Seasonal Parameter in ARIMA and ADF test

r

#1

Hi…

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…

Thanks…


#2

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
pp.test(ts)
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.
yt=alpha*yt-1+error
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.

Thanks!
Happy Learning!


#3

Hi…
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.
Thanks.


#4

Hi Shan,

Found some resources for you:

Let me know if these help.


#5

Shan , I edited my comment. Please go thru again

thanks!