# Relation between AR(1) and Vasicek model

The discrete time version of a Vasicek model is equivalent to an AR(1) model with opportunely chosen parameters, as showed in this paper: http://www.damianobrigo.it/toolboxweb.pdf.

Following this procedure, having fitted an AR(1) model I can recover the parameter of a Vasicek model, but what about the standard errors? Is there a way to obtain them from the AR(1) estimates as well?

Since I'm interested in the regime-switching version of these processes, I cannot use the usual MLE, and all the R or MATLAB packages have implementation just for the regime-switching AR model.

• Are you familiar with the delta method and/or block bootstrapping? Those would be appropriate methodologies for obtaining the standard errors of the Vasicek model given the estimates and standard errors of the AR(1). Jul 19 '15 at 4:27
• I was trying the block bootstrap, but I have the same problem as stated in this question: stats.stackexchange.com/questions/160776/… . I didn't think about the delta method, I will try that. Thanks. Jul 19 '15 at 13:00
• See nccur.lib.nccu.edu.tw/bitstream/140.119/35143/6/51007106.pdf and the references cited therein for a discussion on selecting block length. As with a lot of things in statistics there is no one right answer and block bootstrapping methods range from simple to complex (some argue that selecting the block length itself from another discrete distribution is most appropriate). Jul 19 '15 at 22:18
• Problem with delta method is how to get the variance-covariance matrix for my model (regime-switching autoregressive of order 1) coefficients. Jul 20 '15 at 15:15
• You can still estimate the model with MLE, see this paper by JD Hamilton econweb.ucsd.edu/~jhamilto/palgrav1.pdf . So that will give you standard errors for your coefficients under the iid normality assumptions. Whether or not the iid normality assumptions are met is another story, which is why you might prefer block bootstrapping or going Bayesian. I don't know exactly what you mean. Jul 20 '15 at 16:30