Creating an ARIMA model with Specified Lags and differencing in R

Question

Hello I just finished the ARIMA Models in R course in Data Camp and would like run some ARIMA models. the course used the astsa for ARIMA modeling.

For this question I will using the sunspots data though the data does not matter for the question

My packages

library(astsa)

Some data

Sun.ts <- sunspots

This function with run an AR(12) model with all the lags AR1 though AR12

sarima(Sun.ts, p = 12, d = 0, q = 0)

How can I do an AR or even a ARIMA model with say just 12th lag or 1 and 12?

Eventually for a project I will be doing a ARIMA model that should look something like this

sarima(my_data, p = c(12), d = c(1, 12), q = c(1, 12)) 

Where the model is only including those lags in parenthesis. I have done it in SAS but I want to do it in R.

SAS Code that is model I want to do in R

proc arima data=my_data;
   identify var=Deaths(1, 12);
   estimate  p = (12) q = (1) (12) noint method=ml;
run;

Answer 1

Hello for the sarima function you need to use the fixed argument to specify which coefficients you want.

That is done by making a vector of NAs and not NAs. So for example I wanted a AR(1,12) model so I would need to make a vector that looks like this. With NA is the 1st index and NA in the 12th index. The last index being for the constant and if there is not a constant it needs to be blank.

fixed_constant   <- c(NA,0,0,0,0,0,0,0,0,0,0,NA,NA)
fixed_noconstant <- c(NA,0,0,0,0,0,0,0,0,0,0,NA) #No Constant 

Then use the sarima function.

sarima(Sun.ts, p = 12, d = 0,q = 0, fixed = fixed_constant, no.constant = F)

Then without the constant

sarima(Sun.ts, p = 12, d = 0,q = 0, fixed = fixed_noconstant, no.constant = T)

I created an helper function to make parsimonious ARIMA models. This can be easily extended for the sarima.for

psarima <- function(tsdata, p, d, q, no.constant = FALSE){

pt = max(p)
qt = max(q)

pvector<- rep(0,pt)
qvector <- rep(0,qt)
for (i in p){
  pvector[i] <- NA
}
for (i in q){
  qvector[i] <- NA
}
if (no.constant == T | d > 1){
  intercept <- NULL
} else{
  intercept <- NA
}
parameters<- c(pvector,qvector,intercept)
sarima(tsdata,pt,d,qt, fixed = parameters, no.constant = no.constant)
}

p for parsimonious sarima.

In action This is an ARIMA with AR(12) and MA(2,3).

psarima(Sun.ts,c(12),0,c(2,3), no.constant = F) 

I am still learning about ARIMA models but for some reason doing this doesn't work.

psarima(Sun.ts,1,2,c(2,3), no.constant = F)

Error in optim(init[mask], armafn, method = optim.method, hessian = TRUE,  : 
  non-finite finite-difference value [1]

Which I am not sure what is happening to make that occur. It has to do with differencing though.