An intentionally very fast (S)ARIMA(X) implementation. This intends to be as accurate as possible, overcoming both R and statsforecast implementation of arima, while hopefully also being faster, with a lower memory footprint.
On the roadmap is even more refinements to speed, python bindings, and auto arima functionality akin to R’s forecast::auto.arima.
A simple object oriented R interface exists:
# create a new object
arima_obj <- new(BlazeArima, c(lynx[1:100]), c(4, 0, 1, 0, 0, 0, 1), list(), "Gardner", "CSS-ML", c(TRUE, FALSE, TRUE), 1000000)
# fit model
arima_obj$fit()
# create forecasts
arima_obj$forecast(14, list()) -> cpp_fcst
# showcase of fitted model - this is not a particularly great fit:
plot.ts(c(lynx[91:114]))
lines(c(rep(NA,10), cpp_fcst$forecast), col = "red")
# we can compare this to the R arima implementation:
lines(c(rep(NA,10),predict(arima(c(lynx[1:100]),
order = c(4,0,1), method = "CSS-ML"), 14)$pred),
col = "blue")
There are some cases where our optimizer (we use cppNumericalSolvers) seems to be more accurate than the default R solver:
p <- 2
d <- 1
q <- 1
P <- 2
D <- 1
Q <- 1
season <- 10
use_mean <- TRUE
train <- c(lynx)[1:100]
test <- lynx[101:114]
arima_obj <- new(BlazeArima, train, c(p, d, q, P, D, Q, season), list(), "Gardner", "CSS-ML", c(use_mean, TRUE), 1000000)
arima_obj$fit()
arima_obj$forecast(14, list()) -> cpp_fcst
arima_mod <- arima(train,
order = c(p, d, q), seasonal = list(order = c(P, D, Q), period = season),
include.mean = use_mean,
transform.pars = TRUE, kappa = 1000000, method = "CSS-ML"
)
predict(arima_mod, 14) -> r_fcst
plot.ts(c(lynx)[91:114])
lines(c( rep(NA, 10), cpp_fcst$forecast), col = "red")
lines(c( rep(NA, 10), r_fcst$pred), col = "green")
This could be attributed to numerous factors - R’s optim uses internal parameter scaling for optimizer line searches, whereas we standardize all inputs. optim uses, as far as I can tell, a version of Armijo line-search(TODO: add refs), whereas cppNumericalSolvers can (and is configured here) to use MoreThuente. There are some other differences in implementation, but these, I think, are most important.
This package really follows the ‘I stand on the shoulders of giants’
idea. It would have never been possible without all the careful work put
into R’s arima() implementation done by many member of the R Core Team
and others over the years. I do believe professor Ripley is of
particular note here, and deserves recognition for being one of the
driving forces behind such an awesome project.
I further want to thank the authors of the awesome Eigen C++ template library. This library is one of the silent drivers of much of this computation, particularly the handling of external variables.
Finally, last but not least, I believe the many people who contributed to the great CppNumericalSolvers library deserve recognition. This is the library used for optimization in this package, and it’s relatively straightforward implementation has been a huge boon.