critical values

[selin1000]

I need to re-compute the asymptotic critical values for exisiting cointegration models, could anybody give me a lead on this? I am really lost :( Are critical values obtained with Monte Carlo simulations? Any help would truly be appreciated. Thank you.

[trubador]

Yes, but simulations depend on the structure of the model. So you should give more information on what you are doing.

[selin1000]

I want to understand how Sylvestre and Sanso compute the critical values in their paper "Testing the null of cointegration with structural breaks"
I cant understand what they do in their paper. They state: "Percentage points of the asymptotic distribution are based on n=20000 replications using partial sums of iidN(0,1) variables of T=2000 observations to approximate the Wiener process. lambda denotes the break fraction and k is the number of stochastic regressors in the model(Sylvestre and Sanso, page 9)." What does that mean? So they generate random N(0,1) variables, but where does the number of regressors come into play?
If somebody could enlighten me a bit on this, I would be so grateful!

Thank you very much!

[trubador]

As I understand from your quote, they seem to simulate for both endogenous variables and regressors. The model probably includes at least one regressor, which is usually defined as a random walk process. In other words, the data generating process of endogenous variable depends on some exogenous variables and therefore they should also be randomly generated.

[selin1000]

Thank you so much! Your comment was so helpful! :) I have one endogenous variable y, one regressor x, and a Dynamic OLS Regression of y on x. The test statistic is called SC and is computed with the estimated residuals from this DOLS Regression. (an explicit Formula is given in the paper) Here is how I compute the critical value of the test statistic SC.
I generate two random N(0,1)series(one for endogenous, one for regressor), I regress them one on another and save the residuals. With these residuals, I compute the SC test statistic. I repeat this process 20000 times, find the mean and variance of the SC test statistic and calculate a confidence interval for SC. SC weakly converges to the sum of two Wiener processes so I compute the confidence interval just as SC had a normal distribution. The upper tail value is my critical value.
Do you think that what I am doing is correct? Does it sound logical? Thank you so much again, I appreciate your help! :)

[trubador]

You should check with the original paper, but I do not think you need to compute a confidence interval. If you are trying to determine the critical values, then you can store SC values from these simulations (20000 obs) and compute the upper (or lower depending on your null hypothesis) tail of their distribution. @quantile function in EViews will be helpful in this regard.

[selin1000]

Thank you so much! :) That is so helpful, now I can understand the model! But I never used quantiles before. How can I store the SC values and use the @quantile to compute the upper bound? Do I just add up all the SC values from each simulation? Thank you very much again.

Have a great evening!

Selin

[trubador]

Something along the following lines:

Code: Select all

... ... vector(20000) sc for !i = 1 to 20000 ... ... sc(!i) = ... ... next !critical = @quantile(sc,0.95) ...

[selin1000]

Thank you so much! :) I made it and it works!
Have a great day!
Selin