IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Core concepts of time series models
X_t is a random walk with X_0 = 0 and shock variance sigma squared. For s < t, what is Corr(X_s, X_t) when s = 9 and t = 36?
The correlation is 0.5. The covariance is 9 sigma squared, and the standard deviations are 3 sigma and 6 sigma, so the correlation is 9 divided by 18. Using s/t = 0.25 forgets the square root.
- A0.25
- B0.50Correct
- C0.75
- D0.0
- 0.0625
Explanation
Cov(X_s, X_t) = s sigma^2 = 9 sigma^2. Var(X_s) = 9 sigma^2 and Var(X_t) = 36 sigma^2. Correlation = 9 / sqrt(9 x 36) = 9/18 = 0.5. The value 0.25 is the ratio s/t without the square root.
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