Financial Risk Manager Part 1

A time series is said to be stationary if its statistical properties including the mean and variance do not change over time. This is because the fundamental assumption behind a stationary time series is that the properties that are learned from the data in one time period are consistent and can be applied to any other period. This includes the mean and variance of the series. If these properties remain constant over time, then the series can be said to be stationary. This is important because many statistical modeling techniques require the time series to be stationary to make effective and reliable predictions.

Choice B is incorrect. A time series is considered stationary when its statistical properties do not change over time. This includes the mean, variance, and covariances with lagged and leading values. If these properties change over time, as suggested in this option, the time series would not be stationary.

Choice C is incorrect. While it's true that a constant mean is one of the conditions for stationarity, it's not sufficient on its own. The variance and covariances with lagged and leading values also need to remain constant for a time series to be considered stationary.

Choice D is incorrect. This choice suggests that only the covariances with lagged and leading values need to remain constant for a time series to be stationary. However, this isn't accurate - both the mean and variance also need to remain constant over time.