nb_comparecast_dmgw_miscoverage.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9edba9d5",
   "metadata": {},
   "source": [
    "# Sequentially Comparing Forecasters on Synthetic Data\n",
    "\n",
    "Here, we compare our e-processes against the **Diebold-Mariano (DM)** test of _unconditional_ predictive ability and the **Giacomini-White (GW)** test of _conditional_ predictive ability. \n",
    "Both are asymptotic tests with stationarity/mixing assumptions; each also has some modeling assumption (error-based losses for DM; linear conditional models for GW).\n",
    "\n",
    "We use the package [`epftoolbox`](https://epftoolbox.readthedocs.io/en/latest/) to implement the DM and GW tests. (It requires `tensorflow>=2.2` although we don't use the functionality here.)\n",
    "\n",
    "See also: Section H.2 in our paper.\n",
    "\n",
    "YJ Choe [yjchoe@cmu.edu]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e8a7cd11",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import os.path\n",
    "\n",
    "import comparecast as cc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b4d8e339",
   "metadata": {},
   "outputs": [],
   "source": [
    "from epftoolbox.evaluation import DM\n",
    "from epftoolbox.evaluation.gw import gwtest"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe5f3ce8",
   "metadata": {},
   "source": [
    "## Hyperparameter Settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7fd4fadb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# which scoring rule to use\n",
    "scoring_rule = \"brier\"\n",
    "\n",
    "# significance level\n",
    "alpha = 0.05\n",
    "\n",
    "# whether to use the log scale on x-axis (time)\n",
    "use_logx = False\n",
    "\n",
    "# size up label fonts\n",
    "font_scale = 1.75"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b950921",
   "metadata": {},
   "source": [
    "## Forecasts on Synthetic Data\n",
    "\n",
    "To compare the validity of p-processes, we choose a case where the the null is true, i.e., \n",
    "\n",
    "$$\\mathcal{H}_0: \\Delta_t \\leq 0,\\; \\forall t.$$\n",
    "\n",
    "We create a case where there reality is non-stationary and also not noisy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "bc35b850",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\n",
       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time</th>\n",
       "      <th>y</th>\n",
       "      <th>true_probs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9995</th>\n",
       "      <td>9996</td>\n",
       "      <td>0</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9996</th>\n",
       "      <td>9997</td>\n",
       "      <td>1</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9997</th>\n",
       "      <td>9998</td>\n",
       "      <td>0</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9998</th>\n",
       "      <td>9999</td>\n",
       "      <td>1</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9999</th>\n",
       "      <td>10000</td>\n",
       "      <td>0</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       time  y  true_probs\n",
       "0         1  0         0.5\n",
       "1         2  0         0.5\n",
       "2         3  1         0.5\n",
       "3         4  1         0.5\n",
       "4         5  0         0.5\n",
       "...     ... ..         ...\n",
       "9995   9996  0         0.2\n",
       "9996   9997  1         0.2\n",
       "9997   9998  0         0.2\n",
       "9998   9999  1         0.2\n",
       "9999  10000  0         0.2\n",
       "\n",
       "[10000 rows x 3 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_name = \"default_noiseless\"\n",
    "data_file = f\"forecasts/{data_name}.csv\"\n",
    "plots_dir = f\"plots/dmgw_miscoverage/{data_name}\"\n",
    "savefig_dpi = 300\n",
    "\n",
    "# data = cc.data_utils.synthetic.get_data(\"default\", size=10000, noise=0.0)\n",
    "# data.to_csv(data_file, index=False)\n",
    "data = cc.data_utils.synthetic.get_data(data_file, size=10000, noise=0.0)\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5ffab437",
   "metadata": {},
   "outputs": [],
   "source": [
    "data[\"optimist\"] = np.concatenate([\n",
    "    np.repeat(0.6, 2000+1),\n",
    "    np.repeat(0.9, 2000),\n",
    "    np.repeat(0.3, 2000),\n",
    "    np.repeat(0.9, 2000),\n",
    "    np.repeat(0.3, 2000-1),\n",
    "])    # too optimistic\n",
    "data[\"pessimist\"] = np.concatenate([\n",
