autogen/notebook/flaml_forecast.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Time Series Forecasting with FLAML Library"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## 1. Introduction\r\n",
    "\r\n",
    "FLAML is a Python library (https://github.com/microsoft/FLAML) designed to automatically produce accurate machine learning models with low computational cost. It is fast and cheap. The simple and lightweight design makes it easy to use and extend, such as adding new learners. FLAML can\r\n",
    "\r\n",
    " - serve as an economical AutoML engine,\r\n",
    " - be used as a fast hyperparameter tuning tool, or\r\n",
    " - be embedded in self-tuning software that requires low latency & resource in repetitive tuning tasks.\r\n",
    " - In this notebook, we demonstrate how to use FLAML library to tune hyperparameters of XGBoost with a regression example.\r\n",
    "\r\n",
    "FLAML requires Python>=3.6. To run this notebook example, please install flaml with the notebook option:\r\n",
    "\r\n",
    "> pip install flaml[notebook]"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "!pip install flaml[notebook,forecast]"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## 2. Forecast Problem\r\n",
    "\r\n",
    "### Load data and preprocess\r\n",
    "\r\n",
    "Import co2 data from statsmodel. The dataset is from “Atmospheric CO2 from Continuous Air Samples at Mauna Loa Observatory, Hawaii, U.S.A.,” which collected CO2 samples from March 1958 to December 2001. The task is to predict monthly CO2 samples."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "source": [
    "import statsmodels.api as sm\r\n",
    "data = sm.datasets.co2.load_pandas()\r\n",
    "data = data.data\r\n",
    "# data is given in weeks, but the task is to predict monthly, so use monthly averages instead\r\n",
    "data = data['co2'].resample('MS').mean()\r\n",
    "data = data.fillna(data.bfill())  # makes sure there are no missing values\r\n",
    "data = data.to_frame().reset_index()\r\n",
    "# data = data.rename(columns={'index': 'ds', 'co2': 'y'})"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "source": [
    "# split the data into a train dataframe and X_test and y_test dataframes, where the number of samples for test is equal to\r\n",
    "# the number of periods the user wants to predict\r\n",
    "num_samples = data.shape[0]\r\n",
    "time_horizon = 12\r\n",
    "split_idx = num_samples - time_horizon\r\n",
    "X_train = data[:split_idx]  # X_train is a dataframe with two columns: time and value\r\n",
    "X_test = data[split_idx:]['index']  # X_test is a dataframe with dates for prediction\r\n",
    "y_test = data[split_idx:]['co2']  # y_test is a series of the values corresponding to the dates for prediction"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Run FLAML\r\n",
    "\r\n",
    "In the FLAML automl run configuration, users can specify the task type, time budget, error metric, learner list, whether to subsample, resampling strategy type, and so on. All these arguments have default values which will be used if users do not provide them."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "source": [
    "''' import AutoML class from flaml package '''\r\n",
    "from flaml import AutoML\r\n",
    "automl = AutoML()"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "source": [
    "settings = {\r\n",
    "    \"time_budget\": 180,  # total running time in seconds\r\n",
    "    \"metric\": 'mape',  # primary metric for validation: 'mape' is generally used for forecast tasks\r\n",
    "    \"task\": 'forecast',  # task type\r\n",
    "    \"log_file_name\": 'CO2_forecast.log',  # flaml log file\r\n",
    "    \"eval_method\": \"holdout\",  # validation method can be chosen from ['auto', 'holdout', 'cv']\r\n",
    "    \"split_type\": 'time'  # for foretask task, 'split_type' has to be 'time'\r\n",
    "}"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "source": [
    "'''The main flaml automl API'''\r\n",
    "automl.fit(dataframe=X_train,  # training data\r\n",
    "           label=('index', 'co2'),  # For 'forecast' task, label should be a tuple of strings for timestamp and value columns\r\n",
    "           **settings, \r\n",
    "           period=time_horizon)  # key word argument 'period' must be included for forecast task)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "[flaml.automl: 08-31 21:19:53] {1209} INFO - Evaluation method: holdout\n",
