code: def _coerce_to_period(x, freq=None):
      """Coerce pandas time index to a alternative pandas time index.
  
      This coerces pd.Timestamp to pd.Period or pd.DatetimeIndex to
      pd.PeriodIndex, because pd.Period and pd.PeriodIndex allow more reliable
      arithmetic operations with time indices.
  
      Parameters
      ----------
      x : pandas Index or index element
          pandas Index to convert.
      freq : pandas frequency string
  
      Returns
      -------
      index : pd.Period or pd.PeriodIndex
          Index or index element coerced to period based format.
      """
      if isinstance(x, pd.Timestamp) and freq is None:
          freq = x.freq
          raise ValueError(
              "_coerce_to_period requires freq argument to be passed if x is pd.Timestamp"
          )
      try:
          return x.to_period(freq)
      except (ValueError, AttributeError) as e:
          msg = str(e)
          if "Invalid frequency" in msg or "_period_dtype_code" in msg:
              raise ValueError(
                  "Invalid frequency. Please select a frequency that can "
                  "be converted to a regular `pd.PeriodIndex`. For other "
                  "frequencies, basic arithmetic operation to compute "
                  "durations currently do not work reliably."
              )
          else:
              raise
  
imports: from functools import lru_cache
  from typing import Optional, Union
  import numpy
  import pandas
  from pandas.tseries.frequencies import to_offset
  from sktime.utils.datetime import _coerce_duration_to_int
  from sktime.utils.validation import array_is_int, array_is_timedelta_or_date_offset, is_array, is_int, is_timedelta_or_date_offset
  from sktime.utils.validation._dependencies import _check_soft_dependencies
  from sktime.utils.validation.series import VALID_INDEX_TYPES, is_in_valid_absolute_index_types, is_in_valid_index_types, is_in_valid_relative_index_types, is_integer_index
label_desc: Use image node_id 8 for calling a global function with example usage: _coerce_to_period(x, freq) and returns: x