.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "_examples\forecasting\plot_arima_search.py"
.. LINE NUMBERS ARE GIVEN BELOW.
.. only:: html
.. note::
:class: sphx-glr-download-link-note
:ref:`Go to the end <sphx_glr_download__examples_forecasting_plot_arima_search.py>`
to download the full example code
.. rst-class:: sphx-glr-example-title
.. _sphx_glr__examples_forecasting_plot_arima_search.py:
ARIMA - Search
---------------------------
.. GENERATED FROM PYTHON SOURCE LINES 6-115
.. image-sg:: /_examples/forecasting/images/sphx_glr_plot_arima_search_001.png
:alt: Non-dynamic predictions for ARIMA
:srcset: /_examples/forecasting/images/sphx_glr_plot_arima_search_001.png
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
.. code-block:: none
4/128. ARIMA(0, 1, 0) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
6/128. ARIMA(2, 2, 2) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
8/128. ARIMA(2, 1, 0) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
10/128. ARIMA(0, 1, 3) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
12/128. ARIMA(0, 3, 0) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
14/128. ARIMA(2, 1, 3) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
16/128. ARIMA(0, 3, 3) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
18/128. ARIMA(3, 2, 1) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
20/128. ARIMA(1, 2, 2) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
22/128. ARIMA(1, 3, 3) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
24/128. ARIMA(3, 1, 2) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
26/128. ARIMA(1, 3, 0) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
28/128. ARIMA(3, 3, 2) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
32/128. ARIMA(2, 3, 0) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
34/128. ARIMA(0, 2, 1) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
38/128. ARIMA(2, 3, 3) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
40/128. ARIMA(1, 1, 0) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
44/128. ARIMA(1, 1, 3) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
50/128. ARIMA(2, 1, 2) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
52/128. ARIMA(2, 2, 1) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
54/128. ARIMA(0, 1, 2) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
56/128. ARIMA(0, 3, 2) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
58/128. ARIMA(3, 1, 1) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
60/128. ARIMA(3, 2, 0) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
62/128. ARIMA(1, 2, 1) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
66/128. ARIMA(1, 3, 2) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
68/128. ARIMA(3, 2, 3) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
70/128. ARIMA(3, 3, 1) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
74/128. ARIMA(0, 2, 0) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
78/128. ARIMA(2, 3, 2) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
80/128. ARIMA(0, 2, 3) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
82/128. ARIMA(1, 1, 2) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
94/128. ARIMA(2, 2, 0) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
96/128. ARIMA(0, 1, 1) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
98/128. ARIMA(2, 2, 3) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
100/128. ARIMA(2, 1, 1) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
102/128. ARIMA(0, 3, 1) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
104/128. ARIMA(1, 2, 0) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
106/128. ARIMA(3, 1, 3) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
108/128. ARIMA(1, 3, 1) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
110/128. ARIMA(1, 2, 3) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
112/128. ARIMA(3, 1, 0) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
114/128. ARIMA(3, 2, 2) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
116/128. ARIMA(3, 3, 3) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
118/128. ARIMA(3, 3, 0) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
122/128. ARIMA(2, 3, 1) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
124/128. ARIMA(0, 2, 2) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
128/128. ARIMA(1, 1, 1) [c, False] ... failed: In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.
Summary:
arima-order arima-trend arima-aic arima-bic
0 (0, 2, 2) n 764.0096 771.0797
1 (1, 2, 1) n 765.0853 772.1555
2 (1, 1, 0) n 770.2782 775.0171
3 (0, 1, 1) n 770.4979 775.2368
4 (0, 2, 3) n 765.991 775.4179
.. ... ... ... ...
