Time series analysis by state space methods using statsmodels

This recipe demonstrates how to perform Time Series Analysis using State Space Methods in Python with the StatsModels library

Recipe Objective - How to perform Time Series Analysis by State Space Methods using the StatsModels library in python?

The statsmodels.tsa.statespace contains classes and functions that are useful for time series analysis using statespace methods.

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Seasonal Autoregressive Integrated Moving-Average with eXogenous regressors (SARIMAX)

The SARIMAX class is an example of a full-fledged model created using a state-space backend for estimation. SARIMAX can be used in a very similar way to the tsa model. Still, it works in a broader range of models by adding estimates of the seasonal effects of addition and multiplication and arbitrary propensity polynomials.

Example:

# Load the statsmodels api
import statsmodels.api as sm
import pandas as pd

# Importing moore dataset from carData package
X = sm.datasets.get_rdataset("Moore", "carData").data

# Fitting sarimax model to 'fscore' feature
model = sm.tsa.SARIMAX(X['fscore'], order=(3,0,0))

# Fitting the model
model = model.fit()

# Summary
model.summary()

Output - 
SARIMAX Results
Dep. Variable:	fscore	No. Observations:	45
Model:	SARIMAX(3, 0, 0)	Log Likelihood	-191.045
Date:	Mon, 15 Nov 2021	AIC	390.091
Time:	08:59:03	BIC	397.317
Sample:	0	HQIC	392.785
- 45		
Covariance Type:	opg		
coef	std err	z	P>|z|	[0.025	0.975]
ar.L1	0.1972	0.151	1.309	0.191	-0.098	0.493
ar.L2	0.2844	0.117	2.439	0.015	0.056	0.513
ar.L3	0.4909	0.133	3.696	0.000	0.231	0.751
sigma2	266.9526	71.044	3.758	0.000	127.708	406.197
Ljung-Box (L1) (Q):	1.17	Jarque-Bera (JB):	2.37
Prob(Q):	0.28	Prob(JB):	0.31
Heteroskedasticity (H):	0.30	Skew:	-0.53
Prob(H) (two-sided):	0.03	Kurtosis:	2.62

In this way, we can perform Time Series Analysis by State Space Methods using the StatsModels library in python.

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