I am trying to use Holt-winters Triple Exponential Smoothing technique on a univariate data.
When I am trying to set trend and seasonality component as multiplicative it outputs ‘NAN’ after 12 data points.
This is what I am doing
.plot(figsize=(12,6)).autoscale(axis=’x’,tight=True)

data['TES_12_mul'] = (ExponentialSmoothing(data['auth_rate'],trend='mul',seasonal='mul',seasonal_periods=12).fit().fittedvalues)

This is the output that I get

auth_rate   TES_12_mul
date        
2021-01-01  0.822201    0.000000
2021-02-01  0.845884    0.845884
2021-03-01  0.868405    0.868405
2021-04-01  0.866245    0.866245
2021-05-01  0.861446    0.861446
2021-06-01  0.859356    0.859356
2021-07-01  0.864788    0.864788
2021-08-01  0.868941    0.868941
2021-09-01  0.875224    0.875224
2021-10-01  0.868509    0.868509
2021-11-01  0.859725    0.859725
2021-12-01  0.842220    0.842220
2022-01-01  0.846683    NaN
2022-02-01  0.839865    NaN
2022-03-01  0.829573    NaN
2022-04-01  0.842664    NaN
2022-05-01  0.853426    NaN

This issue seems to go away when I set additive trend and seasonality

data['TES_12_add'] = (ExponentialSmoothing(data['auth_rate'],trend='add',seasonal='add',seasonal_periods=12)
                                            .fit().fittedvalues)
               auth_rate    TES_12_add
    date        
    2021-01-01  0.822201    0.822203
    2021-02-01  0.845884    0.845884
    2021-03-01  0.868405    0.868404
    2021-04-01  0.866245    0.866244
    2021-05-01  0.861446    0.861447
    2021-06-01  0.859356    0.859355
    2021-07-01  0.864788    0.864788
    2021-08-01  0.868941    0.868941
    2021-09-01  0.875224    0.875224
    2021-10-01  0.868509    0.868509
    2021-11-01  0.859725    0.859725
    2021-12-01  0.842220    0.842220
    2022-01-01  0.846683    0.822203
    2022-02-01  0.839865    0.871654
    2022-03-01  0.829573    0.862000
    2022-04-01  0.842664    0.825321
    2022-05-01  0.853426    0.836687

Why is this difference happening?