How to represent an ARIMA(p,d,q) with dlm package in R? - r
I've been using DLM package for modeling my timeseries in state-space format, and then use Kalman Filter to get better 2 step-ahead forecasts.
Even though I've read the vignette and parts of their book, I'm still struggling when it comes to modeling my ARIMA process in state-space format, specifically as the dlm package understands it. My plan is to use auto.arima() to get the best arima model, then represent it as a dlm.
I've seen examples like this.
# Estimation of a state space representation of Arima(1,1,1) model and forecast:
level0 <- data.s.g[1]
slope0 <- mean(diff(data.s.g))
buildGap <- function(u) {
trend <- dlmModPoly(dV = 1e-7, dW = exp(u[1 : 2]),
m0 = c(level0, slope0),
C0 = 2 * diag(2))
gap <- dlmModARMA(ar = ARtransPars(u[4]),ma=u[5], sigma2 = exp(u[3]))
return(trend + gap)}
and the dlmModARMA part seems clear. What is baffling me is, what to do if I want to get for example ARIMA(1,3,1); how would I represent that 3 differencing part?
Related
Is it possible to adapt standard prediction interval code for dlm in R with other distribution?
Using the dlm package in R I fit a dynamic linear model to a time series data set, consisting of 20 observations. I then use the dlmForecast function to predict future values (which I can validate against the genuine data for said period).
I use the following code to create a prediction interval;
ciTheory <- (outer(sapply(fut1$Q, FUN=function(x) sqrt(diag(x))), qnorm(c(0.05,0.95))) +
as.vector(t(fut1$f)))
However my data does not follow a normal distribution and I wondered whether it would be possible to
adapt the qnorm function for other distributions. I have tried qt, but am unable to apply qgamma.......
Just wondered if anyone knew how you would go about sorting this.....
Below is a reproduced version of my code...
library(dlm)
data <- c(20.68502, 17.28549, 12.18363, 13.53479, 15.38779, 16.14770, 20.17536, 43.39321, 42.91027, 49.41402, 59.22262, 55.42043)
mod.build <- function(par) {
dlmModPoly(1, dV = exp(par[1]), dW = exp(par[2]))
}
# Returns most likely estimate of relevant values for parameters
mle <- dlmMLE(a2, rep(0,2), mod.build); #nileMLE$conv
if(mle$convergence==0) print("converged") else print("did not converge")
mod1 <- dlmModPoly(dV = v, dW = c(0, w))
mod1Filt <- dlmFilter(a1, mod1)
fut1 <- dlmForecast(mod1Filt, n = 7)
Cheers
IV Estimation with Cluster Robust Standard Errors using the plm package in R
I'm using the plm package for panel data to do instrumental variable estimation. However, it seems that calculating cluster robust standard errors by using the vcovHC() function is not supported.
More specifically, when I use the vcovHC() function, the following error message is displayed:
Error in vcovG.plm(x, type = type, cluster = cluster, l = 0, inner = >inner, :
Method not available for IV
Example:
data("Wages", package = "plm")
IV <- plm(lwage ~ south + exp | wks + south,
data = Wages, model = "pooling", index = 595)
vcvIV <- vcovHC(IV)
According to this thread, someone worked on a fix two years ago. Is there any progress on the issue? I know that the packages "lfe" and "ivpack" allow to compute cluster robust standard errors for IV estimation but none of them allows for random effects/intercepts.
In fact it's not implemented. However, you can use Schrimpf's clustered errors function which is applied directly to a object of the plm class.
Using your example:
library (plm)
data("Wages", package = "plm")
IV <- plm(lwage ~ south + exp | wks + south, data = Wages, model = "pooling", index = 595)
Wages$id <- rep(1:595, each = 7)
cl.plm(Wages, IV, Wages$id)
Where I'm using Wages$idas the panel first dimension around which clusters will be formed. You may want to compare these results with the obtained in other software. Anyway, the code is simple allowing some tricks. The cl.plm function is based on Arai's clustering notes which can help you further.
You can obtain the same result from cl.plm doing this in Stata:
ivregress 2sls lwage south (exp = wks), vce(cluster id) small
Or for the within model:
xtset id time, generic
xtivreg2 lwage south (exp = wks), fe small cluster(id)
Note however I used the small sample formulation in Stata, which is not big deal. More about this here. Anyway, cl.plm properly deals with the plm class object.