    "    np.repeat(0.4, 2000+1),\n",
    "    np.repeat(0.7, 2000),\n",
    "    np.repeat(0.1, 2000),\n",
    "    np.repeat(0.7, 2000),\n",
    "    np.repeat(0.1, 2000-1),\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0dee4522",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 360x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cc.plot_forecasts(\n",
    "    data, \n",
    "    forecasters=[\"optimist\", \"pessimist\"], \n",
    "    plots_dir=plots_dir, \n",
    "    use_logx=use_logx,\n",
    "    font_scale=font_scale,\n",
    "    figsize=(5, 4),\n",
    "    legend_out=False,\n",
    ")\n",
    "plt.legend(loc=\"lower left\", fontsize=\"small\", bbox_to_anchor=(-0.02, -0.025))\n",
    "#plt.legend(loc=\"upper center\", ncol=3, fontsize=\"small\", bbox_to_anchor=(0.425, 1.35))\n",
    "plt.tight_layout()\n",
    "plt.savefig(os.path.join(plots_dir, \"forecasters.pdf\"), dpi=savefig_dpi)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2618e7f",
   "metadata": {},
   "source": [
    "## CS for $\\Delta_t(\\hat{p}_\\text{k29-poly3}, \\hat{p}_\\text{laplace})$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a25ab08f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time</th>\n",
       "      <th>lcb</th>\n",
       "      <th>ucb</th>\n",
       "      <th>e_pq</th>\n",
       "      <th>e_qp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>-10.286275</td>\n",
       "      <td>9.886275</td>\n",
       "      <td>0.902317</td>\n",
       "      <td>1.054496</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>-5.243138</td>\n",
       "      <td>4.843138</td>\n",
       "      <td>0.835592</td>\n",
       "      <td>1.141155</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>-3.428758</td>\n",
       "      <td>3.295425</td>\n",
       "      <td>0.823937</td>\n",
       "      <td>0.959435</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>-2.521569</td>\n",
       "      <td>2.521569</td>\n",
       "      <td>0.856047</td>\n",
       "      <td>0.856047</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>-2.057255</td>\n",
       "      <td>1.977255</td>\n",
       "      <td>0.778617</td>\n",
       "      <td>0.904531</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9995</th>\n",
       "      <td>9996</td>\n",
       "      <td>-0.008812</td>\n",
       "      <td>0.004930</td>\n",
       "      <td>0.018498</td>\n",
       "      <td>0.117144</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9996</th>\n",
       "      <td>9997</td>\n",
       "      <td>-0.008780</td>\n",
       "      <td>0.004963</td>\n",
       "      <td>0.018673</td>\n",
       "      <td>0.114409</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9997</th>\n",
       "      <td>9998</td>\n",
       "      <td>-0.008787</td>\n",
       "      <td>0.004955</td>\n",
       "      <td>0.018628</td>\n",
       "      <td>0.115070</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9998</th>\n",
       "      <td>9999</td>\n",
       "      <td>-0.008756</td>\n",
       "      <td>0.004987</td>\n",
       "      <td>0.018805</td>\n",
       "      <td>0.112398</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9999</th>\n",
       "      <td>10000</td>\n",
       "      <td>-0.008763</td>\n",
       "      <td>0.004979</td>\n",
       "      <td>0.018760</td>\n",
       "      <td>0.113044</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       time        lcb       ucb      e_pq      e_qp\n",
       "0         1 -10.286275  9.886275  0.902317  1.054496\n",
       "1         2  -5.243138  4.843138  0.835592  1.141155\n",
       "2         3  -3.428758  3.295425  0.823937  0.959435\n",
       "3         4  -2.521569  2.521569  0.856047  0.856047\n",
       "4         5  -2.057255  1.977255  0.778617  0.904531\n",
       "...     ...        ...       ...       ...       ...\n",
       "9995   9996  -0.008812  0.004930  0.018498  0.117144\n",
       "9996   9997  -0.008780  0.004963  0.018673  0.114409\n",
       "9997   9998  -0.008787  0.004955  0.018628  0.115070\n",
       "9998   9999  -0.008756  0.004987  0.018805  0.112398\n",
       "9999  10000  -0.008763  0.004979  0.018760  0.113044\n",
       "\n",
       "[10000 rows x 5 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "name_p, name_q = \"optimist\", \"pessimist\"\n",
    "results = cc.compare_forecasts(\n",
    "    data, \n",
    "    name_p, \n",
    "    name_q, \n",
