Time series analysis and seasonal variation

[Koen Blot]

Dear Statalist members,

I am working with surveillance data of quarterly hospital infections (incidence rate calculated per number of patient days). When plotting the data as a line graph there appears to be an important cyclical change with spikes in incidence in the 3rd trimester (figures 1 & 2). I wish to identify whether the spikes in the 3rd trimester are significant after correcting for temporal autocorrelation. An ARIMA model to correct for autoregression and moving averages will help model the infectious disease incidence:

arima GNrate, arima(1,0,0) sarima(2,0,0,4)
(for output see figure 3)

Is it correct to add the variable trimester3 (1 if data comes from trimester 3 – 0 if data comes from trimester 1, 2 or 4) into the ARIMA model? And if it is significant, is that enough evidence to conclude that seasonality is present? Or am I to interpret the coefficients themselves as evidence of seasonality?

arima GNrate trim3, arima(1,0,0) sarima(2,0,0,4)

Thanks in advance

Figure 1


Figure 2


Figure 3


(Apologies if this is a duplicate, after editing my original post it appeared to disappear from the forum)

[Nick Cox]

There seems to be more structure in your data than just quarter 3 being higher; clearly the other quarters are not identical in their means. So, depending on what you want to do, fitting indicator variables for all the quarters seems a natural first start, except that Stata will only use three of them. Whether there is extra structure apart from that is an open question.