# auto.arima returns a non-seasonal model even though I am forcing seasonality

Per this post, you can force seasonality in auto.arima by selecting D=1.

I have a weekly time series which looks like it might (or might not) have a seasonal component (I have a priori reasons for thinking it might have a seasonal component).

Data <- as.ts(Data$Sales,order.by=Data$Date, frequency=52)
Train <- window(Data,start=3,end=107)
Test <- window(Data,start=108,end=116)


I tried manually fitting a seasonal model:

fit <- arima(Train, order=c(2,0,1) , seasonal = list (order= c(0,1,0) , period = 52))


gave an "OK" forecast (see first graph).

So I tried improving on it by using auto.arima to find the best model.

AutoFit <- auto.arima(Train)


This returned an ARIMA(1,1,1) model, which I then fit using:

#fit <- arima(Train, order=c(1,1,1))


But this gave worse results than the seasonal model I selected manually (see second graph).

So I tried to force seasonality by running:

AutoFit <- auto.arima(Train, D=1)


But I still get the same ARIMA(1,1,1) model.

Why is auto.arima not trying to fit a seasonal model, even why I try to force it?

I've also tried:

AutoFit <- auto.arima(Train, seasonal=TRUE, D=1)


and

AutoFit <- auto.arima(Train, seasonal=TRUE, start.P=0, start.Q=0 , D=1)


Two things come to mind 1) it is silly to try and fit a seasonal ar model of order 52 to 105 obvservations as you only have 2 cycles of data and 2) see I have correlogram ACF and PACF below for a temperature time series. Can I say it is MA(2) from ACF? What about AR? where ignoring the effect of anomalies is discussed causing a flaw in model identification

• "it is silly to try and fit a seasonal ar model of order 52 to 105 obvservations as you only have 2 cycles of data" : I have a priori reasons for thinking my data might be seasonal, which is why I am trying a seasonal model even though I only have 2 years worth. Based on the graphs the seasonal does seem to work better. – Reinstate Monica Dec 29 '17 at 12:47
• You might try estimating a model including lag 52 and follow stats.stackexchange.com/questions/319254/… for ways to improve that model . Alternatively you might set up a regression model with 51 weekly dummies and again consider model modifications per the url I cited. To a large degree due to the paucity of data , one needs to employ alternative approaches to construct a useful model and not depend on pseudo-automatic approaches designed for larger sample sizes like 10 years of weekly data.. – IrishStat Dec 29 '17 at 13:17