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Answer: The autocovariance of a covariance stationary time series depends only on the lag, h, between observations, not on time.
## Explanation **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. **A and B are incorrect.** Covariance stationarity does not place restrictions on other aspects of the distributions or the series, such as kurtosis and skewness. **D is incorrect.** Covariance stationarity does not depend on the symmetry of the autocovariance function. ### Key Concepts: - **Covariance Stationarity** requires three conditions: 1. Constant mean over time 2. Constant variance over time 3. Autocovariance depends only on the lag between observations, not on the specific time period - The autocovariance function γ(h) = Cov(X_t, X_{t+h}) should be independent of t and depend only on h - This property ensures that the statistical properties of the time series remain stable over time, which is crucial for reliable time series analysis and forecasting
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A risk manager at a major global bank is conducting a time series analysis of equity returns. The manager wants to know whether the time series is covariance stationary. Which of the following statements describes one of the requirements for a time series to be 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 0, 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.
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