Time Series Stationarity: First-Differences and Non-Stationary Levels

True. A time series that is non-stationary in levels will necessarily be stationary in first-differences.

The reason for this is that differencing a time series (subtracting each observation from its previous observation) can often remove trends and make the series stationary.

If a time series is non-stationary in levels, it means that it exhibits a trend or a systematic change in its mean over time. This can make statistical analysis and modeling challenging because the mean and other statistical properties of the series can change over time.

However, by taking the first-differences of the series, we are essentially removing the trend component. This differencing process computes the difference between each observation and its previous observation, effectively subtracting the trend from the series.

In many cases, differencing can make the series stationary, meaning that its statistical properties such as mean, variance, and autocorrelation do not change over time. A stationary time series is often easier to analyze and model using various statistical techniques.'}