ARFIMAX time series cross validation
Implements a cross validation method for ARFIMAX models
arfimacv(data, indexin, indexout, ar.max = 2, ma.max = 2,
criterion = c("rmse","mae","berkowitzp"),berkowitz.significance = 0.05,
arfima = FALSE, include.mean = NULL, distribution.model = "norm",
cluster = NULL, external.regressors = NULL, solver = "solnp",
solver.control=list(), fit.control=list(), return.best=TRUE)data |
A univariate xts vector. |
indexin |
A list of the training set indices |
indexout |
A list of the testing set indices, the same list length as that of indexin. This should be a numeric index of points immediately after those in the equivalent indexin slot and contiguous (for time series cross validation). |
ar.max |
Maximum AR order to test for. |
ma.max |
Maximum MA order to test for. |
criterion |
The cv criterion on which the forecasts will be tested against the realized values. Currently “rmse”, “mae” and experimentally “berkowitzp” are implemented. The latter is the Berkowitz test p-value (maximized) and should not be used if your indexout set is very small. |
berkowitz.significance |
The significance level at which the Berkowitz test is evaluated at (this has no value at the moment since we are only looking at the p-values, but may be used in futures to instead aggregate across pass-fail). |
arfima |
Can be TRUE, FALSE or NULL in which case it is tested. |
include.mean |
Can be TRUE, FALSE or NULL in which case it is tested. |
cluster |
A cluster object created by calling |
external.regressors |
An xts matrix object containing the pre-lagged external regressors to include in the mean equation with the same indices as those of the data supplied. |
distribution.model |
The distribution density to use for the innovations (defaults to Normal). |
solver |
One of either “nlminb”, “solnp”, “gosolnp” or “nloptr”. |
solver.control |
Control arguments list passed to optimizer. |
fit.control |
Control arguments passed to the fitting routine. |
return.best |
On completion of the cross-validation, should the best model be re-estimated on the complete dataset and returned (defaults to TRUE). |
The function evaluates all possible combinations of the ARFIMAX model for all the training and testing sets supplied. For the ARMA orders, the orders are evaluated fully (e.g. for ar.max=2, all possible combinations are evaluated including AR(0,0), AR(0,1), AR(0,2), AR(1,0), AR(2,0) AR(1,2), AR(2,1), and AR(2,2)). For each training set in indexin, all model combinations are evaluated and the 1-ahead rolling forecast for the indexout testing set is produced and compared to the realized values under the 3 criteria listed. Once all training/testing is done on all model combinations, the criteria are averaged across all the sets for each combination and the results returned.
A list with the following items:
bestmodel |
The best model based on the criterion chosen is re-estimated on the complete data set and returned. |
cv_matrix |
The model combinations and their average criteria statistics across the training/testing sets. |
Use a cluster...this is an expensive computation, particularly for large ar.max and ma.max orders. The indexin and indexout lists are left to the user to decide how to implement.
Alexios Ghalanos
## Not run:
require(xts)
require(parallel)
data(sp500ret)
spx = as.xts(sp500ret)
nn = nrow(spx)
nx = nn-round(0.9*nn,0)
if(nx
h = (nx/50)-1
indexin = lapply(1:h, function(j){ tail(seq(1,(nn-nx)+j*50, by=1),250) })
indexout = lapply(indexin, function(x){ (tail(x,1)+1):(tail(x,1)+50) })
cl = makePSOCKcluster(5)
mod = arfimacv(spx, indexin, indexout, ar.max = 2, ma.max = 2,
criterion = c("rmse","mae","berkowitzp")[1],
berkowitz.significance = 0.05, arfima = FALSE, include.mean = NULL,
distribution.model = "norm", cluster = cl, external.regressors = NULL,
solver = "solnp")
stopCluster(cl)
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.