Some models create internal representations of the series that can be useful for other models to use as inputs. One example is the MSTL model, which decomposes the series into trend and seasonal components. This guide shows you how to use the mstl_decomposition function to extract those features for training and then use their future values for inference.

from functools import partial

import pandas as pd
import statsforecast
from statsforecast import StatsForecast
from statsforecast.feature_engineering import mstl_decomposition
from statsforecast.models import ARIMA, MSTL
from utilsforecast.evaluation import evaluate
from utilsforecast.losses import smape, mase

df = pd.read_parquet('https://datasets-nixtla.s3.amazonaws.com/m4-hourly.parquet')
uids = df['unique_id'].unique()[:10]
df = df[df['unique_id'].isin(uids)]
df.head()
unique_iddsy
0H11605.0
1H12586.0
2H13586.0
3H14559.0
4H15511.0

Suppose that you want to use an ARIMA model to forecast your series but you want to incorporate the trend and seasonal components from the MSTL model as external regressors. You can define the MSTL model to use and then provide it to the mstl_decomposition function.

freq = 1
season_length = 24
horizon = 2 * season_length
valid = df.groupby('unique_id').tail(horizon)
train = df.drop(valid.index)
model = MSTL(season_length=24)
transformed_df, X_df = mstl_decomposition(train, model=model, freq=freq, h=horizon)

This generates the dataframe that we should use for training (with the trend and seasonal columns added), as well as the dataframe we should use to forecast.

transformed_df.head()
unique_iddsytrendseasonal
0H11605.0502.872910131.419934
1H12586.0507.87345693.100015
2H13586.0512.82253382.155386
3H14559.0517.71748142.412749
4H15511.0522.555849-11.401890
X_df.head()
unique_iddstrendseasonal
0H1701643.801348-29.189627
1H1702644.328207-99.680432
2H1703644.749693-141.169014
3H1704645.086883-173.325625
4H1705645.356634-195.862530

We can now train our ARIMA models and compute our forecasts.

sf = StatsForecast(
    models=[ARIMA(order=(1, 0, 1), season_length=season_length)],
    freq=freq
)
preds = sf.forecast(h=horizon, df=transformed_df, X_df=X_df)
preds.head()
unique_iddsARIMA
0H1701612.737668
1H1702542.851796
2H1703501.931839
3H1704470.248289
4H1705448.115839

We can now evaluate the performance.

def compute_evaluation(preds):
    full = preds.merge(valid, on=['unique_id', 'ds'])
    mase24 = partial(mase, seasonality=24)
    res = evaluate(full, metrics=[smape, mase24], train_df=train).groupby('metric')['ARIMA'].mean()
    res_smape = '{:.1%}'.format(res['smape'])
    res_mase = '{:.1f}'.format(res['mase'])
    return pd.Series({'mase': res_mase, 'smape': res_smape})

compute_evaluation(preds)

mase      1.0
smape    3.9%
dtype: object

And compare this with just using the series values.

preds_noexog = sf.forecast(h=horizon, df=train)
compute_evaluation(preds_noexog)

mase      2.3
smape    7.7%
dtype: object