For sake of completeness: as suggested by #Helix123, you can use the development version (1.6-1) of plm package and proceed as you did in tour question.
arima model for multiple seasonalities in R
I'm learning to create a forecasting model for time series that has multiple seasonalities. Following is the subset of dataset that I'm refering to. This dataset includes hourly data points and I wish to include daily as well as weekly seasonalities in my arima model. Following is the subset of dataset:
data= c(4,4,1,2,6,21,105,257,291,172,72,10,35,42,77,72,133,192,122,59,29,25,24,5,7,3,3,0,7,15,91,230,284,147,67,53,54,55,63,73,114,154,137,57,27,31,25,11,4,4,4,2,7,18,68,218,251,131,71,43,55,62,63,80,120,144,107,42,27,11,10,16,8,10,7,1,4,3,12,17,58,59,68,76,91,95,89,115,107,107,41,40,25,18,14,15,6,12,2,4,1,6,9,14,43,67,67,94,100,129,126,122,132,118,68,26,19,12,9,5,4,2,5,1,3,16,89,233,304,174,53,55,53,52,59,92,117,214,139,73,37,28,15,11,8,1,2,5,4,22,103,258,317,163,58,29,37,46,54,62,95,197,152,58,32,30,17,9,8,1,3,1,3,16,109,245,302,156,53,34,47,46,54,65,102,155,116,51,30,24,17,10,7,4,8,0,11,0,2,225,282,141,4,87,44,60,52,74,135,157,113,57,44,26,29,17,8,7,4,4,2,10,57,125,182,100,33,27,41,39,35,50,69,92,66,30,11,10,11,9,6,5,10,4,1,7,9,17,24,21,29,28,48,38,30,21,26,25,35,10,9,4,4,4,3,5,4,4,4,3,5,10,16,28,47,63,40,49,28,22,18,27,18,10,5,8,7,3,2,2,4,1,4,19,59,167,235,130,57,45,46,42,40,49,64,96,54,27,17,18,15,7,6,2,3,1,2,21,88,187,253,130,77,47,49,48,53,77,109,147,109,45,41,35,16,13)
The code I'm trying to use is following:
tsdata = ts (data, frequency = 24)
aicvalstemp = NULL
aicvals= NULL
for (i in 1:5) {
for (j in 1:5) {
xreg1 = fourier(tsdata,i,24)
xreg2 = fourier(tsdata,j,168)
xregs = cbind(xreg1,xreg2)
armodel = auto.arima(bike_TS_west, xreg = xregs)
aicvalstemp = cbind(i,j,armodel$aic)
aicvals = rbind(aicvals,aicvalstemp)
}
}
The cbind command in the above command fails because the number of rows in xreg1 and xreg2 are different. I even tried using 1:length(data) argument in the fourier function but that also gave me an error. If someone can rectify the mistakes in the above code to produce a forecast of next 24 hours using an arima model with minimum AIC values, it would be really helpful. Also if you can include datasplitting in your code by creating training and testing data sets, it would be totally awesome. Thanks for your help.
I don't understand the desire to fit a weekly "season" to these data as there is no evidence for one in the data subset you provided. Also, you should really log-transform the data because they do not reflect a Gaussian process as is.
So, here's how you could fit models with a some form of hourly signals.
