nb_comparecast_dmgw_power.ipynb

{
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  {
   "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",
    "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": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time</th>\n",
       "      <th>y</th>\n",
       "      <th>true_probs</th>\n",
       "      <th>constant_0.5</th>\n",
       "      <th>constant_0</th>\n",
       "      <th>constant_1</th>\n",
       "      <th>laplace</th>\n",
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       "      <th>k29_poly3</th>\n",
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       "      <th>mix_01_noiseless</th>\n",
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       "      <td>0.5</td>\n",
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       "      <td>0.200000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.384349</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>0.225698</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.166667</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.8</td>\n",
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       "    <tr>\n",
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       "      <td>0.5</td>\n",
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       "      <td>0.273082</td>\n",
       "      <td>0.922852</td>\n",
       "      <td>0.898438</td>\n",
       "      <td>0.945312</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.834358</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.000000</td>\n",
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       "      <td>1.0</td>\n",
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       "      <td>0.925781</td>\n",
       "      <td>0.906250</td>\n",
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       "      <td>0.8</td>\n",
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       "      <td>0.2</td>\n",
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       "      <td>0.928711</td>\n",
       "      <td>0.913086</td>\n",
       "      <td>0.945312</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.632395</td>\n",
       "      <td>0.2</td>\n",
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       "      <td>0.2</td>\n",
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       "      <td>10000</td>\n",
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       "      <td>0.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.273373</td>\n",
       "      <td>0.934570</td>\n",
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       "      <td>0.945312</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.2</td>\n",
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       "  </tbody>\n",
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       "<p>10000 rows × 14 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       time  y  true_probs  constant_0.5  constant_0  constant_1   laplace  \\\n",
       "0         1  0    0.176406           0.5         0.0         1.0  0.500000   \n",
       "1         2  0    0.049999           0.5         0.0         1.0  0.333333   \n",
       "2         3  0    0.117741           0.5         0.0         1.0  0.250000   \n",
       "3         4  0    0.253642           0.5         0.0         1.0  0.200000   \n",
       "4         5  0    0.225698           0.5         0.0         1.0  0.166667   \n",
       "...     ... ..         ...           ...         ...         ...       ...   \n",
       "9995   9996  1    0.857929           0.5         0.0         1.0  0.273082   \n",
       "9996   9997  1    1.000000           0.5         0.0         1.0  0.273155   \n",
       "9997   9998  1    1.000000           0.5         0.0         1.0  0.273227   \n",
       "9998   9999  1    1.000000           0.5         0.0         1.0  0.273300   \n",
       "9999  10000  1    1.000000           0.5         0.0         1.0  0.273373   \n",
       "\n",
       "       k29_epa  k29_poly3  k29_rbf0.01  mix_01_noiseless    mix_01  \\\n",
       "0     0.000000   0.000000     0.000000               0.2  1.000000   \n",
       "1     0.000000   0.000000     0.000000               0.2  0.000000   \n",
       "2     0.000000   0.000000     0.000000               0.2  0.000000   \n",
       "3     0.000000   0.000000     0.000000               0.2  0.000000   \n",
       "4     0.000000   0.000000     0.000000               0.2  0.000000   \n",
       "...        ...        ...          ...               ...       ...   \n",
