Seasonal Parameter in ARIMA and ADF test




While performing ARIMA in R , on data AirPassengers , we can write :
fit <- arima(log(AirPassengers), c(0, 1, 1),seasonal = list(order = c(0, 1, 1), period = 12)))

We can get the values of (p,d,q) from ACF and PACF plots .
Wondering what seasonal = list(order = c(0, 1, 1) signifies.
How we get the values that get passed in the seasonal parameter. An explanation with example will be helpful.

while performing adf we can write
adf.test(diff(log(AirPassengers)), alternative=”stationary”, k=0)
What is k , and how can we identify the value of k while performing the test…



Hi shan,

Really liked the questions that you have put here on discussion forum- shows the curiosity and willingness to know the concepts.

in ARIMA model , we have to determine the order of p,d and q , which we can be known using ACF and PACF plots.

while in SARIMA model, which consider a model equation for pattern when seasonality itself, we determine the seasonal order also i,e, P,D,Q . by looking at the acf and pacf only one can see if the plots showing some upward and downward pattern or rising and diminishing after a particular lag.

so incase of monthly data if the order of SRIMA is (1,0,0)12 - then one could say yt is dependent on yt-12

coming to your next question. First I would suggest that never go for a single Unit Root test atleast try different function also to confirm the hypothesis.
Here are some other functions for stationarity in R
kpss.test() . before using any test , just aware of the Null hypothesis defined in it. As kpss() has null hypothesis to be stationary series.

here parameter k is the number of lags taken to do unit root test. It means every function for stationarity confirms a series to be stationary to a certain value of lag.

for stationary, a test has to be done using a regression fit which is here,incase, of time series an auto regression i.e.lagged value of series . and hypothesis is that coefficient of lagged variable should not be 1.
alpha should not be 1.
for more explanation please refer complete tutorial on time series provided by AV.

Please pardon me for any mistake.
Hope it would be helpful a bit.

Happy Learning!


Thanks for the response. In the following model :

fit <- arima(log(AirPassengers), c(0, 1, 1),seasonal = list(order = c(0, 1, 1), period = 12)))

how we determine what value to pass in seasonal parameter?
Interestingly, p,d,q here is c(0,1,1) which we can find through ACF PACF.
I have searched some R documentation but could not find much about seasonal parameter in arima function.
Suggestions on above will be helpful.


Hi Shan,

Found some resources for you:

Let me know if these help.


Shan , I edited my comment. Please go thru again