# Time Trend Analysis

I have ten-year data for crude number of certain events (cases of disease [counts]) from one country. Would it be appropriate to use Poisson regression with dependent variable as number of cases and only one independent variable 'Year' (coded as 2001, 2002 . . . 2010) to test for linear trend over time? Hence, if 'Year' is statistically significant, would it imply linear time trend?

Would this approach ignore the 'serial dependence'?

How/What would be the best way to study trend over time? R/Stata code/packages would really help me please!

• A quick and dirty way of dealing with the serial dependence would be to employ HAC standard errors when testing for the significance of the Year variable. – Richard Hardy Sep 20 '17 at 11:18
• Thanks, could you elaborate a little more please? Would Poisson regression be the right approach? – J. Dow Sep 20 '17 at 11:36
• I don't know at the moment, that is why I have not commented on that part. – Richard Hardy Sep 20 '17 at 11:50

According to the documentation of the glarma package, the glarma modelling function allows you to specify the negative binomial distribution (type = 'NegBin'). This package appears to accommodate both the PAR (Poisson Autoregressive) model and also the NBAR (Negative Binomial Autoregressive) model. I would generally prefer the latter for the same reasons that the negative-binomial is generally preferred for count data in fixed settings without autocorrelation.