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Answer: The autocovariance of a covariance stationary time series depends only on the lag: h,between observations,not on time.
C is correct. One requirement for a series to be covariance stationary is that its covariance structure be stable over time. If the covariance structure is stable, then the autocovariances depend only on the lag, h, between observations, not on time, t. Covariance stationarity does not place restrictions on other aspects of the distributions or the series, such as kurtosis and skewness. It also does not depend on the symmetry of the autocovariance function.
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A risk manager at a major global bank is conducting a time series analysis on the returns of equities. The manager aims to ascertain whether the time series exhibits covariance stationarity, a crucial property for reliable financial modeling and forecasting. Which of the following statements correctly identifies a necessary condition for a time series to be considered covariance stationary?
A
The distribution of a time series should have a kurtosis value near 3.0, ensuring no fat tails will distort stationarity.
B
The distribution of a time series should have a skewness value near O, so that its mean will fall in the center of the distribution.
C
The autocovariance of a covariance stationary time series depends only on the lag: h,between observations,not on time.
D
When the autocovariance function is asymmetric with respect to lag, h, forward looking stationarity can be achieved