Quantile Regression with Time-Series Models (ARIMA-ARCH) in R

Question

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.

Answer 1

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.

Answer 2

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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.