(OU parameters from an AR(1))

An OLS fit of a daily spread (log units, $\Delta = 1/250$ year) gives $\hat a = 0.0003$, $\hat b = 0.96$, $\hat\sigma_e = 0.008$. (a) Compute $\hat\kappa$ (per year), $\hat\theta$, $\hat\sigma$ and the half-life in trading days. (b) Compute the stationary standard deviation of the spread in two ways and check that they agree. (c) The fit used 18 months of data (375 days). Use (13A.25) to give the approximate relative standard error and relative bias of $\hat\kappa$.