z", "iopub.status.idle": "2026-06-22T16:14:49.586903Z", "shell.execute_reply": "2026-06-22T16:14:49.585973Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "initial=\"random_block\" -> [TSB_UNSUPPORTED_EXOG] exogenous regressors require initial='fixed' (a random initial block would break the exog time alignment)\n", "burn_in=5 -> [TSB_UNSUPPORTED_EXOG] exogenous regressors require burn_in=0 (there is no exog for burn-in steps)\n" ] } ], "source": [ "# The two ARX alignment violations, each raised explicitly.\n", "for bad_model, label in [\n", " (AR(order=1, initial=\"random_block\"), 'initial=\"random_block\"'),\n", " (AR(order=1, initial=\"fixed\", burn_in=5), \"burn_in=5\"),\n", "]:\n", " try:\n", " bootstrap(y, method=ResidualBootstrap(model=bad_model), n_bootstraps=5, exog=z)\n", " except MethodConfigError as exc:\n", " print(f\"{label:24s} -> {exc}\")" ] }, { "cell_type": "markdown", "id": "efb653d5", "metadata": {}, "source": [ "## Working with covariates: the rules\n", "\n", "- `exog` is accepted only by `ResidualBootstrap` (AR, VAR, ARIMA) and `SieveAR`; other methods raise `MethodConfigError`.\n", "- The covariate is held fixed across replicates; only the model innovations are resampled, so the bootstrap spread is the uncertainty in the model given the observed covariate.\n", "- ARX and VARX step through time, so they require `initial=\"fixed\"` and `burn_in=0`. ARIMAX adds the covariate at the level and has no such constraint.\n", "- Across all three shapes the bootstrap distribution recovers the known coefficient, which is the check that the covariate is being handled correctly rather than just accepted." ] } ], "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 }