       "9995  0.922852   0.898438     0.945312               0.8  0.834358   \n",
       "9996  0.925781   0.906250     0.945312               0.8  0.144735   \n",
       "9997  0.928711   0.913086     0.945312               0.8  0.632395   \n",
       "9998  0.932617   0.918945     0.945312               0.8  0.000000   \n",
       "9999  0.934570   0.924805     0.945312               0.8  1.000000   \n",
       "\n",
       "      mix_10_noiseless    mix_10  \n",
       "0                  0.8  1.000000  \n",
       "1                  0.8  0.690548  \n",
       "2                  0.8  1.000000  \n",
       "3                  0.8  0.384349  \n",
       "4                  0.8  0.626115  \n",
       "...                ...       ...  \n",
       "9995               0.2  0.000000  \n",
       "9996               0.2  0.637117  \n",
       "9997               0.2  0.000000  \n",
       "9998               0.2  0.000000  \n",
       "9999               0.2  0.129753  \n",
       "\n",
       "[10000 rows x 14 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_name = \"sigmoid\"\n",
    "data_file = f\"forecasts/{data_name}.csv\"\n",
    "plots_dir = f\"plots/dmgw_power/{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)\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4c9e9b1c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# only use k29_poly3\n",
    "data = data.rename(columns={\"k29_poly3\": \"k29\"})\n",
    "\n",
    "name_p = \"k29\"\n",
    "name_q = \"laplace\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0dee4522",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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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=[name_p, name_q],\n",
    "    plots_dir=plots_dir, \n",
    "    use_logx=use_logx,\n",
    "    font_scale=font_scale,\n",
    "    figsize=(5, 4),\n",
    "    legend_out=False,\n",
    "    savefig_dpi=savefig_dpi,\n",
    ")"
   ]
  },
  {
   "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": "3e3d6816",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.07359446, 0.07568633, 0.05166738, ..., 0.11336776, 0.11340858,\n",
       "       0.11344947])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cc.compute_true_deltas(\n",
    "    data[name_p],\n",
    "    data[name_q],\n",
    "    data[\"true_probs\"],\n",
    "    scoring_rule=scoring_rule\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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>-9.836275</td>\n",
       "      <td>10.336275</td>\n",
       "      <td>1.060372e+00</td>\n",
       "      <td>0.873247</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>-4.862582</td>\n",
       "      <td>5.223693</td>\n",
       "      <td>1.094559e+00</td>\n",
       "      <td>0.827561</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>-3.220888</td>\n",
       "      <td>3.503295</td>\n",
       "      <td>1.112239e+00</td>\n",
       "      <td>0.801757</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>-2.405666</td>\n",
       "      <td>2.637472</td>\n",
       "      <td>1.122837e+00</td>\n",
       "      <td>0.785197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>-1.918977</td>\n",
       "      <td>2.115533</td>\n",
       "      <td>1.129830e+00</td>\n",
       "      <td>0.773679</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>0.097658</td>\n",
       "      <td>0.121120</td>\n",
       "      <td>1.000000e+07</td>\n",
       "      <td>0.001161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9996</th>\n",
       "      <td>9997</td>\n",
       "      <td>0.097700</td>\n",
       "      <td>0.121161</td>\n",
       "      <td>1.000000e+07</td>\n",
       "      <td>0.001161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9997</th>\n",
       "      <td>9998</td>\n",
       "      <td>0.097741</td>\n",
       "      <td>0.121202</td>\n",
       "      <td>1.000000e+07</td>\n",
       "      <td>0.001161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9998</th>\n",
       "      <td>9999</td>\n",
       "      <td>0.097782</td>\n",
       "      <td>0.121243</td>\n",
       "      <td>1.000000e+07</td>\n",
       "      <td>0.001161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9999</th>\n",
       "      <td>10000</td>\n",
       "      <td>0.097823</td>\n",
       "      <td>0.121284</td>\n",
       "      <td>1.000000e+07</td>\n",
       "      <td>0.001160</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 -9.836275  10.336275  1.060372e+00  0.873247\n",
