I have used least squares estimation to obtain estimates for parameters to be used in Ornstein Uhlenbeck process. Now, I would like to compute the standard errors of estimates.

$𝑑𝑆𝑑=πœ†(πœ‡βˆ’π‘†π‘‘)𝑑𝑑+πœŽπ‘‘π‘Šπ‘‘$ (Ornstein Uhlenbeck process and parameters to be estimated)

The regression is as follows:


The estimates for parameters are obtained from the regression coefficients as follows:

$πœ†=βˆ’(lnπ‘Ž)/Δ𝑑, πœ‡=π‘Ž/(1βˆ’π‘)$


$𝜎=sd(πœ–π‘‘) * \sqrt{2πœ†/(1βˆ’π‘’^{βˆ’2πœ†Ξ”π‘‘})}$

I can obtain the standard errors for a and b, but how would I be able to obtain standard errors for the parameters?

Any help is greatly appreciated, I apologize the messy layout of formulas.


If you are reporting to physicists or chemicists, I would recommend the Gaussian error propagation law, because that is what they usually apply in such cases: $$(\Delta f)^2 = \left(\frac{\partial f}{\partial a} \Delta a\right)^2 + \left(\frac{\partial f}{\partial b} \Delta b\right)^2 + \ldots$$ If you are reporting to statisticians, a resampling method like the bootstrap or the jacknife might raise fewer eyebrows ;-) The jackknife is easier and yields reproducibale results, whilst the bootstrap yields a random (albeit not much different) result.

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