def msse(
    df: DFType,
    models: List[str],
    seasonality: int,
    train_df: DFType,
    id_col: str = "unique_id",
    target_col: str = "y",
) -> DFType:
    """Mean Squared Scaled Error (MSSE)

    MSSE measures the relative prediction
    accuracy of a forecasting method by comparinng the mean squared errors
    of the prediction and the observed value against the mean
    squared errors of the seasonal naive model.

    Parameters
    ----------
    df : pandas or polars DataFrame
        Input dataframe with id, actuals and predictions.
    models : list of str
        Columns that identify the models predictions.
    seasonality : int
        Main frequency of the time series;
        Hourly 24, Daily 7, Weekly 52, Monthly 12, Quarterly 4, Yearly 1.
    train_df : pandas or polars DataFrame
        Training dataframe with id and actual values. Must be sorted by time.
    id_col : str (default='unique_id')
        Column that identifies each serie.
    target_col : str (default='y')
        Column that contains the target.

    Returns
    -------
    pandas or polars Dataframe
        dataframe with one row per id and one column per model.

    References
    ----------
    [1] https://robjhyndman.com/papers/mase.pdf
    """
    mean_sq_err = mse(df, models, id_col, target_col)
    if isinstance(train_df, pd.DataFrame):
        mean_sq_err = mean_sq_err.set_index(id_col)
        # assume train_df is sorted
        lagged = train_df.groupby(id_col, observed=True)[target_col].shift(seasonality)
        scale = train_df[target_col].sub(lagged).pow(2)
        scale = scale.groupby(train_df[id_col], observed=True).mean()
        res = mean_sq_err.div(_zero_to_nan(scale), axis=0).fillna(0)
        res.index.name = id_col
        res = res.reset_index()
    else:
        # assume train_df is sorted
        lagged = pl.col(target_col).shift(seasonality).over(id_col)
        scale_expr = pl.col(target_col).sub(lagged).pow(2).alias("scale")
        scale = train_df.select([id_col, scale_expr])
        scale = ufp.group_by(scale, id_col).mean()
        scale = scale.with_columns(_zero_to_nan(pl.col("scale")))

        def gen_expr(model):
            return pl.col(model).truediv(pl.col("scale")).fill_nan(0).alias(model)

        full_df = mean_sq_err.join(scale, on=id_col, how="left")
        res = _pl_agg_expr(full_df, models, id_col, gen_expr)
    return res