def factor_rank_autocorrelation(factor_data, period=1):
    """
    Computes autocorrelation of mean factor ranks in specified time spans.
    We must compare period to period factor ranks rather than factor values
    to account for systematic shifts in the factor values of all names or names
    within a group. This metric is useful for measuring the turnover of a
    factor. If the value of a factor for each name changes randomly from period
    to period, we'd expect an autocorrelation of 0.

    Parameters
    ----------
    factor_data : pd.DataFrame - MultiIndex
        A MultiIndex DataFrame indexed by date (level 0) and asset (level 1),
        containing the values for a single alpha factor, forward returns for
        each period, the factor quantile/bin that factor value belongs to, and
        (optionally) the group the asset belongs to.
        - See full explanation in utils.get_clean_factor_and_forward_returns
    period: string or int, optional
        Period over which to calculate the turnover. If it is a string it must
        follow pandas.Timedelta constructor format (e.g. '1 days', '1D', '30m',
        '3h', '1D1h', etc).
    Returns
    -------
    autocorr : pd.Series
        Rolling 1 period (defined by time_rule) autocorrelation of
        factor values.

    """

    grouper = [factor_data.index.get_level_values('date')]

    ranks = factor_data.groupby(grouper)['factor'].rank()

    asset_factor_rank = ranks.reset_index().pivot(index='date',
                                                  columns='asset',
                                                  values='factor')

    if isinstance(period, int):
        asset_shifted = asset_factor_rank.shift(period)
    else:
        shifted_idx = utils.add_custom_calendar_timedelta(
                asset_factor_rank.index, -pd.Timedelta(period),
                factor_data.index.levels[0].freq)
        asset_shifted = asset_factor_rank.reindex(shifted_idx)
        asset_shifted.index = asset_factor_rank.index

    autocorr = asset_factor_rank.corrwith(asset_shifted, axis=1)
    autocorr.name = period
    return autocorr
Computes autocorrelation of mean factor ranks in specified time spans.
    We must compare period to period factor ranks rather than factor values
    to account for systematic shifts in the factor values of all names or names
    within a group. This metric is useful for measuring the turnover of a
    factor. If the value of a factor for each name changes randomly from period
    to period, we'd expect an autocorrelation of 0.

    Parameters
    ----------
    factor_data : pd.DataFrame - MultiIndex
        A MultiIndex DataFrame indexed by date (level 0) and asset (level 1),
        containing the values for a single alpha factor, forward returns for
        each period, the factor quantile/bin that factor value belongs to, and
        (optionally) the group the asset belongs to.
        - See full explanation in utils.get_clean_factor_and_forward_returns
    period: string or int, optional
        Period over which to calculate the turnover. If it is a string it must
        follow pandas.Timedelta constructor format (e.g. '1 days', '1D', '30m',
        '3h', '1D1h', etc).
    Returns
    -------
    autocorr : pd.Series
        Rolling 1 period (defined by time_rule) autocorrelation of
        factor values.