The RATS Software Forum

No. You're not bootstrapping to get an estimate of alpha; the mean across bootstrap samples should be roughly the same as the mean of the data. Yes, the mean across bootstrap samples is approximately the same as the mean of the data. Instead, you're bootstrapping to get the sampling distribution an...

No. That's a different type of bootstrap (which is bootstrapping data under the null). You need to compare the results with the assumed value of alpha. I can block bootstrap trigger within a loop, ndraws times, and calculate the means. That's straightforward. The question is what’s the p-value? Som...

In https://estima.com/forum/viewtopic.php?p=19882#p19882, I describe a valid test for PoF in overlapping samples. If you aren't satisfied with the Wald test based on QMLE asymptotics, you can block bootstrap the exceedance data and get a bootstrapped distribution for the alphahat. (You don't have t...

TomDoan wrote: ↑Fri Jan 23, 2026 7:31 am Randomly rearranging (block bootstrapping) independent random variables as in your S4 does not produce correlated random variables.

Do you have an alternative solution as a procedure in RATS?

acKupiecBlockBoot.src: S1. Counts actual violations in the VaR OOS sample. S2. Computes Kupiec POF statistic as usual. S3. Generates many synthetic violation series under H0 (correct VaR model): H0 : violation probability = alpha (correct unconditional coverage) S4. Uses block bootstrap with blockle...

You shuffle the values of the trigger series, not a randomized series. Sorry, are you saying the fix is BOOT(block=blocklen) bootentries startl endl startl endl set bootviol startl endl = trigger(bootentries(t)) ? Then, the p-value for Day 1 is completely different from the analytical Kupiec.

I'm not sure what it is that you think that procedure is doing, but it's not block bootstrapping. The only thing that you are reshuffling are the independently drawn random numbers, and reshuffling independent random numbers produces independent random numbers. How do I fix so that it is block boot...

It doesn't work for 0 because there is nothing in the formula that forces the alphahat to [0,1] when there are no data points that apply to the log(alphahat). And even if it's tweaked to limit the alphahat, the asymptotics don't work when the parameters is on the boundary. (The same is true for the...

TomDoan wrote: ↑Thu Jan 22, 2026 8:04 am

ac_1 wrote: ↑Thu Jan 22, 2026 2:57 am If there are 0 or 1 or 2 exceedances, but not >=3, why does Wald QMLE give a p-value of exactly 0.0 ?

For how many observations and what value of alpha?

staggered forecasts 1000 obs down to 991 obs, alpha = 0.01.

If there are 0 or 1 or 2 exceedances, but not >=3, why does Wald QMLE give a p-value of exactly 0.0 ?

The tail index doesn't provide enough information to compute the VaR and the ES. Those need complete distributions. tsay3p355 does that. The thing to note is that the results are sensitive to the number of extreme values that are included, which is the point of the earlier search. Are you saying I ...

Although, @HillGEV is designed for GEV asymptotics, not classical Pareto Hill estimator: 1/ihat = (1/k) summation from j=1 to k [log( X(j)/X(k+1))]. I'd like the classical estimator to complement various risk algos. That's what the procedure computes. Alright if I use @HillGEV(span=CT,tail=left) ys...

Thanks! Based on the HS loop (fixed rolling window) and using @HillGEV, it would be something like the following, however what are the formulae for VaR and ES as positive numbers? comp WIN = 1000 comp SCALE = 100.0 comp CT = 100; * threshold for tail observations *=============================== do ...

Hi Tom, Here's my loop for risk algo Historical Simulation (HS), calculate VaR and ES: *=============================== do i = 1, %allocend() - WIN * clear dlp1 clear y set dlp1 1+i WIN+i = dlp order(index=ix,nodecreasing) dlp1 1+i WIN+i set y 1+i WIN+i = dlp1(ix) comp op = fix(WIN*alpha)+i; * alpha...

Here's an attempt at Block Bootstrap Kupiec , as a minimal procedure. There is a small difference (4th decimal place...) in the results for %%pofbootse from the STATS instruction i.e. all the ndraws of the POF's stored as a vector vs. the Alternative acsum method, not sure why that would be? Please ...