    "    scoring_rule=scoring_rule,\n",
    "    alpha=alpha,\n",
    ")\n",
    "results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "99800e2c",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:root:miscoverage rate calculation may be slow for boundary type mixture\n",
      "calculating diagnostics under repeated sampling: 100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████| 100/100 [34:34<00:00, 20.74s/it]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# takes a long time\n",
    "results, axes = cc.plot_comparison(\n",
    "    data, \n",
    "    name_p, \n",
    "    name_q, \n",
    "    scoring_rule=scoring_rule,    \n",
    "    plots_dir=plots_dir, \n",
    "    alpha=alpha,\n",
    "    baselines=(\"ci\"),\n",
    "    plot_e=False,\n",
    "    plot_diagnostics=True,\n",
    "    diagnostics_fn=\"cfdr\",\n",
    "    diagnostics_baselines=(\"dm\", \"gw\", \"ci\"),\n",
    "    n_repeats=100,\n",
    "    plot_width=False,\n",
    "    use_logx=use_logx,\n",
    "    ylim_scale=0.075,\n",
    "    font_scale=font_scale,\n",
    "    no_title=True,\n",
    "    savefig_dpi=savefig_dpi,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5b22d98",
   "metadata": {},
   "source": [
    "## DM/GW Tests of (Un)conditional Predictive Ability\n",
    "\n",
    "These tests are NOT anytime-valid and are asymptotic. They also come with different assumptions which are not often checked in practice (Diebold 2013)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca9d16e6",
   "metadata": {},
   "source": [
    "### DM Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "362f7f3a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DM p-value at T=4000: [0.71988521 0.71988521]\n",
      "DM p-value at T=10000: [0.86912347 0.86912347]\n"
     ]
    }
   ],
   "source": [
    "# use squared loss\n",
    "norm = 2\n",
    "T = len(data)\n",
    "mid_T = 4000\n",
    "\n",
    "# hack to make it 2 columns (second column not meaningful)\n",
    "y, fc_p, fc_q = [\n",
    "    np.vstack([data[column].values, 1 - data[column].values]).T\n",
    "    for column in [\"y\", name_p, name_q]\n",
    "]\n",
    "\n",
    "# direction is in reverse to our null\n",
    "print(f\"DM p-value at T={mid_T}:\", DM(y[:mid_T], fc_q[:mid_T], fc_p[:mid_T], norm=norm))\n",
    "print(f\"DM p-value at T={T}:\", DM(y, fc_q, fc_p, norm=norm))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "839ed315",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.86912347, 0.86912347])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DM(y, fc_q, fc_p, norm=norm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9dda1373",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cc.compute_cfdr(DM(y, fc_q, fc_p, norm=norm))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27d852a3",
   "metadata": {},
   "source": [
    "### GW Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7130db62",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GW p-value at T=4000: 1.0\n",
      "GW p-value at T=10000: 1.0\n"
     ]
    }
   ],
   "source": [
    "# default option 'GW' only supports (hardcoded) the format of 24-forecasts-per-day\n",
    "from epftoolbox.evaluation.gw import gwtest\n",
    "\n",
    "score_fn = cc.get_scoring_rule(\"brier\")\n",
    "\n",
    "loss_p = 1 - score_fn(y, fc_p)\n",
    "loss_q = 1 - score_fn(y, fc_q)\n",
    "\n",
    "print(f\"GW p-value at T={mid_T}:\", gwtest(loss_q[:mid_T], loss_p[:mid_T], tau=1, conditional=True))\n",
    "print(f\"GW p-value at T={T}:\", gwtest(loss_q, loss_p, tau=1, conditional=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f60c3581",
   "metadata": {},
   "source": [
    "### Both at different sample sizes (unsafe)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e77b473a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d76d74e2085b4cf681e3aad917545452",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Time</th>\n",
       "      <th>Test</th>\n",
       "      <th>p-value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>100</td>\n",
       "      <td>DM</td>\n",
       "      <td>0.579275</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>200</td>\n",
       "      <td>DM</td>\n",
       "      <td>0.714350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>300</td>\n",
       "      <td>DM</td>\n",
       "      <td>0.822537</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>400</td>\n",
       "      <td>DM</td>\n",