      "INFO:flaml.automl:Evaluation method: holdout\n",
      "[flaml.automl: 08-31 21:19:53] {686} INFO - Using TimeSeriesSplit\n",
      "INFO:flaml.automl:Using TimeSeriesSplit\n",
      "[flaml.automl: 08-31 21:19:53] {1237} INFO - Minimizing error metric: mape\n",
      "INFO:flaml.automl:Minimizing error metric: mape\n",
      "[flaml.automl: 08-31 21:19:53] {1259} INFO - List of ML learners in AutoML Run: ['fbprophet', 'arima', 'sarimax']\n",
      "INFO:flaml.automl:List of ML learners in AutoML Run: ['fbprophet', 'arima', 'sarimax']\n",
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      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
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      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
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      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
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      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
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      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
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      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
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      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
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      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
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      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
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      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
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      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
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      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
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      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
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      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
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      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
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      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
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      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
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      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
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      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
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      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
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      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
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      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
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      "[flaml.automl: 08-31 21:22:28] {1349} INFO - iteration 75, current learner fbprophet\n",
      "INFO:flaml.automl:iteration 75, current learner fbprophet\n",
      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
      "[flaml.automl: 08-31 21:22:30] {1502} INFO -  at 156.8s,\tbest fbprophet's error=0.0005,\tbest fbprophet's error=0.0005\n",
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      "INFO:flaml.automl:iteration 76, current learner sarimax\n",
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      "INFO:flaml.automl:iteration 77, current learner sarimax\n",
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      "INFO:flaml.automl:iteration 78, current learner arima\n",
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      "INFO:flaml.automl: at 163.7s,\tbest arima's error=0.0011,\tbest fbprophet's error=0.0005\n",
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      "INFO:flaml.automl:iteration 79, current learner sarimax\n",
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      "INFO:flaml.automl:iteration 80, current learner arima\n",
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      "INFO:flaml.automl:iteration 81, current learner sarimax\n",
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      "INFO:flaml.automl:iteration 82, current learner sarimax\n",
