Time series data is widely used in various fields such as finance, economics, and weather forecasting. One of the key assumptions while working with time series data is stationarity, which means that the statistical properties of the data do not change over time. Analyzing the stationarity of a time series is crucial for making accurate predictions and modeling.

In Python, we can use the Dickey-Fuller Test and Autocorrelation to determine the stationarity of a time series. The Dickey-Fuller Test is a statistical hypothesis test that helps us identify whether a given time series is stationary or not. It calculates various statistical values and p-values to evaluate the null hypothesis that the time series is non-stationary. If the p-value is less than a certain threshold (usually 0.05), we reject the null hypothesis and conclude that the time series is stationary.

Autocorrelation, on the other hand, measures the relationship between a time series and its lagged values. By plotting the autocorrelation function (ACF), we can identify any significant correlations between the time series and its past observations. If the ACF values decay exponentially, it indicates stationarity.

To perform these analyses, we can use popular Python libraries such as pandas, numpy, and statsmodels. First, we load our time series data into a pandas DataFrame. Then, we can apply the Dickey-Fuller Test using the `adfuller` function from the statsmodels library. This function returns various statistical values, including the p-value, which we can compare with the threshold.

To analyze autocorrelation, we can use the `plot_acf` function from the statsmodels library. This function plots the autocorrelation values against the lag. If the ACF values decay quickly or hover around zero, it suggests stationarity.

By combining these techniques, we can gain insights into the stationarity of a time series. This information is valuable for choosing appropriate models, identifying trends, and making accurate predictions. Python provides powerful tools to perform these analyses efficiently, allowing us to leverage the benefits of time series stationarity in our data-driven projects.