# Identification Problem of SARIMA

I am trying to make time series analysis with SARIMA and I have a question. My dataset is a seasonal dataset. I validated that I have stationary series by KPSS test. I also found the following results:

ndiffs(ts) #number of regular difference
 0

nsdiffs(ts) #number of seasonal difference
 1


According to the results, I took the seasonal difference of the dataset, then I drew ACF and PACF of differenced time series:  I think I couldn't make suitable model identification. I thought that following three model could fit the dataset.

SARIMA(1,0,1)(1,1,1) SARIMA(1,0,2)(1,1,1) SARIMA(1,0,3)(1,1,1)

However, when I summary of the three model I got the following results:

Also, I used auto.arima but I found that model is insignificant as well. I think I am missing something because I am very new to this field. Can somebody have an idea?

Edit:

I also used seasonal dummy variables thanks to the advices of @richard As a result of regression, all seasonal dummies are significant and model has 95% R^2 value. When I draw the ACF and PACF functions of residuals of the regression model, I got the following plot:

• @iloloa, ACF and PACF help only in the simplest of cases. auto.arima applied on the original series, with the seasonal dummies in the xreg argument, would be a modern alternative. Nov 21, 2021 at 14:51
• @richard Thank you professor. As you said, I added seasonal dummy variables on my dataset and found that all of the seasonal lags are significant. Then, I applied fit <- auto.arima(ts, xreg=seasonaldummy(ts)) to find suitable model. At this point I have a question: I did not define the linear model on the fit <- auto.arima(ts, xreg=seasonaldummy(ts)). Here, ts represents the time series data. How does auto.arima use the linear model that I found that all the seasonal lags are significant? Nov 24, 2021 at 18:38
• @iloloa, auto.arima does a linear model of ts on seasonaldummy(ts) and then models the error term by ARMA. Thus te linear model is the first part. Nov 24, 2021 at 19:11