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      "INFO:flaml.automl: at 173.8s,\tbest sarimax's error=0.0008,\tbest fbprophet's error=0.0005\n",
      "[flaml.automl: 08-31 21:22:47] {1349} INFO - iteration 83, current learner sarimax\n",
      "INFO:flaml.automl:iteration 83, current learner sarimax\n",
      "[flaml.automl: 08-31 21:22:48] {1502} INFO -  at 174.8s,\tbest sarimax's error=0.0008,\tbest fbprophet's error=0.0005\n",
      "INFO:flaml.automl: at 174.8s,\tbest sarimax's error=0.0008,\tbest fbprophet's error=0.0005\n",
      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
      "[flaml.automl: 08-31 21:22:50] {1534} INFO - retrain sarimax for 2.2s\n",
      "INFO:flaml.automl:retrain sarimax for 2.2s\n",
      "[flaml.automl: 08-31 21:22:50] {1349} INFO - iteration 84, current learner sarimax\n",
      "INFO:flaml.automl:iteration 84, current learner sarimax\n",
      "[flaml.automl: 08-31 21:22:52] {1502} INFO -  at 178.8s,\tbest sarimax's error=0.0008,\tbest fbprophet's error=0.0005\n",
      "INFO:flaml.automl: at 178.8s,\tbest sarimax's error=0.0008,\tbest fbprophet's error=0.0005\n",
      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
      "[flaml.automl: 08-31 21:22:55] {1534} INFO - retrain sarimax for 2.5s\n",
      "INFO:flaml.automl:retrain sarimax for 2.5s\n",
      "[flaml.automl: 08-31 21:22:55] {1558} INFO - selected model: <prophet.forecaster.Prophet object at 0x000002C8485D46D0>\n",
      "INFO:flaml.automl:selected model: <prophet.forecaster.Prophet object at 0x000002C8485D46D0>\n",
      "[flaml.automl: 08-31 21:22:55] {1281} INFO - fit succeeded\n",
      "INFO:flaml.automl:fit succeeded\n",
      "[flaml.automl: 08-31 21:22:55] {1282} INFO - Time taken to find the best model: 71.81526470184326\n",
      "INFO:flaml.automl:Time taken to find the best model: 71.81526470184326\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Best model and metric"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "source": [
    "''' retrieve best config and best learner'''\r\n",
    "print('Best ML leaner:', automl.best_estimator)\r\n",
    "print('Best hyperparmeter config:', automl.best_config)\r\n",
    "print(f'Best mape on validation data: {automl.best_loss}')\r\n",
    "print(f'Training duration of best run: {automl.best_config_train_time}s')"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Best ML leaner: fbprophet\n",
      "Best hyperparmeter config: {'changepoint_prior_scale': 0.02876449933617924, 'seasonality_prior_scale': 1.80360430903146, 'holidays_prior_scale': 2.1243991057068654, 'seasonality_mode': 'additive'}\n",
      "Best mape on validation data: 0.0004765336783587436\n",
      "Training duration of best run: 2.890876531600952s\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "source": [
    "print(automl.model.estimator)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "<prophet.forecaster.Prophet object at 0x000002C8485D46D0>\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "source": [
    "''' pickle and save the automl object '''\r\n",
    "import pickle\r\n",
    "with open('automl.pkl', 'wb') as f:\r\n",
    "    pickle.dump(automl, f, pickle.HIGHEST_PROTOCOL)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "source": [
    "''' compute predictions of testing dataset '''\r\n",
    "flaml_y_pred = automl.predict(X_test)\r\n",
    "print('Predicted labels', flaml_y_pred)\r\n",
    "print('True labels', y_test)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Predicted labels 0     370.179589\n",
      "1     370.897300\n",
      "2     371.950006\n",
      "3     373.135219\n",
      "4     373.634979\n",
      "5     373.104820\n",
      "6     371.760649\n",
      "7     369.848551\n",
      "8     368.250457\n",
      "9     368.318975\n",
      "10    369.517605\n",
      "11    370.783469\n",
      "Name: yhat, dtype: float64\n",
      "True labels 514    370.175\n",
      "515    371.325\n",
      "516    372.060\n",
      "517    372.775\n",
      "518    373.800\n",
      "519    373.060\n",
      "520    371.300\n",
      "521    369.425\n",
      "522    367.880\n",
      "523    368.050\n",
      "524    369.375\n",
      "525    371.020\n",
      "Name: co2, dtype: float64\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "source": [
    "''' compute different metric values on testing dataset'''\r\n",
    "from flaml.ml import sklearn_metric_loss_score\r\n",
