Understanding the Basics of Time Series Analysis with statsmodels

Time series analysis is a statistical technique that deals with time series data, or data that is indexed in time order. It is often used for analyzing historical data to understand patterns over time and to forecast future trends. A commonly used Python package for time series analysis is statsmodels. In this article, we will explore the basics of time series analysis and how to perform it using statsmodels.

What is Time Series Data?

Time series data is a sequence of data points collected over a successive intervals of time. Some examples include daily stock prices, monthly rainfall data, and yearly profit in a business.

Getting Started with statsmodels

First, you will need to install the statsmodels library. You can do this using pip:

pip install statsmodels

Once installed, let's start by loading some example data and walking through the different components of a time series analysis.

Loading Data

You can use any time series data, but for demonstration purposes, let's use a dataset provided by the statsmodels.api:

import statsmodels.api as sm

data = sm.datasets.co2.load_pandas().data
print(data.head())

This piece of code loads the CO2 dataset, which contains measurements of atmospheric carbon dioxide collected monthly.

Decomposing Time Series

To understand the underlying patterns in time series data, it can be helpful to decompose it into its various components: trend, seasonality, and noise. Statsmodels provides a function to do this:

from statsmodels.tsa.seasonal import seasonal_decompose

result = seasonal_decompose(data['co2'].dropna(), model='additive', period=12)
result.plot()

This code performs an additive decomposition, separating the time series into trend, seasonal, and residual (noise) components for better analysis.

Creating an ARIMA Model

One of the classical methods for time series forecasting is the ARIMA (AutoRegressive Integrated Moving Average) model.

from statsmodels.tsa.arima.model import ARIMA

# Fit model
diff_data = data['co2'].diff().dropna()
model = ARIMA(diff_data, order=(1, 1, 1))
model_fit = model.fit()
print(model_fit.summary())

In the above code, we're creating an ARIMA model to fit our CO2 dataset and then printing a summary of the results.

Forecasting with ARIMA

After fitting the model, you can use it to make predictions about future values.

forecast = model_fit.forecast(steps=10)
print(forecast)

Using the ARIMA model, the above code provides a forecast of CO2 levels for the next 10 intervals.

Conclusion

Time series analysis is a powerful tool for understanding and forecasting data indexed over time. The statsmodels library provides a comprehensive set of tools for performing these analyses in an efficient and effective manner. We've covered the basics of loading data, decomposing into components, and building predictive models using ARIMA, highlighting only a few of the capabilities available in statsmodels.

By gaining a solid understanding of these basic techniques, you can begin to explore more complex models and analyses, opening a world of insights into your time-relevant data.