1
$\begingroup$

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:

$S(t+1)=a*S(t)+b+πœ–$

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

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

and

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

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.

$\endgroup$
0
$\begingroup$

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.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking β€œPost Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.