    "print('mape', '=', sklearn_metric_loss_score('mape', flaml_y_pred, y_test))"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "mape = 0.0006780276756290267\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Log history"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "source": [
    "from flaml.data import get_output_from_log\r\n",
    "time_history, best_valid_loss_history, valid_loss_history, config_history, train_loss_history = \\\r\n",
    "    get_output_from_log(filename=settings['log_file_name'], time_budget=180)\r\n",
    "\r\n",
    "for config in config_history:\r\n",
    "    print(config)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "{'Current Learner': 'fbprophet', 'Current Sample': 502, 'Current Hyper-parameters': {'changepoint_prior_scale': 0.010000000000000002, 'seasonality_prior_scale': 1.0, 'holidays_prior_scale': 1.0, 'seasonality_mode': 'multiplicative'}, 'Best Learner': 'fbprophet', 'Best Hyper-parameters': {'changepoint_prior_scale': 0.010000000000000002, 'seasonality_prior_scale': 1.0, 'holidays_prior_scale': 1.0, 'seasonality_mode': 'multiplicative'}}\n",
      "{'Current Learner': 'fbprophet', 'Current Sample': 502, 'Current Hyper-parameters': {'changepoint_prior_scale': 0.0091602623296037, 'seasonality_prior_scale': 0.8823866403788657, 'holidays_prior_scale': 3.2294014074557995, 'seasonality_mode': 'additive'}, 'Best Learner': 'fbprophet', 'Best Hyper-parameters': {'changepoint_prior_scale': 0.0091602623296037, 'seasonality_prior_scale': 0.8823866403788657, 'holidays_prior_scale': 3.2294014074557995, 'seasonality_mode': 'additive'}}\n",
      "{'Current Learner': 'fbprophet', 'Current Sample': 502, 'Current Hyper-parameters': {'changepoint_prior_scale': 0.010000000000000002, 'seasonality_prior_scale': 1.0, 'holidays_prior_scale': 0.999999999999999, 'seasonality_mode': 'additive'}, 'Best Learner': 'fbprophet', 'Best Hyper-parameters': {'changepoint_prior_scale': 0.010000000000000002, 'seasonality_prior_scale': 1.0, 'holidays_prior_scale': 0.999999999999999, 'seasonality_mode': 'additive'}}\n",
      "{'Current Learner': 'fbprophet', 'Current Sample': 502, 'Current Hyper-parameters': {'changepoint_prior_scale': 0.05247335998097256, 'seasonality_prior_scale': 0.987707602743762, 'holidays_prior_scale': 0.5484274380225445, 'seasonality_mode': 'additive'}, 'Best Learner': 'fbprophet', 'Best Hyper-parameters': {'changepoint_prior_scale': 0.05247335998097256, 'seasonality_prior_scale': 0.987707602743762, 'holidays_prior_scale': 0.5484274380225445, 'seasonality_mode': 'additive'}}\n",
      "{'Current Learner': 'fbprophet', 'Current Sample': 502, 'Current Hyper-parameters': {'changepoint_prior_scale': 0.02876449933617924, 'seasonality_prior_scale': 1.80360430903146, 'holidays_prior_scale': 2.1243991057068654, 'seasonality_mode': 'additive'}, 'Best Learner': 'fbprophet', 'Best Hyper-parameters': {'changepoint_prior_scale': 0.02876449933617924, 'seasonality_prior_scale': 1.80360430903146, 'holidays_prior_scale': 2.1243991057068654, 'seasonality_mode': 'additive'}}\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "source": [
    "import matplotlib.pyplot as plt\r\n",
    "import numpy as np\r\n",
    "\r\n",
    "plt.title('Learning Curve')\r\n",
    "plt.xlabel('Wall Clock Time (s)')\r\n",
    "plt.ylabel('Validation Accuracy')\r\n",
    "plt.scatter(time_history, 1 - np.array(valid_loss_history))\r\n",
    "plt.step(time_history, 1 - np.array(best_valid_loss_history), where='post')\r\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## 3. Comparison with Alternatives"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "FLAML's MAPE"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "from flaml.ml import sklearn_metric_loss_score\r\n",
    "print('flaml mape', '=', sklearn_metric_loss_score('mape', flaml_y_pred, y_test))"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "flaml mape = 0.0006780276756290267\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Default Prophet"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "from prophet import Prophet\r\n",
    "prophet_model = Prophet()"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "X_train_prophet = X_train.copy()\r\n",
    "X_train_prophet = X_train_prophet.rename(columns={'index': 'ds', 'co2': 'y'})\r\n",
    "prophet_model.fit(X_train_prophet)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.\n",
      "INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "<prophet.forecaster.Prophet at 0x2c84853f9d0>"
