code: def exog_format(request):
      xtyp, shape, full = request.param
      rng = RandomState(123456)
      x_fcast = rng.standard_normal(shape)
      orig = x_fcast.copy()
      nobs = SP500.shape[0]
      if full:
          if x_fcast.ndim == 2:
              _x = np.full((nobs, shape[1]), np.nan)
              _x[-1:] = x_fcast
              x_fcast = _x
          elif x_fcast.ndim == 3:
              _x = np.full((shape[0], nobs, shape[-1]), np.nan)
              _x[:, -1:] = x_fcast
              x_fcast = _x
          else:
              # No full 1d
              return None, None
      if xtyp == "pandas":
          if x_fcast.ndim == 3:
              return None, None
          if x_fcast.ndim == 1:
              x_fcast = pd.Series(x_fcast)
          else:
              x_fcast = pd.DataFrame(x_fcast)
          x_fcast.index = SP500.index[-x_fcast.shape[0] :]
      elif xtyp == "dict":
          if x_fcast.ndim == 3:
              keys = [f"x{i}" for i in range(1, x_fcast.shape[0] + 1)]
              x_fcast = {k: x_fcast[i] for i, k in enumerate(keys)}
          else:
              x_fcast = {"x1": x_fcast}
      return x_fcast, orig
  
imports: import datetime
  from itertools import product
  import numpy
  from numpy.random import RandomState
  from numpy.testing import assert_allclose
  import pandas
  from pandas.testing import assert_frame_equal
  import pytest
  from arch.data import sp500
  from arch.tests.univariate.test_variance_forecasting import preserved_state
  from arch.univariate import APARCH, ARX, EGARCH, FIGARCH, GARCH, HARCH, HARX, ConstantMean, ConstantVariance, EWMAVariance, MIDASHyperbolic, RiskMetrics2006, ZeroMean, arch_model
  from arch.univariate.mean import _ar_forecast, _ar_to_impulse
label_desc: Use image node_id 6 for calling a global function with example usage: exog_format(request) and returns: x_fcast,  orig, None,  None, None,  None