ARIMA model

[waynelapierre]

I am looking for an ARIMA package in Julia. I want to make sure fitting an ARIMA(1, 0, 1) is coded as

model = SARIMA(data, order = (1, 0, 1))

fit!(model)

[guilhermebodin]

It is! 👍🏻 Also equivalent to an ARMA(1, 1)

[waynelapierre]

I find it much slower than the R package forecast's ARIMA function. How can I increase it speed?

[guilhermebodin]

Can you post both R and Julia codes?

[waynelapierre]

R

require(forecast)
data <- rnorm(1000000000)
system.time(arima(data, c(1, 0, 1)))

Julia

using StateSpaceModels
data = randn(1_000_000_000)
model = SARIMA(data, order = (1, 0, 1))
@time fit!(model)

[guilhermebodin]

I think the problem is the time to first plot issue, for more information please see https://discourse.julialang.org/t/roadmap-for-a-faster-time-to-first-plot/22956/16.

One possible solution is to make the first fit! with a small part of the time series. Also note that @time should be called twice to give the better idea of the code performance after compilation https://docs.julialang.org/en/v1/manual/performance-tips/#Measure-performance-with-[@time](@ref)-and-pay-attention-to-memory-allocation

julia> using StateSpaceModels

julia> data = randn(100);

julia> model = SARIMA(data, order = (1, 0, 1))
SARIMA(1, 0, 1)x(0, 0, 0, 0) model

julia> @time fit!(model)
 16.776509 seconds (56.96 M allocations: 2.864 GiB, 8.90% gc time)
SARIMA(1, 0, 1)x(0, 0, 0, 0) model

julia> @time fit!(model)
  0.002102 seconds (4.01 k allocations: 450.500 KiB)
SARIMA(1, 0, 1)x(0, 0, 0, 0) model

julia> data = randn(100_000);

julia> model = SARIMA(data, order = (1, 0, 1))
SARIMA(1, 0, 1)x(0, 0, 0, 0) model

julia> @time fit!(model)
  0.692014 seconds (5.93 k allocations: 23.525 MiB, 1.28% gc time)
SARIMA(1, 0, 1)x(0, 0, 0, 0) model

> require(forecast)
> data <- rnorm(100000)
> system.time(arima(data, c(1, 0, 1)))
  usuário   sistema decorrido 
    4.219     0.474     4.952 
Warning message:
In arima(data, c(1, 0, 1)) :
  possible convergence problem: optim gave code = 1

For 100000 observations the Julia code seems to be faster than forecast.

[waynelapierre]

My understanding is that precompilation time is fixed. For computationally intensive tasks, there is no need to warm up a function with smaller data. You seem to suggest the precompilation time is not fixed.

[guilhermebodin]

Honestly I am not sure if the precompilation time is fixed, but it is a good practice to keep the results from the second time you run @time.

I think it is fairer to compare the times after the precompilation is done. To be even fairer we should benchmark the packages in the same data. StateSpaceModels.jl might also not be faster than R forecast in all cases, which uses C++ under the hood. In all cases the estimation times of the packages are comparable.

I ran for 10M observations this time

julia> data = randn(10_000_000);
er = (1, 0, 1))
@time fit!(model)

julia> model = SARIMA(data, order = (1, 0, 1))
SARIMA(1, 0, 1)x(0, 0, 0, 0) model

julia> @time fit!(model)
 32.786926 seconds (2.80 k allocations: 2.175 GiB, 2.53% gc time)
SARIMA(1, 0, 1)x(0, 0, 0, 0) model

> data <- rnorm(10000000)
system.time(arima(data, c(1, 0, 1)))
> system.time(arima(data, c(1, 0, 1)))
  usuário   sistema decorrido 
   35.186     1.274    38.186

[waynelapierre]

Thanks for your explanation! I really like your great package. The name SpaceStateModels scared me off when I was trying to find an ARIMA modeling package in Julia. I have no idea what space state models mean. By reading the documents, I find it offers many common time series modeling functions. This package seems to be much more general than its name suggests.

[guilhermebodin]

I agree that the name is not super accurate, it is closer to R forecast than from any control toolbox. Thank you for your feedback, I am always happy to see people using it :)