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Evaluating Stationarity And Cointegration With Statsmodels

Leo Migdal
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evaluating stationarity and cointegration with statsmodels

In time series analysis, understanding the concepts of stationarity and cointegration is critical, especially when you work with financial or economic data. These properties affect how we model time series data, and whether we can make reliable forecasts or inferences from them. A time series is considered stationary if its statistical properties such as mean, variance, and autocorrelation are constant over time. Stationarity is a crucial assumption for many time series models because it simplifies the analysis and forecasting of time series data. The statsmodels library in Python provides tools to test for stationarity. The most commonly used test is the Augmented Dickey-Fuller (ADF) test.

Let's see how this can be implemented: If the p-value is less than a pre-specified threshold (often 0.05), the null hypothesis of non-stationarity is rejected, indicating the series is stationary. Cointegration refers to a scenario where two or more non-stationary series are linearly related in such a way that a linear combination of them is stationary. This is significant in econometrics and pairs trading strategies in finance. Stationarity means that the statistical properties of a time series i.e. mean, variance and covariance do not change over time.

Many statistical models require the series to be stationary to make effective and precise predictions. Two statistical tests would be used to check the stationarity of a time series – Augmented Dickey Fuller (“ADF”) test and Kwiatkowski-Phillips-Schmidt-Shin (“KPSS”) test. A method to convert a non-stationary time series into stationary series shall also be used. This first cell imports standard packages and sets plots to appear inline. Sunspots dataset is used. It contains yearly (1700-2008) data on sunspots from the National Geophysical Data Center.

Some preprocessing is carried out on the data. The “YEAR” column is used in creating index. Time series analysis often grapples with non-stationary data, where traditional regression can lead to spurious results. Cointegration offers a powerful solution, revealing long-term relationships between variables that move together despite individual fluctuations. In this comprehensive tutorial, we”ll demystify cointegration tests in Python, focusing on the robust capabilities of the Statsmodels library. You”ll learn what cointegration is, why it”s crucial for accurate time series modeling, and how to implement the Johansen cointegration test effectively with practical examples.

Imagine two non-stationary time series, like the prices of two related stocks. Individually, they might wander randomly. However, if a linear combination of these series *is* stationary, they are said to be cointegrated. This means they share a common stochastic trend and will not drift infinitely far apart over time. Think of it as two drunks walking: individually they stumble, but if they are holding hands, they won”t drift too far from each other. Cointegration identifies these “holding hands” relationships.

Identifying cointegrated series is vital for several reasons. Firstly, it allows us to perform meaningful long-run equilibrium analysis, even with non-stationary data. This prevents spurious regressions, where unrelated series appear to have a relationship due to shared trends. The concept of stationarity in time series data — not to be mixed up with that of seasonality — refers to maintaining similar statistical properties across the time. In other words, aspects in the time series like mean, variances, and autocorrelation remain constant. It is somehow the opposite to exhibiting trends or seasonality.

When things seem to behave in a stable manner across time (stationarity), there are little or not patterns that hint at seasonal phenomena or trends. This article describes how to analyze and understand stationarity in time series data in Python. Following some previous articles in this series, we will use the Chicago rides public version with a CSV version I made available here. One novel aspect in this initial part of the code is the imported function adfuller() from the statsmodels.tsa.stattools module, which we will use to conduct the Augmented Dickey-Fuller (ADF) test, a well-known statistical test... Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Stack Overflow for Teams is now called Stack Internal.

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Find centralized, trusted content and collaborate around the technologies you use most. Bring the best of human thought and AI automation together at your work. Last modified: Jan 26, 2025 By Alexander Williams Cointegration is a key concept in time series analysis. It helps identify long-term relationships between variables. The coint() function in Python's Statsmodels library is a powerful tool for this purpose.

This guide will walk you through the basics of using coint(). You'll learn its syntax, how to interpret results, and see practical examples. Let's dive in! Cointegration refers to a statistical relationship between two or more time series. Even if individual series are non-stationary, their linear combination can be stationary. This implies a long-term equilibrium relationship.

For example, stock prices and dividends may be cointegrated. While both series may trend over time, their relationship remains stable. Cointegration is crucial in econometrics and finance. Test for no-cointegration of a univariate equation. The null hypothesis is no cointegration. Variables in y0 and y1 are assumed to be integrated of order 1, I(1).

This uses the augmented Engle-Granger two-step cointegration test. Constant or trend is included in 1st stage regression, i.e. in cointegrating equation. Warning: The autolag default has changed compared to statsmodels 0.8. In 0.8 autolag was always None, no the keyword is used and defaults to “aic”. Use autolag=None to avoid the lag search.

The first element in cointegrated system. Must be 1-d. In time series analysis, many variables show trends over time, meaning they are non-stationary. This non-stationarity can be a problem when building statistical models because it can lead to misleading results. However, sometimes two or more non-stationary time series move together in such a way that their combination becomes stationary. This relationship is called cointegration.

Cointegration occurs when two or more non-stationary time series move together in such a way that their linear combination becomes stationary. This indicates a long-term equilibrium relationship between the variables, even if each one individually trends or drifts over time. Reveals stable, long-run relationships between non-stationary variables. Facilitates the use of Error Correction Models (ECM), which capture: Before diving into cointegration, it’s important to understand stationarity: Step 1: Check Stationarity of Individual Series:

Understanding stationarity is crucial when working with time series data to ensure accurate models and forecasts. Stationarity refers to a time series whose statistical properties such as mean, variance, and autocorrelation are constant over time. Most statistical forecasting methods assume that the time series is stationary. There are two main types of stationarity: Non-stationary data, in contrast, can have trends, seasonal variations, and other structures that depend on the time index. This non-stationarity can be problematic because it can lead to misleading statistics and analytical results.

To effectively analyze and forecast time series data, it is often necessary to transform non-stationary data into a stationary state. This transformation might involve differencing the data, logarithmic or square root transformations, or decomposing the data into trend and seasonal components. Understanding whether your data is stationary or not can significantly impact the performance of your time series models. Therefore, it’s essential to test for stationarity using visual and statistical methods, which will be discussed in the following sections.

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