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.
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I used the forecast package to forecast the daily time-series of variable Y using its lag values and a time series of an external parameter X. I found nnetar model (a NARX model) was the best in terms of overall performance. However, I was not able to get the prediction of peaks of the time series well despite my various attempts with parameter tuning.
I then extracted the peak values (above a threshold) of Y (and of course this is not a regular time series anymore) and corresponding X values and tried to fit a regression model (note: not an autoregression model) using various models in carat package. I found out the prediction of peak values using brnn(Bidirectional recurrent neural networks) model just using X values is better than that of nnetar which uses both lag values and X values.
Now my question is how do I go from here to create ensamples of these two models (i.e whenever the prediction using brnn regression model ( or any other regression model) is better I want to replace the prediction using nnetar and move forward - I am mostly concerned about the peaks)? Is this a commonly used approach?
Instead of trying to pick one model that would be the superior at anytime, it's typically better to do an average of the models, in order to include as many individual views as possible.
In the experiments I've been involved in, where we tried to pick one model that would outperform, based on historical performance, it's typically shown that a simple average was as good or better. Which is in line with the typical results on this problem: https://otexts.com/fpp2/combinations.html
So, before you try to go more advanced at it by using trying to pick a specific model based on previous performance, or by using an weighted average, consider doing a simple average of the two models.
If you want to continue with a sort of selection/weighted averaging, try to have a look at the FFORMA package in R: https://github.com/pmontman/fforma
I've not tried the specific package (yet), but have seen promising results in my test using the original m4metalearning package.
As you might be able to tell from the sample of my dataset, it contains a lot of dependency, with each study providing multiple outcomes for the construct I am looking at. I was planning on using the metacor library because I only have information about the sample size but not variance. However, all methods I came across to that deal with dependency such as the package rubometa use variance (I know some people average the effect size for the study but I read that tends to produce larger error rates). Do you know if there is an equivalent package that uses only sample size or is it mathematically impossible to determine the weights without it?
Please note that I am a student, no expert.
You could use the escalc function of the metafor package to calculate variances for each effect size. In the case of correlations, it only needs the raw correlation coefficients and the corresponding sample sizes.
See section "Outcome Measures for Variable Association" # https://www.rdocumentation.org/packages/metafor/versions/2.1-0/topics/escalc
I am currently using the Marima package for R invented by Henrik Spliid in order to forecast multivariate time series with ARIMA.
Overview can be found here:
https://cran.r-project.org/web/packages/marima/marima.pdf
http://orbit.dtu.dk/files/123996117/marima.anv.talk.pdf
When using the Marima function, it is required to define both the order of AR(p) and MA(q) first.
My question is, how can I determine appropriate values for p and q?
I know when it comes to univariate ARIMA analysis, that auto.arima gives a good suggestion for p and q. However, when I use auto.arima for every single univariate time series I want to analyze, there are (slightly) different suggestions for each time series. (For example (2,2,1) for the first, (1,1,1) for the second and so on)
Since I want to analyze all of the time series combined in the multivariate ARIMA model and I only can choose one value for each p and q (if I understood it correctly), I wonder how I can choose those values the most accurate way.
Could I just try to run the model a couple times and see what values for p and q work best (e.g. by testing the residuals of the forecast)?
What are your suggestions?
I would appreciate any help!
I hope I have come to the right forum. I'm an ecologist making species distribution models using the maxent (version 3.3.3, http://www.cs.princeton.edu/~schapire/maxent/) function in R, through the dismo package. I have used the argument "replicates = 5" which tells maxent to do a 5-fold cross-validation. When running maxent from the maxent.jar file directly (the maxent software), an html file with statistics will be made, including the prediction maps. In R, an html file is also made, but the prediction maps have to be extracted afterwards, using the function "predict" in the dismo package in r. When I do this, I get 5 maps, due to the 5-fold cross-validation setting. However, (and this is the problem) I want only one output map, one "summary" prediction map. I assume this is possible, although I don't know how maxent computes it. The maxent tutorial (see link above) says that:
"...you may want to avoid eating up disk space by turning off the “write output grids” option, which will suppress writing of output grids for the replicate runs, so that you only get the summary statistics grids (avg, stderr etc.)."
A list of arguments that can be put into R is found in this forum https://groups.google.com/forum/#!topic/maxent/yRBlvZ1_9rQ.
