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Answer: The autocovariance of a covariance stationary time series depends only on displacement, τ, not on time.
## Explanation For a time series to be covariance stationary, it must satisfy three conditions: 1. **Constant mean**: The expected value of the time series is constant over time 2. **Constant variance**: The variance of the time series is finite and constant over time 3. **Autocovariance depends only on displacement**: The covariance between observations at times t and t+τ depends only on the displacement τ, not on the specific time t **Option C** correctly describes the third requirement - that the autocovariance depends only on the displacement τ, not on the specific time period. This means that the relationship between observations separated by τ periods remains the same regardless of when in the time series we measure it. **Why the other options are incorrect:** - **Option A**: Kurtosis near 3.0 (normal distribution kurtosis) is not a requirement for covariance stationarity. Stationarity relates to the statistical properties over time, not the specific shape of the distribution. - **Option B**: Skewness near 0 is not a requirement for covariance stationarity. A time series can be skewed and still be stationary. - **Option D**: The autocovariance function for a covariance stationary time series must be symmetric with respect to displacement τ, not asymmetric.
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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 displacement, τ, not on time.
D
When the autocovariance function is asymmetric with respect to displacement, τ, forward looking stationarity can be achieved.
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