📚 Topic Summary
Stationarity in time series analysis means that the statistical properties of a process (like the mean and variance) don't change over time. Think of it like a calm lake – the water level (mean) and the ripples (variance) stay roughly the same. Non-stationary data, on the other hand, behaves like a stormy sea with unpredictable changes. Unit root tests, such as the Augmented Dickey-Fuller (ADF) test, help us determine if a time series is stationary or not. They check for the presence of a 'unit root,' which indicates non-stationarity and often suggests that the series needs to be differenced to become stationary.
Why does this matter? Most statistical models assume stationarity. Using non-stationary data can lead to spurious regressions, where you find a relationship between variables that doesn't actually exist. So, understanding stationarity and using unit root tests are crucial for reliable time series analysis.
🧠 Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Stationarity |
A. A test for unit roots in a time series. |
| 2. Unit Root |
B. A time series whose statistical properties are constant over time. |
| 3. Dickey-Fuller Test |
C. A transformation that subtracts the previous observation from the current one. |
| 4. Differencing |
D. A characteristic of a time series that indicates non-stationarity. |
| 5. Spurious Regression |
E. A regression that shows a statistically significant relationship when no true relationship exists. |
(Answers: 1-B, 2-D, 3-A, 4-C, 5-E)
✏️ Part B: Fill in the Blanks
Complete the following paragraph using the words: trend, stationary, Augmented Dickey-Fuller, differencing, non-stationary.
A time series is considered __________ if its statistical properties do not change over time. If a time series has a __________ or exhibits unpredictable behavior, it is likely __________. To test for stationarity, one might use the __________ test. A common technique to transform a non-stationary series into a stationary one is __________.
(Answers: stationary, trend, non-stationary, Augmented Dickey-Fuller, differencing)
🤔 Part C: Critical Thinking
Why is it important to test for stationarity before building a time series model? What are the potential consequences of using non-stationary data in a regression analysis?