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What is stationarity and how can you achieve it in time series data?

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Time series data are observations collected over time, such as stock prices, weather, or sales. They often exhibit patterns and trends that can be used for forecasting or analysis. However, to apply many statistical methods and models to time series data, you need to ensure that they are stationary. This means that their mean, variance, and autocorrelation do not change over time. In this article, you will learn what stationarity is, why it is important, and how you can achieve it in your time series data.

本文章的要点总结

Apply differencing:

To make time series data stationary, differencing is a go-to method. Subtract consecutive observations or those at a specific lag to stabilize the mean, which can reveal hidden patterns for analysis.
Use transformation:

Converting your data with logarithms or square roots can tame wild swings in variance and uncover stable trends, making your time series data more predictable and easier to work with.

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MD TANZIR ISLAM

Resident Doctor @ Chittagong Medical…
Tanisha Verma

Embracing real life challenges with AI…

1 Types of stationarity

When defining stationarity, the most common approaches are strict stationarity, weak stationarity, trend-stationary, and difference-stationary. Strict stationarity is difficult to verify in practice and rarely holds for real-world data. Weak stationarity is more realistic and easier to test than strict stationarity. Trend-stationary means that the observations have a deterministic trend that can be removed by subtracting or differencing, resulting in a weakly stationary series. Difference-stationary means that the observations have a stochastic trend which can be removed by differencing, creating a weakly stationary series.

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MD TANZIR ISLAM

Resident Doctor @ Chittagong Medical University | Healthcare Expert and Government Certified Physician
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Strict Stationarity: All aspects of the series' distribution are constant over time, a condition that's difficult to test in practice. Weak Stationarity: The series' mean, variance, and covariance between two time periods remain constant over time. This is a more practical form for analysis. Trend Stationarity: The series becomes stationary once a deterministic trend is removed. Difference Stationarity: The series becomes stationary after differencing, typically used for series with a unit root.

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Tanisha Verma

Embracing real life challenges with AI ? Aspiring Data Scientist ? SheCodes Foundation Scholar ? Proficient in C, C++, Python, HTML, SQL.
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There are 2 types of stationarity: 1. Strict Stationarity: The Statistical features like mean, variance, autocorrelation remains constant over the period of time. 2. Weak Stationarity: Similar to strict stationarity, the statistical features like mean, variance remains constant whereas autocorrelation changes over the period of time.

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Emmanuel Boamah

Aspiring Fellow Actuary who seeks to use his actuarial and Risk management skills with both statistical and mathematical concepts to solve societal problems.
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In my experience, stationary is the process of making a series of observations independent of time. In other words, when observations in time periods have no trend. Types of stationarity 1. Weak stationary The mean and variance of the time series are constant over time. 2. Strict stationary The times series of observations from time apart, all have the same distribution Ways of making time series stationary. 1. Differencing: This is the act of taking the difference of the previous time series from the current time series until you get to the point that the mean and your variance of your results become constant. First order differencing is given as Y(t)-Y(t-1) 2. Detrending i.e removing the trend in the time series observation.

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2 Importance of stationarity

Stationarity is important because many statistical methods and models assume that the data are stationary. For example, linear regression, ARIMA, and hypothesis testing rely on stationarity to produce valid results. If the data are not stationary, these methods and models may produce misleading or inaccurate estimates, predictions, or conclusions. Therefore, checking and ensuring stationarity is a crucial step in any time series analysis.

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Tanisha Verma

Embracing real life challenges with AI ? Aspiring Data Scientist ? SheCodes Foundation Scholar ? Proficient in C, C++, Python, HTML, SQL.
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In time series analyses, it is very crucial to check the robustness of the data set. Stationary time series are more robust to outliers, hence applying the stationarity becomes essential. On the other hand, Time series models like ARIMA, Exponential smoothing, requires stationarity before hand. Thus, making non stationary series into stationary increases the range of applicability and improvise the accuracy of the output.

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Emmanuel Boamah

Aspiring Fellow Actuary who seeks to use his actuarial and Risk management skills with both statistical and mathematical concepts to solve societal problems.
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Stationarity is important because every statistical inferences that you want to make is based on the assumption that it is suppose to be independent of time. If not there will be misleadings in your analysis.

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3 How to check stationarity

In order to check stationarity, two main approaches are visual inspection and statistical tests. Visual inspection requires plotting the time series and searching for any noticeable trends, seasonality, or changes in mean, variance, or autocorrelation. Statistical tests involve using a formal criterion to determine if the data is stationary or not. Some popular tests are the Augmented Dickey-Fuller (ADF) test, which checks for difference-stationary; the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test, which looks for trend-stationary; and the Phillips-Perron (PP) test which is more reliable for autocorrelation and heteroscedasticity.

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Emmanuel Boamah

Aspiring Fellow Actuary who seeks to use his actuarial and Risk management skills with both statistical and mathematical concepts to solve societal problems.
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1.Stationarity in times series can be checked by plotting the time series observations over time and checking if there is no trend. 2. It can also be checked by finding the expectation and the variance of the time series function to see if both are time dependent or not. If they are all time dependent, it means the time series is non stationary. Otherwise stationary.

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4 How to achieve stationarity

If the data are not stationary, you need to transform them to make them stationary. Different methods can be used depending on the type and source of non-stationarity. Detrending, for example, involves subtracting or dividing by a fitted trend line, which can be done using linear or nonlinear regression, smoothing, or decomposition methods. Differencing is another method which takes the difference between consecutive observations or between observations at a certain lag. This can be done using the diff() function in R or Python. Transforming involves applying a mathematical function to the data, such as logarithm, square root, or power. Standardizing is a final method that scales the data to have zero mean and unit variance, using the scale() function in R or the StandardScaler() class in Python. All of these methods can reduce variability or heteroscedasticity of the data and make them more symmetric and easier to analyze.

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Tanisha Verma

Embracing real life challenges with AI ? Aspiring Data Scientist ? SheCodes Foundation Scholar ? Proficient in C, C++, Python, HTML, SQL.
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To achieve stationarity, we can use --> differencing --> calculating the log or square root of the data --> using a moving average filter Using the above methods we can easily achieve stationarity which will help in better prediction in time series data.

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Emmanuel Boamah

Aspiring Fellow Actuary who seeks to use his actuarial and Risk management skills with both statistical and mathematical concepts to solve societal problems.
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Detrending and differencing can both achieve stationarity. Detrending can by done by subtracting the fitted trend from the time series observations. Differencing is by subtracting the previous time series observations from the current one by mth order until stationarity is achieved.

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5 How to verify stationarity

After transforming the data, you need to verify that they are stationary. You can do this by repeating the visual inspection and statistical tests that you used before. If the plots show no obvious trends, seasonality, or changes in mean, variance, or autocorrelation, and if the tests confirm that the data are stationary, you can proceed with your analysis. However, if the plots still show some non-stationarity, or if the tests reject stationarity, you may need to try a different method or a higher order of transformation. You should also be careful not to over-transform the data, as this may introduce noise or distort the original information.

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6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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What is stationarity and how can you achieve it in time series data?

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6

1 Types of stationarity

2 Importance of stationarity

3 How to check stationarity

4 How to achieve stationarity

5 How to verify stationarity

6 Here’s what else to consider

Critical Thinking

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What is stationarity and how can you achieve it in time series data?

1

2

3

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5

6

1 Types of stationarity

2 Importance of stationarity

3 How to check stationarity

4 How to achieve stationarity

5 How to verify stationarity

6 Here’s what else to consider

Critical Thinking

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