      ]
     },
     "metadata": {},
     "execution_count": 38
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "X_test_prophet = X_test.copy()\r\n",
    "X_test_prophet = X_test_prophet.rename(columns={'index': 'ds'})\r\n",
    "prophet_y_pred = prophet_model.predict(X_test_prophet)['yhat']\r\n",
    "print('Predicted labels', prophet_y_pred)\r\n",
    "print('True labels', y_test)\r\n",
    "from flaml.ml import sklearn_metric_loss_score\r\n",
    "print('default prophet mape', '=', sklearn_metric_loss_score('mape', prophet_y_pred, y_test))"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Predicted labels 0     370.450675\n",
      "1     371.177764\n",
      "2     372.229577\n",
      "3     373.419835\n",
      "4     373.914917\n",
      "5     373.406484\n",
      "6     372.053428\n",
      "7     370.149037\n",
      "8     368.566631\n",
      "9     368.646853\n",
      "10    369.863891\n",
      "11    371.135959\n",
      "Name: yhat, dtype: float64\n",
      "True labels          co2\n",
      "514  370.175\n",
      "515  371.325\n",
      "516  372.060\n",
      "517  372.775\n",
      "518  373.800\n",
      "519  373.060\n",
      "520  371.300\n",
      "521  369.425\n",
      "522  367.880\n",
      "523  368.050\n",
      "524  369.375\n",
      "525  371.020\n",
      "default prophet mape = 0.0011396920680673015\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Auto Arima"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# !pip install pmdarima"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "from pmdarima.arima import auto_arima\r\n",
    "import pandas as pd\r\n",
    "import time"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "X_train_arima = X_train.copy()\r\n",
    "X_train_arima.index = pd.to_datetime(X_train_arima['index'])\r\n",
    "X_train_arima = X_train_arima.drop('index', axis=1)\r\n",
    "X_train_arima = X_train_arima.rename(columns={'co2': 'y'})\r\n",
    "# use same search space as FLAML\r\n",
    "arima_model = auto_arima(X_train_arima, \r\n",
    "                         start_p=2, d=None, start_q=2, max_p=10, max_d=2, max_q=10, \r\n",
    "                         suppress_warnings=True, stepwise=False, seasonal=False, \r\n",
    "                         error_action='ignore', trace=True, n_fits=500)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      " ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=1638.009, Time=0.02 sec\n",
      " ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=1344.207, Time=0.10 sec\n",
      " ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=1222.286, Time=0.17 sec\n",
      " ARIMA(0,1,3)(0,0,0)[0] intercept   : AIC=1174.928, Time=0.22 sec\n",
      " ARIMA(0,1,4)(0,0,0)[0] intercept   : AIC=1188.947, Time=0.37 sec\n",
      " ARIMA(0,1,5)(0,0,0)[0] intercept   : AIC=1091.452, Time=0.46 sec\n",
      " ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=1298.693, Time=0.07 sec\n",
      " ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=1240.963, Time=0.15 sec\n",
      " ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=1196.535, Time=0.21 sec\n",
      " ARIMA(1,1,3)(0,0,0)[0] intercept   : AIC=1176.484, Time=0.31 sec\n",
      " ARIMA(1,1,4)(0,0,0)[0] intercept   : AIC=inf, Time=1.11 sec\n",
      " ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=1180.404, Time=0.11 sec\n",
      " ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=990.719, Time=0.32 sec\n",
      " ARIMA(2,1,2)(0,0,0)[0] intercept   : AIC=988.094, Time=0.48 sec\n",
      " ARIMA(2,1,3)(0,0,0)[0] intercept   : AIC=1140.469, Time=0.54 sec\n",
      " ARIMA(3,1,0)(0,0,0)[0] intercept   : AIC=1126.139, Time=0.29 sec\n",
      " ARIMA(3,1,1)(0,0,0)[0] intercept   : AIC=989.496, Time=0.71 sec\n",
      " ARIMA(3,1,2)(0,0,0)[0] intercept   : AIC=991.599, Time=0.89 sec\n",
      " ARIMA(4,1,0)(0,0,0)[0] intercept   : AIC=1125.025, Time=0.20 sec\n",
      " ARIMA(4,1,1)(0,0,0)[0] intercept   : AIC=988.660, Time=0.72 sec\n",
      " ARIMA(5,1,0)(0,0,0)[0] intercept   : AIC=1113.673, Time=0.20 sec\n",
      "\n",
      "Best model:  ARIMA(2,1,2)(0,0,0)[0] intercept\n",
      "Total fit time: 7.677 seconds\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "autoarima_y_pred = arima_model.predict(n_periods = 12)\r\n",
    "print('Predicted labels', y_pred)\r\n",
    "print('True labels', y_test)\r\n",