       "      <td>0.971845</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>500</td>\n",
       "      <td>DM</td>\n",
       "      <td>0.858712</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>195</th>\n",
       "      <td>9600</td>\n",
       "      <td>GW</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>196</th>\n",
       "      <td>9700</td>\n",
       "      <td>GW</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>197</th>\n",
       "      <td>9800</td>\n",
       "      <td>GW</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>198</th>\n",
       "      <td>9900</td>\n",
       "      <td>GW</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>199</th>\n",
       "      <td>10000</td>\n",
       "      <td>GW</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>200 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Time Test   p-value\n",
       "0      100   DM  0.579275\n",
       "1      200   DM  0.714350\n",
       "2      300   DM  0.822537\n",
       "3      400   DM  0.971845\n",
       "4      500   DM  0.858712\n",
       "..     ...  ...       ...\n",
       "195   9600   GW  1.000000\n",
       "196   9700   GW  1.000000\n",
       "197   9800   GW  1.000000\n",
       "198   9900   GW  1.000000\n",
       "199  10000   GW  1.000000\n",
       "\n",
       "[200 rows x 3 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# non-anytime-valid p-values\n",
    "from tqdm.notebook import tqdm\n",
    "\n",
    "n_interval = 100\n",
    "unsafe_p = pd.DataFrame([\n",
    "    {\n",
    "        \"Time\": t,\n",
    "        \"DM\": DM(y[:t], fc_q[:t], fc_p[:t], norm=norm)[0],\n",
    "        \"GW\": gwtest(loss_q[:t], loss_p[:t], tau=1, conditional=True),\n",
    "    }\n",
    "    for t in tqdm(data.time[n_interval-1::n_interval])\n",
    "]).melt(id_vars=[\"Time\"], var_name=\"Test\", value_name=\"p-value\")\n",
    "\n",
    "unsafe_p"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "901232cc",
   "metadata": {},
   "source": [
    "## Comparison with Anytime-Valid $p$-Values\n",
    "\n",
    "Any e-process $(E_t)_{t \\geq 0}$ can be converted into an anytime-valid p-process $(\\mathsf{p}_t)_{t\\geq0}$ via the simple conversion formula $\\mathsf{p}_t = 1/E_t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "78037387",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time</th>\n",
       "      <th>lcb</th>\n",
       "      <th>ucb</th>\n",
       "      <th>e_pq</th>\n",
       "      <th>e_qp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>-10.286275</td>\n",
       "      <td>9.886275</td>\n",
       "      <td>0.902317</td>\n",
       "      <td>1.054496</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>-5.243138</td>\n",
       "      <td>4.843138</td>\n",
       "      <td>0.835592</td>\n",
       "      <td>1.141155</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>-3.428758</td>\n",
       "      <td>3.295425</td>\n",
       "      <td>0.823937</td>\n",
       "      <td>0.959435</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>-2.521569</td>\n",
       "      <td>2.521569</td>\n",
       "      <td>0.856047</td>\n",
       "      <td>0.856047</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>-2.057255</td>\n",
       "      <td>1.977255</td>\n",
       "      <td>0.778617</td>\n",
       "      <td>0.904531</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9995</th>\n",
       "      <td>9996</td>\n",
       "      <td>-0.008812</td>\n",
       "      <td>0.004930</td>\n",
       "      <td>0.018498</td>\n",
       "      <td>0.117144</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9996</th>\n",
       "      <td>9997</td>\n",
       "      <td>-0.008780</td>\n",
       "      <td>0.004963</td>\n",
       "      <td>0.018673</td>\n",
       "      <td>0.114409</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9997</th>\n",
       "      <td>9998</td>\n",
       "      <td>-0.008787</td>\n",
       "      <td>0.004955</td>\n",
       "      <td>0.018628</td>\n",
       "      <td>0.115070</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9998</th>\n",
       "      <td>9999</td>\n",
       "      <td>-0.008756</td>\n",
       "      <td>0.004987</td>\n",
       "      <td>0.018805</td>\n",
       "      <td>0.112398</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9999</th>\n",
       "      <td>10000</td>\n",
       "      <td>-0.008763</td>\n",