       "1         2 -4.862582   5.223693  1.094559e+00  0.827561\n",
       "2         3 -3.220888   3.503295  1.112239e+00  0.801757\n",
       "3         4 -2.405666   2.637472  1.122837e+00  0.785197\n",
       "4         5 -1.918977   2.115533  1.129830e+00  0.773679\n",
       "...     ...       ...        ...           ...       ...\n",
       "9995   9996  0.097658   0.121120  1.000000e+07  0.001161\n",
       "9996   9997  0.097700   0.121161  1.000000e+07  0.001161\n",
       "9997   9998  0.097741   0.121202  1.000000e+07  0.001161\n",
       "9998   9999  0.097782   0.121243  1.000000e+07  0.001161\n",
       "9999  10000  0.097823   0.121284  1.000000e+07  0.001160\n",
       "\n",
       "[10000 rows x 5 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = cc.compare_forecasts(\n",
    "    data, \n",
    "    name_p, \n",
    "    name_q, \n",
    "    aligned_forecasts=True,\n",
    "    compute_cs=True,\n",
    "    lag=1,\n",
    "    scoring_rule=scoring_rule,\n",
    "    alpha=alpha,\n",
    ")\n",
    "results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "7937ebc9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results, axes = cc.plot_comparison(\n",
    "    data, \n",
    "    name_p, \n",
    "    name_q, \n",
    "    scoring_rule=scoring_rule,    \n",
    "    plots_dir=None, \n",
    "    alpha=alpha,\n",
    "    baselines=(),\n",
    "    plot_e=False,\n",
    "    plot_diagnostics=False,\n",
    "    plot_width=False,\n",
    "    use_logx=use_logx,\n",
    "    ylim_scale=0.2,\n",
    "    font_scale=font_scale,\n",
    "    no_title=True,\n",
    ")\n",
    "axes[0].set(ylabel=\"CS\")\n",
    "plt.tight_layout()\n",
    "plt.savefig(os.path.join(plots_dir, \"ebcs.pdf\"), dpi=savefig_dpi)\n",
    "None"
   ]
  },
  {
   "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": 10,
   "id": "362f7f3a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DM p-value at T=4000: [0.99644733 0.99644733]\n",
      "DM p-value at T=10000: [0. 0.]\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": 11,
   "id": "839ed315",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0.])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DM(y, fc_q, fc_p, norm=norm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9dda1373",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True])"
      ]
     },
     "execution_count": 12,
     "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": 13,
   "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: 0.0\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": 14,
   "id": "e77b473a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6e49324984f0482f89e452595fdd894b",
       "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>0.807841</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>200</td>\n",
       "      <td>DM</td>\n",
       "      <td>0.799895</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>300</td>\n",
       "      <td>DM</td>\n",
       "      <td>0.738469</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>400</td>\n",
       "      <td>DM</td>\n",
       "      <td>0.782820</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>500</td>\n",
       "      <td>DM</td>\n",
       "      <td>0.809458</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>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>196</th>\n",
       "      <td>9700</td>\n",
       "      <td>GW</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>197</th>\n",
       "      <td>9800</td>\n",
       "      <td>GW</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>198</th>\n",
       "      <td>9900</td>\n",
       "      <td>GW</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>199</th>\n",
       "      <td>10000</td>\n",
       "      <td>GW</td>\n",
       "      <td>0.000000</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  0.807841\n",
       "1      200   DM  0.799895\n",
       "2      300   DM  0.738469\n",
       "3      400   DM  0.782820\n",
       "4      500   DM  0.809458\n",
       "..     ...  ...       ...\n",
       "195   9600   GW  0.000000\n",
       "196   9700   GW  0.000000\n",
       "197   9800   GW  0.000000\n",
       "198   9900   GW  0.000000\n",
       "199  10000   GW  0.000000\n",
       "\n",
       "[200 rows x 3 columns]"
      ]
     },
     "execution_count": 14,
     "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": 15,
   "id": "78037387",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        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>-13.692169</td>\n",