    "from flaml.ml import sklearn_metric_loss_score\r\n",
    "print('auto arima', '=', sklearn_metric_loss_score('mape', autoarima_y_pred, y_test))"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Predicted labels [370.543233   371.28354891 372.2267332  373.49227877 373.88691133\n",
      " 373.34103694 371.86609201 369.82045256 368.08845427 368.31840709\n",
      " 369.67730838 371.05530796]\n",
      "True labels          co2\n",
      "514  370.175\n",
      "515  371.325\n",
      "516  372.060\n",
      "517  372.775\n",
      "518  373.800\n",
      "519  373.060\n",
      "520  371.300\n",
      "521  369.425\n",
      "522  367.880\n",
      "523  368.050\n",
      "524  369.375\n",
      "525  371.020\n",
      "auto arima = 0.003201746906460404\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Auto SARIMA"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# !pip install pmdarima"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "from pmdarima.arima import auto_arima\r\n",
    "import pandas as pd\r\n",
    "import time"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "X_train_arima = X_train.copy()\r\n",
    "X_train_arima.index = pd.to_datetime(X_train_arima['index'])\r\n",
    "X_train_arima = X_train_arima.drop('index', axis=1)\r\n",
    "X_train_arima = X_train_arima.rename(columns={'co2': 'y'})\r\n",
    "# use same search space as FLAML\r\n",
    "arima_model = auto_arima(X_train_arima, \r\n",
    "                         start_p=2, d=None, start_q=2, max_p=10, max_d=2, max_q=10,\r\n",
    "                         start_P=1, D=None, start_Q=1, max_P=10, max_D=2, max_Q=10, m=12,\r\n",
    "                         suppress_warnings=True, stepwise=False, seasonal=True, \r\n",
    "                         error_action='ignore', trace=True, n_fits=50)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      " ARIMA(0,1,0)(0,0,0)[12] intercept   : AIC=1638.009, Time=0.03 sec\n",
      " ARIMA(0,1,0)(0,0,1)[12] intercept   : AIC=1238.943, Time=0.24 sec\n",
      " ARIMA(0,1,0)(0,0,2)[12] intercept   : AIC=1040.890, Time=0.41 sec\n",
      " ARIMA(0,1,0)(0,0,3)[12] intercept   : AIC=911.545, Time=1.12 sec\n",
      " ARIMA(0,1,0)(0,0,4)[12] intercept   : AIC=823.103, Time=2.17 sec\n",
      " ARIMA(0,1,0)(0,0,5)[12] intercept   : AIC=792.850, Time=3.83 sec\n",
      " ARIMA(0,1,0)(1,0,0)[12] intercept   : AIC=inf, Time=0.29 sec\n",
      " ARIMA(0,1,0)(1,0,1)[12] intercept   : AIC=inf, Time=1.09 sec\n",
      " ARIMA(0,1,0)(1,0,2)[12] intercept   : AIC=inf, Time=1.95 sec\n",
      " ARIMA(0,1,0)(1,0,3)[12] intercept   : AIC=442.078, Time=4.98 sec\n",
      " ARIMA(0,1,0)(1,0,4)[12] intercept   : AIC=inf, Time=7.63 sec\n",
      " ARIMA(0,1,0)(2,0,0)[12] intercept   : AIC=inf, Time=0.82 sec\n",
      " ARIMA(0,1,0)(2,0,1)[12] intercept   : AIC=inf, Time=1.83 sec\n",
      " ARIMA(0,1,0)(2,0,2)[12] intercept   : AIC=inf, Time=2.20 sec\n",
      " ARIMA(0,1,0)(2,0,3)[12] intercept   : AIC=427.410, Time=6.58 sec\n",
      " ARIMA(0,1,0)(3,0,0)[12] intercept   : AIC=inf, Time=2.77 sec\n",
      " ARIMA(0,1,0)(3,0,1)[12] intercept   : AIC=438.942, Time=3.45 sec\n",
      " ARIMA(0,1,0)(3,0,2)[12] intercept   : AIC=431.438, Time=5.52 sec\n",
      " ARIMA(0,1,0)(4,0,0)[12] intercept   : AIC=inf, Time=5.85 sec\n",
      " ARIMA(0,1,0)(4,0,1)[12] intercept   : AIC=430.317, Time=8.43 sec\n",
      " ARIMA(0,1,0)(5,0,0)[12] intercept   : AIC=inf, Time=12.20 sec\n",
      " ARIMA(0,1,1)(0,0,0)[12] intercept   : AIC=1344.207, Time=0.10 sec\n",
      " ARIMA(0,1,1)(0,0,1)[12] intercept   : AIC=1112.274, Time=0.28 sec\n",
      " ARIMA(0,1,1)(0,0,2)[12] intercept   : AIC=993.565, Time=0.56 sec\n",
      " ARIMA(0,1,1)(0,0,3)[12] intercept   : AIC=891.683, Time=1.83 sec\n",
      " ARIMA(0,1,1)(0,0,4)[12] intercept   : AIC=820.025, Time=3.45 sec\n",
      " ARIMA(0,1,1)(1,0,0)[12] intercept   : AIC=612.811, Time=0.48 sec\n",
      " ARIMA(0,1,1)(1,0,1)[12] intercept   : AIC=392.523, Time=1.06 sec\n",
      " ARIMA(0,1,1)(1,0,2)[12] intercept   : AIC=424.761, Time=2.34 sec\n",
      " ARIMA(0,1,1)(1,0,3)[12] intercept   : AIC=423.152, Time=5.78 sec\n",
      " ARIMA(0,1,1)(2,0,0)[12] intercept   : AIC=510.637, Time=1.20 sec\n",
      " ARIMA(0,1,1)(2,0,1)[12] intercept   : AIC=412.849, Time=2.22 sec\n",
      " ARIMA(0,1,1)(2,0,2)[12] intercept   : AIC=396.908, Time=2.52 sec\n",
      " ARIMA(0,1,1)(3,0,0)[12] intercept   : AIC=467.985, Time=3.81 sec\n",
