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.automl.seasonality_mixin import SeasonalityLayer
from merlion.models.forecast.sarima import Sarima

from ts_datasets.forecast import M4

logging.basicConfig(level=logging.DEBUG)

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.")

plotly not installed, so plotly visualizations will not work.
INFO:ts_datasets.forecast.m4:M4 Hourly dataset cannot be found from /Users/chenghao.liu/Documents/research-project/Merlion_backup/public_merlion/Merlion/data/M4.
M4 Hourly dataset will be downloaded from https://github.com/Mcompetitions/M4-methods/raw/master/Dataset/{}.csv.

INFO:ts_datasets.forecast.m4:Downloading https://github.com/Mcompetitions/M4-methods/raw/master/Dataset/M4-info.csv
INFO:ts_datasets.forecast.m4:Downloading https://github.com/Mcompetitions/M4-methods/raw/master/Dataset/Train/Hourly-train.csv
INFO:ts_datasets.forecast.m4:Downloading https://github.com/Mcompetitions/M4-methods/raw/master/Dataset/Test/Hourly-test.csv
100%|██████████| 414/414 [00:05<00:00, 72.11it/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
config1 = AutoSarimaConfig(max_forecast_steps=len(train_data), order=("auto", "auto", "auto"),
                           seasonal_order=("auto", "auto", "auto", "auto"), approximation=True, maxiter=5)
model1  = SeasonalityLayer(model = AutoSarima(model = Sarima(config1)))

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

# 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}")

INFO:merlion.models.forecast.base:Automatically detect the periodicity is 24
INFO:merlion.models.forecast.sarima:Seasonal difference order is 1
INFO:merlion.models.forecast.sarima:Difference order is 0
INFO:merlion.models.automl.autosarima:Seasonal difference order is 1
INFO:merlion.models.automl.autosarima:Difference order is 0
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(2,0,2)(0,1,1)[24] without constant

Full AutoSarima with approximation sMAPE is 3.4491

# Visualize the groud truth, actual forecast and confident 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
config2 = AutoSarimaConfig(max_forecast_steps=len(train_data), order=("auto", "auto", "auto"),
                           seasonal_order=("auto", "auto", "auto", "auto"), approximation=False, maxiter=5)
model2  = SeasonalityLayer(model = AutoSarima(model = Sarima(config2)))

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

# 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}")

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

Full AutoSarima without approximation sMAPE is 3.6991

# Visualize the groud truth, actual forecast and confident 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
config3 = AutoSarimaConfig(max_forecast_steps=len(train_data), order=(15, "auto", 5),
                           seasonal_order=(2, "auto", 1, "auto"), maxiter=5)
model3  = SeasonalityLayer(model = AutoSarima(model = Sarima(config3)))

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

# 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}")

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

Partial AutoSarima without approximation sMAPE is 3.5288

# Visualize the groud truth, actual forecast and confident 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(max_forecast_steps=len(train_data), order=("auto", "auto", "auto"),
                           seasonal_order=("auto", "auto", "auto", "auto"), maxiter=5)
model4  = SeasonalityLayer(model = AutoSarima(model = Sarima(config4)))

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

# 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}")

INFO:merlion.models.forecast.base:Automatically detect the periodicity is 24
INFO:merlion.models.forecast.sarima:Seasonal difference order is 1
INFO:merlion.models.forecast.sarima:Difference order is 0
INFO:merlion.models.automl.autosarima:Seasonal difference order is 1
INFO:merlion.models.automl.autosarima:Difference order is 0
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(1,0,5)(0,1,2)[24] without constant

AutoSarima without enforcing stationarity and invertibility sMAPE is 3.4972