Financial Risk Manager Part 1
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The key difference between a moving average representation and an autoregressive process is that:
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A
An autoregressive process is never covariance stationary.
B
An autoregressive process shows evidence of autocorrelation cutoff.
C
Unlike the autoregressive process, a moving average representation shows evidence of gradual decay.
D
A moving average representation shows evidence of autocorrelation cutoff.
Explanation:
Explanation
Correct Answer: D
A moving average representation shows evidence of autocorrelation cutoff. This means that the correlation between a variable and its lagged values abruptly drops to zero after a certain point. This is a key characteristic of moving average models.
Why the other options are incorrect:
- A: Autoregressive processes can be covariance stationary under certain conditions (when the roots of the characteristic equation lie outside the unit circle).
- B: This is actually the opposite - autoregressive processes show gradual decay in autocorrelations, not cutoff.
- C: This statement is reversed - moving average processes show autocorrelation cutoff, while autoregressive processes show gradual decay.
Key Distinction:
- Moving Average (MA) Process: Autocorrelation function cuts off after q lags (for MA(q) process)
- Autoregressive (AR) Process: Autocorrelation function decays gradually (exponentially or sinusoidally)
This difference is crucial in time series analysis for identifying the appropriate model type based on the observed autocorrelation pattern in the data.
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