      " ARIMA(0,1,1)(3,0,1)[12] intercept   : AIC=405.933, Time=6.55 sec\n",
      " ARIMA(0,1,1)(4,0,0)[12] intercept   : AIC=448.948, Time=5.47 sec\n",
      " ARIMA(0,1,2)(0,0,0)[12] intercept   : AIC=1222.286, Time=0.16 sec\n",
      " ARIMA(0,1,2)(0,0,1)[12] intercept   : AIC=1046.922, Time=0.27 sec\n",
      " ARIMA(0,1,2)(0,0,2)[12] intercept   : AIC=947.532, Time=0.69 sec\n",
      " ARIMA(0,1,2)(0,0,3)[12] intercept   : AIC=867.310, Time=1.82 sec\n",
      " ARIMA(0,1,2)(1,0,0)[12] intercept   : AIC=608.450, Time=0.55 sec\n",
      " ARIMA(0,1,2)(1,0,1)[12] intercept   : AIC=402.050, Time=1.26 sec\n",
      " ARIMA(0,1,2)(1,0,2)[12] intercept   : AIC=422.338, Time=2.51 sec\n",
      " ARIMA(0,1,2)(2,0,0)[12] intercept   : AIC=507.685, Time=1.49 sec\n",
      " ARIMA(0,1,2)(2,0,1)[12] intercept   : AIC=408.472, Time=3.02 sec\n",
      " ARIMA(0,1,2)(3,0,0)[12] intercept   : AIC=460.596, Time=5.35 sec\n",
      " ARIMA(0,1,3)(0,0,0)[12] intercept   : AIC=1174.928, Time=0.18 sec\n",
      " ARIMA(0,1,3)(0,0,1)[12] intercept   : AIC=1037.324, Time=0.42 sec\n",
      " ARIMA(0,1,3)(0,0,2)[12] intercept   : AIC=947.471, Time=1.02 sec\n",
      " ARIMA(0,1,3)(1,0,0)[12] intercept   : AIC=602.141, Time=0.73 sec\n",
      " ARIMA(0,1,3)(1,0,1)[12] intercept   : AIC=399.087, Time=1.92 sec\n",
      " ARIMA(0,1,3)(2,0,0)[12] intercept   : AIC=500.296, Time=1.92 sec\n",
      " ARIMA(0,1,4)(0,0,0)[12] intercept   : AIC=1188.947, Time=0.36 sec\n",
      " ARIMA(0,1,4)(0,0,1)[12] intercept   : AIC=999.240, Time=0.71 sec\n",
      " ARIMA(0,1,4)(1,0,0)[12] intercept   : AIC=604.133, Time=0.88 sec\n",
      " ARIMA(0,1,5)(0,0,0)[12] intercept   : AIC=1091.452, Time=0.50 sec\n",
      " ARIMA(1,1,0)(0,0,0)[12] intercept   : AIC=1298.693, Time=0.08 sec\n",
      " ARIMA(1,1,0)(0,0,1)[12] intercept   : AIC=1075.553, Time=0.26 sec\n",
      " ARIMA(1,1,0)(0,0,2)[12] intercept   : AIC=971.074, Time=0.58 sec\n",
      " ARIMA(1,1,0)(0,0,3)[12] intercept   : AIC=882.846, Time=2.20 sec\n",
      " ARIMA(1,1,0)(0,0,4)[12] intercept   : AIC=818.711, Time=3.59 sec\n",
      " ARIMA(1,1,0)(1,0,0)[12] intercept   : AIC=inf, Time=0.50 sec\n",
      " ARIMA(1,1,0)(1,0,1)[12] intercept   : AIC=400.766, Time=1.07 sec\n",
      " ARIMA(1,1,0)(1,0,2)[12] intercept   : AIC=423.718, Time=2.76 sec\n",
      " ARIMA(1,1,0)(1,0,3)[12] intercept   : AIC=428.842, Time=5.94 sec\n",
      " ARIMA(1,1,0)(2,0,0)[12] intercept   : AIC=inf, Time=1.41 sec\n",
      " ARIMA(1,1,0)(2,0,1)[12] intercept   : AIC=416.666, Time=2.17 sec\n",
      " ARIMA(1,1,0)(2,0,2)[12] intercept   : AIC=409.065, Time=2.83 sec\n",
      " ARIMA(1,1,0)(3,0,0)[12] intercept   : AIC=inf, Time=3.85 sec\n",
      " ARIMA(1,1,0)(3,0,1)[12] intercept   : AIC=403.682, Time=6.69 sec\n",
      " ARIMA(1,1,0)(4,0,0)[12] intercept   : AIC=inf, Time=7.60 sec\n",
      " ARIMA(1,1,1)(0,0,0)[12] intercept   : AIC=1240.963, Time=0.14 sec\n",
      " ARIMA(1,1,1)(0,0,1)[12] intercept   : AIC=1069.162, Time=0.37 sec\n",
      " ARIMA(1,1,1)(0,0,2)[12] intercept   : AIC=973.065, Time=0.94 sec\n",
      " ARIMA(1,1,1)(0,0,3)[12] intercept   : AIC=884.323, Time=3.38 sec\n",
      " ARIMA(1,1,1)(1,0,0)[12] intercept   : AIC=588.156, Time=1.15 sec\n",
      " ARIMA(1,1,1)(1,0,1)[12] intercept   : AIC=399.033, Time=1.21 sec\n",
      " ARIMA(1,1,1)(1,0,2)[12] intercept   : AIC=409.596, Time=3.22 sec\n",
      " ARIMA(1,1,1)(2,0,0)[12] intercept   : AIC=503.551, Time=1.60 sec\n",
      " ARIMA(1,1,1)(2,0,1)[12] intercept   : AIC=402.095, Time=2.40 sec\n",
      " ARIMA(1,1,1)(3,0,0)[12] intercept   : AIC=457.277, Time=5.79 sec\n",
      " ARIMA(1,1,2)(0,0,0)[12] intercept   : AIC=1196.535, Time=0.25 sec\n",
      " ARIMA(1,1,2)(0,0,1)[12] intercept   : AIC=1042.432, Time=0.35 sec\n",
      " ARIMA(1,1,2)(0,0,2)[12] intercept   : AIC=948.444, Time=0.95 sec\n",
      " ARIMA(1,1,2)(1,0,0)[12] intercept   : AIC=583.862, Time=1.14 sec\n",
      " ARIMA(1,1,2)(1,0,1)[12] intercept   : AIC=403.010, Time=1.36 sec\n",
      " ARIMA(1,1,2)(2,0,0)[12] intercept   : AIC=502.719, Time=2.87 sec\n",
      " ARIMA(1,1,3)(0,0,0)[12] intercept   : AIC=1176.484, Time=0.30 sec\n",
      " ARIMA(1,1,3)(0,0,1)[12] intercept   : AIC=1039.309, Time=0.65 sec\n",
      " ARIMA(1,1,3)(1,0,0)[12] intercept   : AIC=604.131, Time=0.79 sec\n",
      " ARIMA(1,1,4)(0,0,0)[12] intercept   : AIC=inf, Time=1.05 sec\n",
      " ARIMA(2,1,0)(0,0,0)[12] intercept   : AIC=1180.404, Time=0.10 sec\n",
