code: def grid_search_forecaster(
      forecaster,
      y: pd.Series,
      param_grid: dict,
      steps: int,
      metric: Union[str, Callable, list],
      initial_train_size: int,
      fixed_train_size: bool = True,
      gap: int = 0,
      allow_incomplete_fold: bool = True,
      exog: Optional[Union[pd.Series, pd.DataFrame]] = None,
      lags_grid: Optional[Union[list, dict]] = None,
      refit: Optional[Union[bool, int]] = False,
      return_best: bool = True,
      n_jobs: Optional[Union[int, str]] = "auto",
      verbose: bool = True,
      show_progress: bool = True,
  ) -> pd.DataFrame:
      """
      Exhaustive search over specified parameter values for a Forecaster object.
      Validation is done using time series backtesting.
  
      Parameters
      ----------
      forecaster : ForecasterAutoreg, ForecasterAutoregCustom, ForecasterAutoregDirect
          Forecaster model.
      y : pandas Series
          Training time series.
      param_grid : dict
          Dictionary with parameters names (`str`) as keys and lists of parameter
          settings to try as values.
      steps : int
          Number of steps to predict.
      metric : str, Callable, list
          Metric used to quantify the goodness of fit of the model.
  
          - If `string`: {'mean_squared_error', 'mean_absolute_error',
          'mean_absolute_percentage_error', 'mean_squared_log_error'}
          - If `Callable`: Function with arguments y_true, y_pred that returns
          a float.
          - If `list`: List containing multiple strings and/or Callables.
      initial_train_size : int
          Number of samples in the initial train split.
      fixed_train_size : bool, default `True`
          If True, train size doesn't increase but moves by `steps` in each iteration.
      gap : int, default `0`
          Number of samples to be excluded after the end of each training set and
          before the test set.
      allow_incomplete_fold : bool, default `True`
          Last fold is allowed to have a smaller number of samples than the
          `test_size`. If `False`, the last fold is excluded.
      exog : pandas Series, pandas DataFrame, default `None`
          Exogenous variable/s included as predictor/s. Must have the same
          number of observations as `y` and should be aligned so that y[i] is
          regressed on exog[i].
      lags_grid : list, dict, default `None`
          Lists of lags to try, containing int, lists, numpy ndarray, or range
          objects. If `dict`, the keys are used as labels in the `results`
          DataFrame, and the values are used as the lists of lags to try. Ignored
          if the forecaster is an instance of `ForecasterAutoregCustom` or
          `ForecasterAutoregMultiSeriesCustom`.
      refit : bool, int, default `False`
          Whether to re-fit the forecaster in each iteration. If `refit` is an integer,
          the Forecaster will be trained every that number of iterations.
      return_best : bool, default `True`
          Refit the `forecaster` using the best found parameters on the whole data.
      n_jobs : int, 'auto', default `'auto'`
          The number of jobs to run in parallel. If `-1`, then the number of jobs is
          set to the number of cores. If 'auto', `n_jobs` is set using the function
          skforecast.utils.select_n_jobs_backtesting.
          **New in version 0.9.0**
      verbose : bool, default `True`
          Print number of folds used for cv or backtesting.
      show_progress: bool, default `True`
          Whether to show a progress bar.
  
      Returns
      -------
      results : pandas DataFrame
          Results for each combination of parameters.
  
          - column lags: lags configuration for each iteration.
          - column params: parameters configuration for each iteration.
          - column metric: metric value estimated for each iteration.
          - additional n columns with param = value.
  
      """
  
      param_grid = list(ParameterGrid(param_grid))
  
      results = _evaluate_grid_hyperparameters(
          forecaster=forecaster,
          y=y,
          param_grid=param_grid,
          steps=steps,
          metric=metric,
          initial_train_size=initial_train_size,
          fixed_train_size=fixed_train_size,
          gap=gap,
          allow_incomplete_fold=allow_incomplete_fold,
          exog=exog,
          lags_grid=lags_grid,
          refit=refit,
          return_best=return_best,
          n_jobs=n_jobs,
          verbose=verbose,
          show_progress=show_progress,
      )
  
      return results
  
imports: from typing import Union, Tuple, Optional, Callable
  import numpy
  import pandas
  import warnings
  import logging
  from copy import deepcopy
  from joblib import Parallel, delayed, cpu_count
  from tqdm.auto import tqdm
  from sklearn.metrics import mean_squared_error, mean_absolute_error, mean_absolute_percentage_error, mean_squared_log_error
  from sklearn.model_selection import ParameterGrid
  from sklearn.model_selection import ParameterSampler
  import optuna
  from optuna.samplers import TPESampler, RandomSampler
  from ..exceptions import LongTrainingWarning
  from ..utils import check_backtesting_input
  from ..utils import initialize_lags_grid
  from ..utils import select_n_jobs_backtesting
label_desc: Use image node_id 5 for calling a global function with example usage: grid_search_forecaster(forecaster, y, param_grid, steps, metric, initial_train_size, fixed_train_size, gap, allow_incomplete_fold, exog, lags_grid, refit, return_best, n_jobs, verbose, show_progress) and returns: results