from scipy import optimize


def calc_shifted_ewm(series, alpha, adjust=True):
    return series.shift().ewm(alpha=alpha, adjust=adjust).mean()


def find_best_signal(series, adjust=False, eps=10e-5):

    def f(alpha):
        shifted_ewm = calc_shifted_ewm(series=series, alpha=min(max(alpha, 0), 1), adjust=adjust)
        corr = np.mean(np.power(series - shifted_ewm, 2))
        return corr

    res = optimize.differential_evolution(func=f, bounds=[(0 + eps, 1 - eps)])

    return calc_shifted_ewm(series=series, alpha=res['x'][0], adjust=adjust)

#############################################

roll = df.groupby(['entity', 'i_n_dow']).apply(lambda g: find_best_signal(g['target']))
df['i_n_optimized_ewm_by_entity_dow'] = roll.sort_index(level=['entity', 'time_stamp']).values