62 (0, 0, 1) c 937.348 944.4941
63 (0, 0, 2) n 1008.9601 1016.1062
64 (0, 0, 0) c 1014.6352 1019.3993
65 (0, 0, 1) n 1076.0548 1080.8188
66 (0, 0, 0) n 1173.6025 1175.9846
[67 rows x 4 columns]
0. Estimator (bic=771.08): ARIMA(0, 2, 2) [n, False]
1. Estimator (bic=772.16): ARIMA(1, 2, 1) [n, False]
2. Estimator (bic=775.02): ARIMA(1, 1, 0) [n, False]
3. Estimator (bic=775.24): ARIMA(0, 1, 1) [n, False]
4. Estimator (bic=775.42): ARIMA(0, 2, 3) [n, False]
5. Estimator (bic=775.42): ARIMA(1, 2, 2) [n, False]
6. Estimator (bic=775.53): ARIMA(2, 2, 1) [n, False]
7. Estimator (bic=776.41): ARIMA(0, 3, 3) [n, False]
8. Estimator (bic=776.77): ARIMA(0, 2, 1) [n, False]
|
.. code-block:: default
:lineno-start: 6
# Import.
import sys
import warnings
import pandas as pd
import matplotlib as mpl
import matplotlib.pyplot as plt
# Import ARIMA from statsmodels.
from statsmodels.tsa.arima.model import ARIMA
# import weights.
from pyamr.datasets.load import make_timeseries
from pyamr.core.regression.arima import ARIMAWrapper
# Filter warnings
warnings.simplefilter(action='ignore', category=FutureWarning)
# ----------------------------
# set basic configuration
# ----------------------------
# Matplotlib options
mpl.rc('legend', fontsize=6)
mpl.rc('xtick', labelsize=6)
mpl.rc('ytick', labelsize=6)
# Set pandas configuration.
pd.set_option('display.max_colwidth', 14)
pd.set_option('display.width', 150)
pd.set_option('display.precision', 4)
# ----------------------------
# create data
# ----------------------------
# Create timeseries data
x, y, f = make_timeseries()
# Create exogenous variable
exog = x
# Variables.
s, e = 50, 120
# -------------------------------
# create arima model
# -------------------------------
# This example shows how to use auto to find the best overall model using
# a particular seletion criteria. It also demonstrates how to plot the
# resulting data for visualization purposes. Note that it only prints
# the top best classifier according to the information criteria.
# Find the best arima model (bruteforce).
models, best = ARIMAWrapper(estimator=ARIMA) \
.auto(endog=y[:80], ic='bic', max_ar=3,
max_ma=3, max_d=3, return_fits=True)
# Sort the list (from lower to upper)
models.sort(key=lambda x: x.bic, reverse=False)
# Summary
summary = ARIMAWrapper().from_list_dataframe(models)
# Show summary
print("\nSummary:")
print(summary[['arima-order',
'arima-trend',
'arima-aic',
'arima-bic']])
# -------------------------------
# plot results
# -------------------------------
# Create figure
fig, axes = plt.subplots(3,3, figsize=(10,6))
axes = axes.flatten()
# Loop for the selected models
for i,estimator in enumerate(models[:9]):
# Show information
print("%2d. Estimator (bic=%.2f): %s " % \
(i, estimator.bic, estimator._identifier()))
# Get the predictions
preds = estimator.get_prediction(start=s, end=e, dynamic=False)
# Plot truth values.
axes[i].plot(y, color='#A6CEE3', alpha=0.5, marker='o',
markeredgecolor='k', markeredgewidth=0.5,
markersize=5, linewidth=0.75, label='Observed')
# Plot forecasted values.
axes[i].plot(preds[0,:], preds[1,:], color='#FF0000', alpha=1.00,
linewidth=2.0, label=estimator._identifier())
# Plot the confidence intervals.
axes[i].fill_between(preds[0,:], preds[2,:],
preds[3,:],
color='#FF0000',
alpha=0.25)
# Configure axes
axes[i].legend(loc=3)
axes[i].grid(True, linestyle='--', linewidth=0.25)
# Set superior title
plt.suptitle("Non-dynamic predictions for ARIMA")
# Show
plt.show()
.. rst-class:: sphx-glr-timing
**Total running time of the script:** ( 0 minutes 9.920 seconds)
.. _sphx_glr_download__examples_forecasting_plot_arima_search.py:
.. only:: html
.. container:: sphx-glr-footer sphx-glr-footer-example
.. container:: sphx-glr-download sphx-glr-download-python
:download:`Download Python source code: plot_arima_search.py <plot_arima_search.py>`
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: plot_arima_search.ipynb <plot_arima_search.ipynb>`
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_