def METHOD_NAME(time_window):
    in_df = pd.DataFrame(data=[10, 95, 85], columns=['Feature_1'])
    out_df = deepcopy(in_df)
    for c in in_df.columns: out_df[c] = out_df[c].rolling(window=int(time_window), win_type='gaussian', center=True).mean(std=5).fillna(out_df[c]).abs().astype(int)
    if time_window == 1: assert out_df.equals(in_df)
    else: assert out_df.equals(pd.DataFrame(data=[10, 63, 85], columns=['Feature_1']))