## the data are not normal, so log transform to meet assumption of Gaussian errors
ln_dat <- log(tsdata)
## number of hours to forecast
hrs_out <- 24
## max number of Fourier terms
max_F <- 5
## empty list for model fits
mod_res <- vector("list", max_F)
## fit models with increasing Fourier terms
for (i in 1:max_F) {
xreg <- fourier(ln_dat,i)
mod_res[[i]] <- auto.arima(tsdata, xreg = xreg)
}
## table of AIC results
aic_tbl <- data.frame(F=seq(max_F), AIC=sapply(mod_res, AIC))
## number of Fourier terms in best model
F_best <- which(aic_tbl$AIC==min(aic_tbl$AIC))
## forecast from best model
fore <- forecast(mod_res[[F_best]], xreg=fourierf(ln_dat,F_best,hrs_out))
Weighted Portmanteau Test for Fitted GARCH process
I have fitted a GARCH process to a time series and analyzed the ACF for squared and absolute residuals to check the model goodness of fit. But I also want to do a formal test and after searching the internet, The Weighted Portmanteau Test (originally by Li and Mak) seems to be the one. It's from the WeightedPortTest package and is one of the few (perhaps the only one?) that properly tests the GARCH residuals. While going through the instructions in various documents I can't wrap my head around what the "h.t" argument wants. It says in the info in R that I need to assign "a numeric vector of the conditional variances". This may be simple to an experienced user, though I'm struggling to understand. What is it that I need to do and preferably how would I code it in R? Thankful for any kind of help
Taken directly from the documentation: h.t: a numeric vector of the conditional variances A little toy example using the fGarch package follows: library(fGarch) library(WeightedPortTest) spec <- garchSpec(model = list(alpha = 0.6, beta = 0)) simGarch11 <- garchSim(spec, n = 300) fit <- garchFit(formula = ~ garch(1, 0), data = simGarch11) Weighted.LM.test(fit#residuals, fit#h.t, lag = 10) And using garch() from the tseries package: library(tseries) fit2 <- garch(as.numeric(simGarch11), order = c(0, 1)) summary(fit2) # comparison of fitted values: tail(fit2$fitted.values[,1]^2) tail(fit#h.t) # comparison of residuals after unstandardizing: unstd <- fit2$residuals*fit2$fitted.values[,1] tail(unstd) tail(fit#residuals) Weighted.LM.test(unstd, fit2$fitted.values[,1]^2, lag = 10)
Using r and weka. How can I use meta-algorithms along with nfold evaluation method?
Here is an example of my problem
library(RWeka)
iris <- read.arff("iris.arff")
Perform nfolds to obtain the proper accuracy of the classifier.
m<-J48(class~., data=iris)
e<-evaluate_Weka_classifier(m,numFolds = 5)
summary(e)
The results provided here are obtained by building the model with a part of the dataset and testing it with another part, therefore provides accurate precision
Now I Perform AdaBoost to optimize the parameters of the classifier
m2 <- AdaBoostM1(class ~. , data = temp ,control = Weka_control(W = list(J48, M = 30)))
summary(m2)
The results provided here are obtained by using the same dataset for building the model and also the same ones used for evaluating it, therefore the accuracy is not representative of real life precision in which we use other instances to be evaluated by the model. Nevertheless this procedure is helpful for optimizing the model that is built.
The main problem is that I can not optimize the model built, and at the same time test it with data that was not used to build the model, or just use a nfold validation method to obtain the proper accuracy.
I guess you misinterprete the function of evaluate_Weka_classifier. In both cases, evaluate_Weka_classifier does only the cross-validation based on the training data. It doesn't change the model itself. Compare the confusion matrices of following code: m<-J48(Species~., data=iris) e<-evaluate_Weka_classifier(m,numFolds = 5) summary(m) e m2 <- AdaBoostM1(Species ~. , data = iris , control = Weka_control(W = list(J48, M = 30))) e2 <- evaluate_Weka_classifier(m2,numFolds = 5) summary(m2) e2 In both cases, the summary gives you the evaluation based on the training data, while the function evaluate_Weka_classifier() gives you the correct crossvalidation. Neither for J48 nor for AdaBoostM1 the model itself gets updated based on the crossvalidation. Now regarding the AdaBoost algorithm itself : In fact, it does use some kind of "weighted crossvalidation" to come to the final classifier. Wrongly classified items are given more weight in the next building step, but the evaluation is done using equal weight for all observations. So using crossvalidation to optimize the result doesn't really fit into the general idea behind the adaptive boosting algorithm. If you want a true crossvalidation using a training set and a evaluation set, you could do the following : id <- sample(1:length(iris$Species),length(iris$Species)*0.5) m3 <- AdaBoostM1(Species ~. , data = iris[id,] , control = Weka_control(W = list(J48, M=5))) e3 <- evaluate_Weka_classifier(m3,numFolds = 5) # true crossvalidation e4 <- evaluate_Weka_classifier(m3,newdata=iris[-id,]) summary(m3) e3 e4 If you want a model that gets updated based on a crossvalidation, you'll have to go to a different algorithm, eg randomForest() from the randomForest package. That collects a set of optimal trees based on crossvalidation. It can be used in combination with the RWeka package as well. edit : corrected code for a true crossvalidation. Using the subset argument has effect in the evaluate_Weka_classifier() as well.