       "      <td>14.192169</td>\n",
       "      <td>1.046004e+00</td>\n",
       "      <td>0.951207</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>-6.790529</td>\n",
       "      <td>7.151640</td>\n",
       "      <td>1.067782e+00</td>\n",
       "      <td>0.930943</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>-4.506186</td>\n",
       "      <td>4.788593</td>\n",
       "      <td>1.080131e+00</td>\n",
       "      <td>0.919685</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>-3.369639</td>\n",
       "      <td>3.601445</td>\n",
       "      <td>1.088061e+00</td>\n",
       "      <td>0.912527</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>-2.690156</td>\n",
       "      <td>2.886711</td>\n",
       "      <td>1.093577e+00</td>\n",
       "      <td>0.907577</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>0.099133</td>\n",
       "      <td>0.119645</td>\n",
       "      <td>1.000000e+07</td>\n",
       "      <td>0.005566</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9996</th>\n",
       "      <td>9997</td>\n",
       "      <td>0.099174</td>\n",
       "      <td>0.119687</td>\n",
       "      <td>1.000000e+07</td>\n",
       "      <td>0.005564</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9997</th>\n",
       "      <td>9998</td>\n",
       "      <td>0.099215</td>\n",
       "      <td>0.119728</td>\n",
       "      <td>1.000000e+07</td>\n",
       "      <td>0.005563</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9998</th>\n",
       "      <td>9999</td>\n",
       "      <td>0.099256</td>\n",
       "      <td>0.119769</td>\n",
       "      <td>1.000000e+07</td>\n",
       "      <td>0.005562</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9999</th>\n",
       "      <td>10000</td>\n",
       "      <td>0.099297</td>\n",
       "      <td>0.119810</td>\n",
       "      <td>1.000000e+07</td>\n",
       "      <td>0.005561</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 -13.692169  14.192169  1.046004e+00  0.951207\n",
       "1         2  -6.790529   7.151640  1.067782e+00  0.930943\n",
       "2         3  -4.506186   4.788593  1.080131e+00  0.919685\n",
       "3         4  -3.369639   3.601445  1.088061e+00  0.912527\n",
       "4         5  -2.690156   2.886711  1.093577e+00  0.907577\n",
       "...     ...        ...        ...           ...       ...\n",
       "9995   9996   0.099133   0.119645  1.000000e+07  0.005566\n",
       "9996   9997   0.099174   0.119687  1.000000e+07  0.005564\n",
       "9997   9998   0.099215   0.119728  1.000000e+07  0.005563\n",
       "9998   9999   0.099256   0.119769  1.000000e+07  0.005562\n",
       "9999  10000   0.099297   0.119810  1.000000e+07  0.005561\n",
       "\n",
       "[10000 rows x 5 columns]"
      ]
     },
     "execution_count": 15,
     "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",
    "    v_opt=100,\n",
    ")\n",
    "results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "2925a7f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def convert_e_to_p(e, running_max=True):\n",
    "    \"\"\"Convert an e-process into an anytime-valid p-process via\n",
    "    \n",
    "    p_t = 1/E_t.\n",
    "    \"\"\"\n",
    "    if running_max:\n",
    "        return np.clip(1.0 / (np.maximum.accumulate(e) + 1e-8), 0, 1)\n",
    "    else:\n",
    "        return np.clip(1.0 / (e + 1e-8), 0, 1)        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "356d695a",
   "metadata": {},
   "outputs": [],
   "source": [
    "safe_e = results[\"e_pq\"].values\n",
    "safe_p = convert_e_to_p(safe_e, running_max=False)\n",
    "safe_p = pd.DataFrame([\n",
    "    {\n",
    "        \"Time\": t,\n",
    "        \"Test\": \"CR [SAVI]\",\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": 18,
   "id": "b7d4968d",
   "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>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>HZ [SAVI]</td>\n",
       "      <td>1.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>200</td>\n",
       "      <td>HZ [SAVI]</td>\n",
       "      <td>1.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>300</td>\n",
       "      <td>HZ [SAVI]</td>\n",
       "      <td>1.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>400</td>\n",
       "      <td>HZ [SAVI]</td>\n",
       "      <td>1.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>500</td>\n",
       "      <td>HZ [SAVI]</td>\n",
       "      <td>1.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>9600</td>\n",