I have tried to use the argument "outputgrids=FALSE" both in the maxent function itself, and in the predict function, but it doesn't work. I still get 5 maps, even though I don't get any errors in R.
So my question is: How do I get one "summary" prediction map instead of the five prediction maps that results from the cross-validation?
I hope someone can help me with this, I am really stuck and haven't found any answers anywhere on the internet. Not even a discussion about this. Hope my question is clear. This is the R-script that I use:
model1<-maxent(x=predvars, p=presence_points, a=target_group_absence, path="//home//...//model1", args=c("replicates=5", "outputgrids=FALSE"))
model1map<-predict(model1, predvars, filename="//home//...//model1map.tif", outputgrids=FALSE)
Best regards,
Kristin
Sorry to be the bearer of bad news, but based on the source code, it looks like Dismo's predict function does not have the ability to generate a summary map.
Nitty-gritty details for those who care: When you call maxent with replicates set to something greater than 1, the maxent function returns a MaxEntReplicates object, rather than a normal MaxEnt object. When predict receives a MaxEntReplicates object, it just iterates through all of the models that it contains and calls predict on them individually.
So, what next? Fortunately, all is not lost! The reason that Dismo doesn't have this functionality is that for most kinds of model-building, there isn't actually a valid way to average parameters across your cross-validation models. I don't want to go so far as to say that that's definitely the case for MaxEnt specifically, but I suspect it is. As such, cross-validation is usually used more as a way of checking that your model building methodology works for your data than as a way of building your model directly (see this question for further discussion of that point). After verifying via cross-validation that models built using a given procedure seem to be accurate for the phenomenon you're modelling, it's customary to build a final model using all of your data. In theory this new model should only be better than models trained on a subset of your data.
So basically, assuming your cross-validated models look reasonable, you can run MaxEnt again with only one replicate. Your final result will be a model accuracy estimate based on the cross-validation and a map based on the second run with all of your data lumped together. Depending on what exactly your question is, there might be other useful summary statistics from the cross-validation that you want to use, but those are all things you've already seen in the html output.
I may have found this a couple of years later. But you could do something like this:
xm <- maxent(predictors, pres_train) # basically the maxent model
px <- predict(predictors, xm, ext=ext, progress= '' ) #prediction
px2 <- predict(predictors, xm2, ext=ext, progress= '' ) #prediction #02
models <- stack(px,px2) # create a stack of prediction from all the models
final_map <- mean(px,px2) # Take a mean of all the prediction
plot(final_map) #plot the averaged map
xm1,xm2,.. would be the maxent models for each partitions in cross-validation, and px, px2,.. would be the predicted maps.
I'm using the fourier() and fourierf() functions in Ron Hyndman's excellent forecast package in R. Looking to verify whether the same terms are selected and used in fourier() and fourierf(), I plotted a few of the output terms.
Below is the original data using ts.plot(data). There's a frequency of 364 in the time series, FYI.
Below is the plot of the terms using fourier(data,3). Basically, it looks like mirror images of the existing data.
Looking at just the sin1 term of the output, again, we get some variation that shows similar 364-day seasonality in line with the data above.
However, when I plot the results of the Fourier forecast using fourierf(data,3, 410) I see the below data. It appears far more smooth than the terms provided by the original fourier function.
So, I wonder how the results of fourier() and fourierf() are related. Is it possible to just see one consolidated Fourier result, so that you can see the sin or cosine result moving through existing data and then through the forecasting period? If not, how can I confirm that the terms created by fourierf() fit the in-sample data?
I want to use it in an auto.arima or glm function with other external regressors like this:
trainFourier<-fourier(data,3)
trainFourier<-as.data.frame(trainFourier)
trainFourier$exogenous<-exogenousData
arima.object<-auto.arima(data, xreg=trainFourier)
futureFourier<-fourierf(data,3, 410)
fourierForecast<-forecast(arima.object, xreg=futureFourier, h=410)
and want to be completely sure that the auto.arima has the proper fitting (using the terms from fourier()) to what I'll put in under xreg for forecast (which has terms from a different function, i.e. ffourier()).
Figured out the problem. I was using both the fda and forecast packages. fda, which is for functional data analysis and regression, has its own fourier() function. If I detach fda, my S1 term from fourier(data,3) looks like this:
which lines up nicely with the Fourier forecast if I use ts.plot(c(trainFourier$S1,futureFourier$S1))
Moral of the story -- watch what your packages supress, folks!