how to extract integration order (d) from auto.arima - r

Question

basically we can extract optimum AR order from auto.arima by
> auto.arima(ret.fin.chn,trace=TRUE,allowdrift=TRUE)
ARIMA(2,0,2) with non-zero mean : -14242.19
ARIMA(0,0,0) with non-zero mean : -14239.24
ARIMA(1,0,0) with non-zero mean : -14241.3
ARIMA(0,0,1) with non-zero mean : -14238.16
ARIMA(1,0,2) with non-zero mean : -14237.65
ARIMA(3,0,2) with non-zero mean : -14242.72
ARIMA(3,0,1) with non-zero mean : -14239.52
ARIMA(3,0,3) with non-zero mean : -14242.5
ARIMA(2,0,1) with non-zero mean : -14237.15
ARIMA(4,0,3) with non-zero mean : -14238.06
ARIMA(3,0,2) with zero mean : -14244.39
ARIMA(2,0,2) with zero mean : -14243.98
ARIMA(4,0,2) with zero mean : -14241.45
ARIMA(3,0,1) with zero mean : -14241.23
ARIMA(3,0,3) with zero mean : -14244.04
ARIMA(2,0,1) with zero mean : -14238.78
ARIMA(4,0,3) with zero mean : -14239.73
Best model: ARIMA(3,0,2) with zero mean
Series: ret.fin.chn
ARIMA(3,0,2) with zero mean
Coefficients:
ar1 ar2 ar3 ma1 ma2
0.5497 -0.4887 0.0461 -0.5691 0.4923
s.e. 0.3525 0.1764 0.0232 0.3534 0.1878
sigma^2 estimated as 0.0003277: log likelihood=7127.67
AIC=-14243.35 AICc=-14243.32 BIC=-14207.83
Warning messages:
1: In if (is.constant(x)) { :
the condition has length > 1 and only the first element will be used
2: In if (is.constant(x)) return(d) :
the condition has length > 1 and only the first element will be used
3: In if (is.constant(dx)) { :
the condition has length > 1 and only the first element will be used
now store the result to object a
> a<-auto.arima(ts(ret.fin.chn),trace=TRUE,allowdrift=TRUE)
then
> a$arma[1]
while for optimum MA order by
> a$arma[2]
now look at this part Best model: ARIMA(3,0,2) with zero mean
this is the ARIMA(p,d,q) order
i've known how to extract the AR(p) and MA(q) order but how to extract the Integration(d) order and note in mind that i've tried the ndiffs and sometimes it gives different result than the best model perhaps it's somewhere in $arma[?]???

Answer 1

More generally, the order (d) is the next to last element; the seasonal order (D) is the last. So-
a$arma[length(a$arma)-1] is the order d
a$arma[length(a$arma)] is the seasonal order

Answer 2

As pointed out by Rob Hyndman, one of the authors of the forecast package, in an answer to a similar question on Cross Validated, an easy way to extract the order vector (p,d,q) is to use the forecast::arimaorder function.
In your example, this would work as follows:
arimaorder(a)
The output is a named integer with the values of p, d and q:
p d q
3 0 2

Answer 3

You can see from the help file of arima under Value (auto.arima has the same Value as arima)
arma
A compact form of the specification, as a vector giving the number of AR, MA, seasonal AR and seasonal MA coefficients, plus the period and the number of non-seasonal and seasonal differences.
So value a$arma[6] contains non-seasonal difference and a$arma[7] contains seasonal difference.

Answer 4

I'm really sorry Metrics it seems that your solution isn't quite right
> auto.arima(fin.gre,trace=TRUE,allowdrift=TRUE)$arma
ARIMA(2,2,2) : 26148.84
ARIMA(0,2,0) : 27846.32
ARIMA(1,2,0) : 27209.88
ARIMA(0,2,1) : 26161.36
ARIMA(1,2,2) : 26146.27
ARIMA(1,2,1) : 26144.37
ARIMA(1,2,1) : 26144.37
ARIMA(2,2,1) : 26146.69
Best model: ARIMA(1,2,1)
a<-auto.arima(fin.gre,trace=TRUE,allowdrift=TRUE)
a$arma
[1] 1 1 0 0 1 2 0
while doing str(a) yields
> str(a)
List of 16
$ coef : Named num [1:2] 0.0715 -0.9969
..- attr(*, "names")= chr [1:2] "ar1" "ma1"
$ sigma2 : num 795
$ var.coef : num [1:2, 1:2] 3.65e-04 -3.19e-06 -3.19e-06 3.39e-06
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:2] "ar1" "ma1"
.. ..$ : chr [1:2] "ar1" "ma1"
$ mask : logi [1:2] TRUE TRUE
$ loglik : num -13078
$ aic : num 26162
$ arma : int [1:7] 1 1 0 0 1 2 0
$ residuals: Time-Series [1:2750] from 1 to 2750: 0.39 -1.15 -3.64 -4.65 -11.57 ...
$ call : language auto.arima(x = structure(list(x = c(872.5, 880.78, 884.1, 884.1, 874.45, 855.3, 844.81, 837.14, 828.08, 830.74, 835.36, 839.25, 819.54, 802.27, 798.25, 793.01, 816.43, 831.87, ...
$ series : chr "fin.gre"
$ code : int 0
$ n.cond : int 0
$ model :List of 10
..$ phi : num 0.0715
..$ theta: num -0.997
..$ Delta: num [1:2] 2 -1
..$ Z : num [1:4] 1 0 2 -1
..$ a : num [1:4] 1.01 -1.72 62.87 62.78
..$ P : num [1:4, 1:4] -2.22e-16 2.21e-16 1.74e-16 4.62e-17 2.21e-16 ...
..$ T : num [1:4, 1:4] 0.0715 0 1 0 1 ...
..$ V : num [1:4, 1:4] 1 -0.997 0 0 -0.997 ...
..$ h : num 0
..$ Pn : num [1:4, 1:4] 1.00 -9.97e-01 9.51e-17 1.71e-16 -9.97e-01 ...
$ bic : num 26180
$ aicc : num 26162
$ x :An ‘xts’ object on 2003-01-01/2013-07-16 containing:
Data: num [1:2750, 1] 872 881 884 884 874 ...
Indexed by objects of class: [Date] TZ: UTC
xts Attributes:
NULL
- attr(*, "class")= chr "Arima"
as you can see the $model[3] contain two number from $arma[5] and $arma[6]it seems that $arma[5] represent integration order d, but im not really sure about it