       "      <td>HZ [SAVI]</td>\n",
       "      <td>1.000000e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>9700</td>\n",
       "      <td>HZ [SAVI]</td>\n",
       "      <td>1.000000e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>9800</td>\n",
       "      <td>HZ [SAVI]</td>\n",
       "      <td>1.000000e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>9900</td>\n",
       "      <td>HZ [SAVI]</td>\n",
       "      <td>1.000000e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>10000</td>\n",
       "      <td>HZ [SAVI]</td>\n",
       "      <td>1.000000e-07</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Time       Test       p-value\n",
       "0     100  HZ [SAVI]  1.000000e+00\n",
       "1     200  HZ [SAVI]  1.000000e+00\n",
       "2     300  HZ [SAVI]  1.000000e+00\n",
       "3     400  HZ [SAVI]  1.000000e+00\n",
       "4     500  HZ [SAVI]  1.000000e+00\n",
       "..    ...        ...           ...\n",
       "95   9600  HZ [SAVI]  1.000000e-07\n",
       "96   9700  HZ [SAVI]  1.000000e-07\n",
       "97   9800  HZ [SAVI]  1.000000e-07\n",
       "98   9900  HZ [SAVI]  1.000000e-07\n",
       "99  10000  HZ [SAVI]  1.000000e-07\n",
       "\n",
       "[100 rows x 3 columns]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "safe_e_hz = cc.eprocess_hz(data[name_p].values, \n",
    "                           data[name_q].values, \n",
    "                           data[\"y\"].values,\n",
    "                           scoring_rule=scoring_rule,\n",
    "                           alt_prob=0.55)\n",
    "safe_p_hz = convert_e_to_p(safe_e_hz, running_max=False)\n",
    "safe_p_hz = pd.DataFrame([\n",
    "    {\n",
    "        \"Time\": t,\n",
    "        \"Test\": \"HZ [SAVI]\",\n",
    "        \"p-value\": p,\n",
    "    }\n",
    "    for t, p in zip(data.time[n_interval-1::n_interval], \n",
    "                    safe_p_hz[n_interval-1::n_interval])\n",
    "])\n",
    "safe_p_hz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "edaa629b",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pvalues = pd.concat([safe_p, safe_p_hz, unsafe_p], ignore_index=True)\n",
    "#pvalues = pvalues.rename(columns={\"p-value\": \"P-value\"})\n",
    "\n",
    "plt.figure(figsize=(5, 4))\n",
    "ax = sns.lineplot(\n",
    "    x=\"Time\",\n",
    "    y=\"p-value\",\n",
    "    linewidth=2,\n",
    "    hue=\"Test\",\n",
    "    style=\"Test\",\n",
    "    style_order=[\"CR [SAVI]\", \"DM\", \"HZ [SAVI]\", \"GW\"],\n",
    "    data=pvalues,\n",
    ")\n",
    "ax.set_title(\n",
    "    r\"$H_0:$\" + \"\\\"p is no better than q\\\"\",\n",
    "    fontsize=\"large\",\n",
    ")\n",
    "ax.axhline(y=0.05, color=\"gray\", alpha=0.5, linewidth=2, linestyle=\"dashed\")\n",
    "plt.tight_layout()\n",
    "plt.savefig(os.path.join(plots_dir, \"pvalue_comparison.pdf\"),\n",
    "            dpi=savefig_dpi)\n",
    "None"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52469e14",
   "metadata": {},
   "source": [
    "## *Checking DM Assumptions (stationarity)\n",
    "\n",
    "In particular: covariance stationarity (clearly violated in the above examples)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "fcaf88f7",
   "metadata": {},
   "outputs": [],
   "source": [
    "deltas = cc.cumul_mean(loss_q - loss_p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "e3bf3d05",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5, 4))\n",
    "sns.lineplot(x=data.time, y=deltas, label=r\"$\\hat\\Delta_t$\")\n",
    "None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "190697ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "# ignore the first few steps\n",
    "offset = 500"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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>9492.371155</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       lb_stat  lb_pvalue\n",
       "1  9492.371155        0.0"
      ]
     },
     "execution_count": 23,
     "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[offset:], lags=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "2a7dd8a2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7.200598693670573,\n",
       " 1.0,\n",
       " 38,\n",
       " 9461,\n",
       " {'1%': -3.431041372489004,\n",
       "  '5%': -2.8618455435967367,\n",
       "  '10%': -2.5669326357576447},\n",
       " -170529.86979810375)"
      ]
     },
     "execution_count": 24,
     "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[offset:])"
   ]
  }
 ],
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