      " ARIMA(2,1,0)(0,0,1)[12] intercept   : AIC=1058.115, Time=0.25 sec\n",
      " ARIMA(2,1,0)(0,0,2)[12] intercept   : AIC=973.051, Time=0.74 sec\n",
      " ARIMA(2,1,0)(0,0,3)[12] intercept   : AIC=883.377, Time=1.90 sec\n",
      " ARIMA(2,1,0)(1,0,0)[12] intercept   : AIC=inf, Time=0.43 sec\n",
      " ARIMA(2,1,0)(1,0,1)[12] intercept   : AIC=416.799, Time=1.05 sec\n",
      " ARIMA(2,1,0)(1,0,2)[12] intercept   : AIC=400.863, Time=2.36 sec\n",
      " ARIMA(2,1,0)(2,0,0)[12] intercept   : AIC=inf, Time=1.49 sec\n",
      " ARIMA(2,1,0)(2,0,1)[12] intercept   : AIC=400.859, Time=2.41 sec\n",
      " ARIMA(2,1,0)(3,0,0)[12] intercept   : AIC=inf, Time=4.49 sec\n",
      " ARIMA(2,1,1)(0,0,0)[12] intercept   : AIC=990.719, Time=0.26 sec\n",
      " ARIMA(2,1,1)(0,0,1)[12] intercept   : AIC=881.526, Time=0.73 sec\n",
      " ARIMA(2,1,1)(0,0,2)[12] intercept   : AIC=837.402, Time=2.20 sec\n",
      " ARIMA(2,1,1)(1,0,0)[12] intercept   : AIC=584.097, Time=1.56 sec\n",
      " ARIMA(2,1,1)(1,0,1)[12] intercept   : AIC=443.589, Time=1.83 sec\n",
      " ARIMA(2,1,1)(2,0,0)[12] intercept   : AIC=494.535, Time=2.78 sec\n",
      " ARIMA(2,1,2)(0,0,0)[12] intercept   : AIC=988.094, Time=0.48 sec\n",
      " ARIMA(2,1,2)(0,0,1)[12] intercept   : AIC=757.307, Time=1.35 sec\n",
      " ARIMA(2,1,2)(1,0,0)[12] intercept   : AIC=594.527, Time=2.10 sec\n",
      " ARIMA(2,1,3)(0,0,0)[12] intercept   : AIC=1140.469, Time=0.53 sec\n",
      " ARIMA(3,1,0)(0,0,0)[12] intercept   : AIC=1126.139, Time=0.30 sec\n",
      " ARIMA(3,1,0)(0,0,1)[12] intercept   : AIC=996.923, Time=0.36 sec\n",
      " ARIMA(3,1,0)(0,0,2)[12] intercept   : AIC=918.438, Time=0.87 sec\n",
      " ARIMA(3,1,0)(1,0,0)[12] intercept   : AIC=inf, Time=0.62 sec\n",
      " ARIMA(3,1,0)(1,0,1)[12] intercept   : AIC=406.333, Time=1.24 sec\n",
      " ARIMA(3,1,0)(2,0,0)[12] intercept   : AIC=inf, Time=2.16 sec\n",
      " ARIMA(3,1,1)(0,0,0)[12] intercept   : AIC=989.496, Time=0.80 sec\n",
      " ARIMA(3,1,1)(0,0,1)[12] intercept   : AIC=856.486, Time=1.45 sec\n",
      " ARIMA(3,1,1)(1,0,0)[12] intercept   : AIC=604.951, Time=0.76 sec\n",
      " ARIMA(3,1,2)(0,0,0)[12] intercept   : AIC=991.599, Time=0.86 sec\n",
      " ARIMA(4,1,0)(0,0,0)[12] intercept   : AIC=1125.025, Time=0.20 sec\n",
      " ARIMA(4,1,0)(0,0,1)[12] intercept   : AIC=987.621, Time=0.41 sec\n",
      " ARIMA(4,1,0)(1,0,0)[12] intercept   : AIC=inf, Time=0.83 sec\n",
      " ARIMA(4,1,1)(0,0,0)[12] intercept   : AIC=988.660, Time=0.74 sec\n",
      " ARIMA(5,1,0)(0,0,0)[12] intercept   : AIC=1113.673, Time=0.23 sec\n",
      "\n",
      "Best model:  ARIMA(0,1,1)(1,0,1)[12] intercept\n",
      "Total fit time: 249.429 seconds\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "autosarima_y_pred = arima_model.predict(n_periods = 12)\r\n",
    "print('Predicted labels', autosarima_y_pred)\r\n",
    "print('True labels', y_test)\r\n",
    "from flaml.ml import sklearn_metric_loss_score\r\n",
    "print('auto sarima', '=', sklearn_metric_loss_score('mape', autosarima_y_pred, y_test))"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Predicted labels [370.543233   371.28354891 372.2267332  373.49227877 373.88691133\n",
      " 373.34103694 371.86609201 369.82045256 368.08845427 368.31840709\n",
      " 369.67730838 371.05530796]\n",
      "True labels          co2\n",
      "514  370.175\n",
      "515  371.325\n",
      "516  372.060\n",
      "517  372.775\n",
      "518  373.800\n",
      "519  373.060\n",
      "520  371.300\n",
      "521  369.425\n",
      "522  367.880\n",
      "523  368.050\n",
      "524  369.375\n",
      "525  371.020\n",
      "auto sarima = 0.0007724244328789994\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# !pip install matplotlib"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "source": [
    "import matplotlib.pyplot as plt\r\n",
    "plt.plot(X_test, y_test, label='Actual level')\r\n",
    "plt.plot(X_test, flaml_y_pred, label='FLAML forecast')\r\n",
    "plt.plot(X_test, autoarima_y_pred, label='Auto ARIMA forecast')\r\n",
    "plt.plot(X_test, autosarima_y_pred, label='Auto SARIMA forecast')\r\n",
    "plt.xlabel('Date')\r\n",
    "plt.ylabel('CO2 Levels')\r\n",
    "plt.legend()"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2c8518e4580>"
      ]
     },
     "metadata": {},
     "execution_count": 79
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
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