The researchers developed an improved test called the Optimized Dickey-Fuller Test to better analyze time series data. They found that traditional tests had issues with sign and boundary problems, which made it harder to detect patterns in the data. By using the error sum of squares method and setting limits on parameters, the new test outperformed the old one in terms of accuracy and power. The Optimized Dickey-Fuller Test was able to capture more nonstationarity in the data, making it a more effective tool for analyzing time-related information.