Tutorial for AutoSARIMA Forecasting Model

This notebook provides an advanced example on how to use the Auto Sarima forecasting model.

AutoSARIMA runs in 4 settings: 1. Full AutoSARIMA with approximation 2. Full AutoSARIMA without approximation 3. Partial AutoSARIMA (Predefined AR, MA, Seasonal AR, Seasonal MA hyper-parameters) 4. Autosarima without enforcing stationarity and invertibility (this is the default setting)

Example codes are provided for both cases below.

Prepare dataset

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from scipy.stats import norm
import logging

from merlion.utils.time_series import TimeSeries
from merlion.evaluate.forecast import ForecastMetric
from merlion.models.automl.autosarima import AutoSarima, AutoSarimaConfig
from merlion.models.forecast.sarima import Sarima

from ts_datasets.forecast import M4

logging.basicConfig(level=logging.INFO)

time_series, metadata = M4("Hourly")[0]
train_data = TimeSeries.from_pd(time_series[metadata.trainval])
test_data = TimeSeries.from_pd(time_series[~metadata.trainval])

# Visualize the time series and draw a dotted line to indicate the train/test split
fig = plt.figure(figsize=(10, 6))
ax = fig.add_subplot(111)
ax.plot(time_series)
ax.axvline(metadata[metadata.trainval].index[-1], ls="--", lw="2", c="k")
plt.show()

# Print the length of training data and test data
print(f"{len(train_data)} points in train split, "
      f"{len(test_data)} points in test split.")

100%|██████████| 414/414 [00:00<00:00, 650.30it/s]

700 points in train split, 48 points in test split.

Train a full AutoSarima model with approximation (suggested)

# Specify the configuration of AutoSarima with approximation
#
# p, q, P, Q refer to the AR, MA, seasonal AR, and seasonal MA params, so
# auto_pqPQ=True (default) means select them automatically
#
# d is the difference order, and D is the seasonal difference order, so
# auto_d=True (default) and auto_D=True (default) means select them automatically
#
# auto_seasonality=True (default) means to automatically select the seasonality
config1 = AutoSarimaConfig(auto_pqPQ=True, auto_d=True, auto_D=True, auto_seasonality=True,
                           approximation=True, maxiter=5)
model1  = AutoSarima(config1)

# Model training
train_pred, train_err = model1.train(
    train_data, train_config={"enforce_stationarity": True,"enforce_invertibility": True})

INFO:merlion.models.automl.seasonality:Automatically detect the periodicity is 24
INFO:merlion.models.automl.autosarima:Seasonal difference order is 1
INFO:merlion.models.automl.autosarima:Difference order is 0
INFO:merlion.models.automl.autosarima:Fitting models using approximations(approx_iter is 1) to speed things up
INFO:merlion.models.automl.autosarima:Best model:  SARIMA(2,0,3)(1,1,1)[24] without constant

# Model forecasting
forecast1, stderr1 = model1.forecast(len(test_data))

# Model evaluation
smape1 = ForecastMetric.sMAPE.value(ground_truth=test_data, predict=forecast1)
print(f"Full AutoSarima with approximation sMAPE is {smape1:.4f}")

Full AutoSarima with approximation sMAPE is 3.4736

# Visualize the groud truth, actual forecast and confidence interval
fig, ax = model1.plot_forecast(time_series=test_data, plot_forecast_uncertainty=True)
plt.show()

Train a full AutoSarima model without approximation

# Specify the configuration of full AutoSarima without approximation
# Note that the default values of all the auto_* parameters are True
config2 = AutoSarimaConfig(approximation=False, maxiter=5)
model2  = AutoSarima(config2)

# Model training
train_pred, train_err = model2.train(
    train_data, train_config={"enforce_stationarity": True,"enforce_invertibility": True})

INFO:merlion.models.automl.seasonality:Automatically detect the periodicity is 24
INFO:merlion.models.automl.autosarima:Seasonal difference order is 1
INFO:merlion.models.automl.autosarima:Difference order is 0
INFO:merlion.models.automl.autosarima:Best model:  SARIMA(2,0,3)(1,1,1)[24] without constant

# Model forecasting
forecast2, stderr2 = model2.forecast(len(test_data))

# Model evaluation
smape2 = ForecastMetric.sMAPE.value(ground_truth=test_data, predict=forecast2)
print(f"Full AutoSarima without approximation sMAPE is {smape2:.4f}")

Full AutoSarima without approximation sMAPE is 3.6991

# Visualize the groud truth, actual forecast and confidence interval
fig, ax = model2.plot_forecast(time_series=test_data, plot_forecast_uncertainty=True)
plt.show()

Train a partial autosarima model

Here, the user has pre-defined the AR, MA, Seasonal AR, and Seasonal MA hyper-parameters.

# Specify the configuration of partial AutoSarima
# We explicitly specify values of p, q, P, Q in the order and seasonal order,
# and we set auto_pqPQ=False.
# Because auto_d=True, auto_D=True, and auto_seasonality=True by default, we
# can specify arbitrary values for them in the order and seasonal order (e.g. "auto")
config3 = AutoSarimaConfig(auto_pqPQ=False, order=(15, "auto", 5),
                           seasonal_order=(2, "auto", 1, "auto"), maxiter=5)
model3  = AutoSarima(config3)

# Model training
train_pred, train_err = model3.train(
    train_data, train_config={"enforce_stationarity": True,"enforce_invertibility": True})

INFO:merlion.models.automl.seasonality:Automatically detect the periodicity is 24
INFO:merlion.models.automl.autosarima:Seasonal difference order is 1
INFO:merlion.models.automl.autosarima:Difference order is 0

# Model forecasting
forecast3, stderr3 = model3.forecast(len(test_data))

# Model evaluation
smape3 = ForecastMetric.sMAPE.value(ground_truth=test_data, predict=forecast3)
print(f"Partial AutoSarima without approximation sMAPE is {smape3:.4f}")

Partial AutoSarima without approximation sMAPE is 3.5288

# Visualize the groud truth, actual forecast and confidence interval
fig, ax = model3.plot_forecast(time_series=test_data, plot_forecast_uncertainty=True)
plt.show()

Train without enforcing stationarity and invertibility (default)

# Specify the configuration of AutoSarima without enforcing stationarity and invertibility
config4 = AutoSarimaConfig(approximation=True, maxiter=5)
model4  = AutoSarima(config4)

# Model training
train_pred, train_err = model4.train(
    train_data, train_config={"enforce_stationarity": False,"enforce_invertibility": False})

INFO:merlion.models.automl.seasonality:Automatically detect the periodicity is 24
INFO:merlion.models.automl.autosarima:Seasonal difference order is 1
INFO:merlion.models.automl.autosarima:Difference order is 0
INFO:merlion.models.automl.autosarima:Fitting models using approximations(approx_iter is 1) to speed things up
INFO:merlion.models.automl.autosarima:Best model:  SARIMA(5,0,1)(2,1,0)[24] without constant

# Model forecasting
forecast4, stderr4 = model4.forecast(len(test_data))

# Model evaluation
smape4 = ForecastMetric.sMAPE.value(ground_truth=test_data, predict=forecast4)
print(f"AutoSarima without enforcing stationarity and invertibility sMAPE is {smape4:.4f}")

AutoSarima without enforcing stationarity and invertibility sMAPE is 4.2063

# Visualize the groud truth, actual forecast and confidence interval
fig, ax = model4.plot_forecast(time_series=test_data, plot_forecast_uncertainty=True)
plt.show()