# Statistical test for comparing two different speed of mean reversion parameters for CIR model

I am trying to compare two different values of speed of mean reversion parameter for CIR model. I would like to know if there exists a statistical test for comparing these two parameters. the estimate of speed of mean reversion is being calculated as follows: $$\alpha = \frac{1}{2\delta t}ln(1-(\frac{\sigma_{shortTerm}}{\sigma_{longTerm}})^2)$$ Where, $$\alpha$$ is the speed of mean reversion. $$\sigma_{shortTerm}$$ and $$\sigma_{longTerm}$$ are the short term and long term volatilities respectively. $$\delta t$$ is the time step.

so basically,I have two estimates of $$\alpha$$. Lets call them $$\alpha_1$$ and $$\alpha_2$$. Is there a statistical test to compare these two estimates.

• Please define how you are computing the two volatility estimates. – oliversm Jun 12 at 21:17