Suppose that (X_{1}) is the change in the value of a variable during one time period and

Question:

Suppose that $X_{1}$ is the change in the value of a variable during one time period and $X_{2}$ is the change in its value during the next time period. What is the correlation between $X_{1}$ and $X_{2}$ when the variable follows fractional Brownian motion with

(a) $H>0.5$,

(b) $H=0.5$, and

(c) $H<0.5$, where $H$ is the Hurst exponent?

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