code: def engle_granger_pval(stat: float, trend: str, num_x: int) -> float:
      """
      Asymptotic P-values for Engle-Granger t-tests
  
      Parameters
      ----------
      stat : float
          The test statistic
      trend : {"n", "c", "ct", "ctt"}
          The trend included in the model
      num_x : The number of cross-sectional regressors in the model.
          Must be between 1 and 12.
  
      Returns
      -------
      Series
          The critical values for 1, 5 and 10%
      """
      trends = ("n", "c", "ct", "ctt")
      if trend not in trends:
          valid = ",".join(trends)
          raise ValueError(f"Trend must by one of: {valid}")
      if not 1 <= num_x <= 12:
          raise ValueError(
              "The number of cross-sectional variables must be between 1 and "
              "12 (inclusive)"
          )
      key = (trend, num_x)
      if stat > TAU_MAX[key]:
          return 1.0
      elif stat < TAU_MIN[key]:
          return 0.0
      if stat > TAU_STAR[key]:
          params = np.array(LARGE_PARAMETERS[key])
      else:
          params = np.array(SMALL_PARAMETERS[key])
      order = params.shape[0]
      x = stat ** np.arange(order)
      return stats.norm().cdf(params @ x)
  
imports: from __future__ import annotations
  import numpy
  import pandas
  from scipy import stats
  from statsmodels.iolib.summary import Summary
  from statsmodels.iolib.table import SimpleTable
  from statsmodels.regression.linear_model import RegressionResults
  from arch.typing import ArrayLike1D, ArrayLike2D, Literal, UnitRootTrend
  from arch.unitroot._shared import ResidualCointegrationTestResult, _check_cointegrating_regression, _cross_section
  from arch.unitroot.critical_values.engle_granger import CV_PARAMETERS, LARGE_PARAMETERS, SMALL_PARAMETERS, TAU_MAX, TAU_MIN, TAU_STAR
  from arch.unitroot.unitroot import ADF, TREND_DESCRIPTION
label_desc: Use image node_id 3 for calling a global function with example usage: engle_granger_pval(stat, trend, num_x) and returns: stats, int, int