def METHOD_NAME(x: pd.Series, min_value: float = 0.1) -> pd.Series:
    """
    >>> import datetime
    >>> from syscore.pandas.pdutils import create_arbitrary_pdseries
    >>> s1=create_arbitrary_pdseries([1,2,3,-1,-2,-3], date_start = datetime.datetime(2000,1,1))
    >>> apply_abs_min(s1, 2)
    2000-01-03    2
    2000-01-04    2
    2000-01-05    3
    2000-01-06   -2
    2000-01-07   -2
    2000-01-10   -3
    Freq: B, dtype: int64
    """
    ## Could also use clip but no quicker and this is more intuitive
    x[(x < min_value) & (x > 0)] = min_value
    x[(x > -min_value) & (x < 0)] = -min_value
    return x