In R, I would like to use rugarch and stabledist/fBasics packages together to fit a univariate time-series object to be modeled as an ARMA(1,1)-GARCH(1,1) process with the innovation term/conditional distribution term being modeled as a stable distribution. Is there a way to to this? given that the fBasics package allows one to have a dstable() function, which I'm guessing would be used to optimise a maximum-likelihood function.
And as a follow up, how would one go about simulating several thousand iterations of x days forward returns assuming it follows the same process. (I'm guessing here using the function rstable() with the parameters estimated above.)
Any other packages that you might think would do the job better would gladly be looked at as well.
Yes, you can use dstable and rstable, but they come from package stabledist...
If you want to estimate the stable parameters, you can use
fBasics::stableFit(data, type="mle")
to give you MLE estimate, but usually takes few minutes to compute.
Faster, but little less precise is the quantile method (implicit for stableFit, i.e. dont specify the type).
Then if you get the fit, you extract the resulting estimates from result#fit$estiamte and can use it in rstable to draw random variates..
Related
I want to train SVMs in R and I know there are functions such as e1071::tune.svm() that can be used to find the optimal parameters for the SVM. However, it seems there are some formulas out there (e.g. used in this report) that can give you a reasonable estimate of these parameters.
Since a grid-search for the parameters can take quite a lot of time on larger datasets and usually, one has to provide a range of possible values anyway, I wondered whether there is a package that implements formulas to get a quick estimate for the gamma and cost parameters for the SVM?
So far, I've found out that caret::train() might use such an approach to estimate sigma (which should be the reciprocal of 2*gamma^2) but I haven't tried it yet, since other calculations are still running (and will be, probably for the next days). Is there also an implementation to estimate cost or at least give a range of reasonable values?
I have found a similar question that asks for alternatives to grid-search in general. However, I would be interested in an R implementation of such alternatives and also, I hope things have developed further since the more general question was posted years ago.
The packages that calculate AUCs I've found so far do not contemplate sample clustering, which increases standard errors compared to simple random sampling. I wonder if the ones provided by these packages could be recalculated to allow for clustering.
Thank you.
Your best bet is probably replicate weights, as long as you can get point estimates of AUC that incorporate weights.
If you convert your design into a replicate-weights design object (using survey::as.svrepdesign()), you can then run any R function or expression using the replicate weights using survey::withReplicates() and return a standard error.
Which are the best metrics to evaluate the fit of a GBM algorithm in R (metrics, graphs, ratios)? And how interpret them?
I think maybe you are overthinking this one! Take a step back and think about what matters... the error. You have forecasted values and you have observed values. the difference tells you most of what you need to know when comparing across models. Basic measures like MSE, MPE, etc. should do fine. If you are looking to refine within a given model, I would recommend taking a look at the gbm documentation. For example, you can pass your gbm model object to summary(), to get the relative influence of each of your variables. Additionally, you can find a lot of information in the documentation, so if you haven't taken a look, I would recommend doing so! I have posted the link at the bottom.
-Carmine
gbm_documentation
I am working on quantile forecasting with time-series data. The model I am using is ARIMA(1,1,2)-ARCH(2) and I am trying to get quantile regression estimates of my data.
So far, I have found "quantreg" package to perform quantile regression, but I have no idea how to put ARIMA-ARCH models as the model formula in function rq.
rq function seems to work for regressions with dependent and independent variables but not for time-series.
Is there some other package that I can put time-series models and do quantile regression in R? Any advice is welcome. Thanks.
I just put an answer on the Data Science forum.
It basically says that most of the ready made packages are using so called exact test based on assumption on the distribution (independent identical normal-Gauss distribution, or wider).
You also have a family of resampling methods in which you simulate a sample with a similar distribution of your observed sample, perform your ARIMA(1,1,2)-ARCH(2) and repeat the process a great number of times. Then you analyze this great number of forecast and measure (as opposed to compute) your confidence intervals.
The resampling methods differs in the way to generate the simulated samples. The most used are:
The Jackknife: in which you "forget" one point, that is you simulate a n samples of size n-1 (if n is the size of the observed sample).
The Bootstrap: in which you simulate a sample by taking n values of the original sample with replacements: some will be taken once, some twice or more, some never,...
It is a (not easy) theorem that the expectation of the confidence intervals, as most of the usual statistical estimators, are the same on the simulated sample than on the original sample. With the difference that you can measure them with a great number of simulations.
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I can try to address your question, although this is hard since you don't provide any code/data. Also, I guess by "put ARIMA-ARCH models" you actually mean that you want to make an integrated series stationary using an ARIMA(1,1,2) plus an ARCH(2) filters.
For an overview of the R time-series capabilities you can refer to the CRAN task list.
You can easily apply these filters in R with an appropriate function.
For instance, you could use the Arima() function from the forecast package, then compute the residuals with residuals() from the stats package. Next, you can use this filtered series as input for the garch() function from the tseries package. Other possibilities are of course possible. Finally, you can apply quantile regression on this filtered series. For instance, you can check out the dynrq() function from the quantreg package, which allows time-series objects in the data argument.
I can perform a 1 sample t-test in R with the t.test command. This requires actual sets of data. I can't use summary statistics (sample size, sample mean, standard deviation). I can work around this utilizing the BSDA package. But are there any other ways to accomplish this 1-sample-T in R without the BSDA pacakage?
Many ways. I'll list a few:
directly calculate the p-value by computing the statistic and calling pt with that and the df as arguments, as commenters suggest above (it can be done with a single short line in R - ekstroem shows the two-tailed test case; for the one tailed case you wouldn't double it)
alternatively, if it's something you need a lot, you could convert that into a nice robust function, even adding in tests against non-zero mu and confidence intervals if you like. Presumably if you go this route you'' want to take advantage of the functionality built around the htest class
(code and even a reasonably complete function can be found in the answers to this stats.SE question.)
If samples are not huge (smaller than a few million, say), you can simulate data with the exact same mean and standard deviation and call the ordinary t.test function. If m and s and n are the mean, sd and sample size, t.test(scale(rnorm(n))*s+m) should do (it doesn't matter what distribution you use, so runif would suffice). Note the importance of calling scale there. This makes it easy to change your alternative or get a CI without writing more code, but it wouldn't be suitable if you had millions of observations and needed to do it more than a couple of times.
call a function in a different package that will calculate it -- there's at least one or two other such packages (you don't make it clear whether using BSDA was a problem or whether you wanted to avoid packages altogether)