       "      <td>0.004979</td>\n",
       "      <td>0.018760</td>\n",
       "      <td>0.113044</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       time        lcb       ucb      e_pq      e_qp\n",
       "0         1 -10.286275  9.886275  0.902317  1.054496\n",
       "1         2  -5.243138  4.843138  0.835592  1.141155\n",
       "2         3  -3.428758  3.295425  0.823937  0.959435\n",
       "3         4  -2.521569  2.521569  0.856047  0.856047\n",
       "4         5  -2.057255  1.977255  0.778617  0.904531\n",
       "...     ...        ...       ...       ...       ...\n",
       "9995   9996  -0.008812  0.004930  0.018498  0.117144\n",
       "9996   9997  -0.008780  0.004963  0.018673  0.114409\n",
       "9997   9998  -0.008787  0.004955  0.018628  0.115070\n",
       "9998   9999  -0.008756  0.004987  0.018805  0.112398\n",
       "9999  10000  -0.008763  0.004979  0.018760  0.113044\n",
       "\n",
       "[10000 rows x 5 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = cc.compare_forecasts(\n",
    "    data, \n",
    "    name_p, \n",
    "    name_q, \n",
    "    scoring_rule=scoring_rule,\n",
    "    alpha=alpha,\n",
    ")\n",
    "results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "2925a7f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def convert_e_to_p(e):\n",
    "    \"\"\"Convert an e-process into an anytime-valid p-process via\n",
    "    \n",
    "    p_t = 1/E_t.\n",
    "    \"\"\"\n",
    "    return np.clip(1.0 / (e + 1e-8), 0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "356d695a",
   "metadata": {},
   "outputs": [],
   "source": [
    "safe_e = results[\"e_pq\"].values\n",
    "safe_p = convert_e_to_p(safe_e)\n",
    "safe_p = pd.DataFrame([\n",
    "    {\n",
    "        \"Time\": t,\n",
    "        \"Test\": \"CR (anytime-valid)\",\n",
    "        \"p-value\": p,\n",
    "    }\n",
    "    for t, p in zip(data.time[n_interval-1::n_interval], \n",
    "                    safe_p[n_interval-1::n_interval])\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3b7dba03",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720.065x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pvalues = pd.concat([safe_p, unsafe_p], ignore_index=True)\n",
    "\n",
    "fg = sns.relplot(\n",
    "    x=\"Time\",\n",
    "    y=\"p-value\",\n",
    "    kind=\"line\",\n",
    "    linewidth=2,\n",
    "    hue=\"Test\",\n",
    "    style=\"Test\",\n",
    "    aspect=1.5,\n",
    "    data=pvalues\n",
    ")\n",
    "fg.ax.set(\n",
    "    title=\"p-values for \" + r\"$H_0:$\" + \"\\\"p is no better than q\\\"\",\n",
    ")\n",
    "# fg.ax.axhline(y=0.05, color=\"gray\", alpha=0.5, linewidth=2)\n",
    "fg.savefig(os.path.join(plots_dir, \"pvalue_comparison.pdf\"),\n",
    "           dpi=savefig_dpi)\n",
    "None"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52469e14",
   "metadata": {},
   "source": [
    "## *DM Assumptions\n",
    "\n",
    "In particular: covariance stationarity (clearly violated in the above examples)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "fcaf88f7",
   "metadata": {},
   "outputs": [],
   "source": [
    "deltas = cc.cumul_mean(loss_q - loss_p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "e3bf3d05",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lineplot(x=data.time, y=deltas, label=r\"$\\hat\\Delta_t$\")\n",
    "None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "c931195c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>lb_stat</th>\n",
       "      <th>lb_pvalue</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>7039.560538</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       lb_stat  lb_pvalue\n",
       "1  7039.560538        0.0"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "# H_0: white noise vs. H_1: not white noise\n",
    "sm.stats.acorr_ljungbox(deltas, lags=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "2a7dd8a2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-6.253783289287301,\n",
       " 4.388988062747655e-08,\n",
       " 38,\n",
       " 9961,\n",
       " {'1%': -3.4310066595695945,\n",
       "  '5%': -2.861830204343065,\n",
       "  '10%': -2.5669244706354584},\n",
       " -134957.87532730523)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.tsa.api as tsa\n",
    "\n",
    "# H_0: non-stationary vs. H_1: AR(1) stationary\n",
    "tsa.adfuller(deltas)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}