How to present seasonality in time series? I study the temperature related mortality using daily data of 25 years and I am confused about the effect of seasonality. In many papers, the only variable is used to present seasonality is Time (Time=1:length(Data$date)), and day of the week(dow) as factor:
model<-glm(mortality ~ crossbasis_matrix_Temp + ns(Time, df=8*35) + dow,family=quasipoisson,Data)

other papers use day of the year(doy) as factor:
model<-glm(mortality ~ crossbasis_matrix_Temp + ns(Time, df=8*35) + dow + doy ,family=quasipoisson,Data)

and others use a variable called Season
model<-glm(mortality ~ crossbasis_matrix_Temp + ns(Time, df=8*35) + dow + ns (Season, df=3),family=quasipoisson,Data)

I would like to ask what exactly is the variable "Season" and how should I present the seasonality?
 A: There are different methods to handle time and they address seasonality very differently. I assume you are using some form of regression, in which case dummies are most common. I think that the answer to your question is that various authors have different theories about what causes seasonality and thus they model it differently. You have to look into the article, or contact them if its recent, and see why they modeled it the way they did. Its a substantive not statistical issue.
A: Characteristically, seasonality  can be addressed as a simple dummy variable or variables.
Assume, for example, we are living in a factory town which pays every two weeks on Friday.  As a result one would expect to see significantly more spending occurring on Pay Days and following days thereafter (likely an exponential decay pattern, as an example of a distributed lag model).
A more sophisticated look at seasonality is under the guise of a noise model, that can be addressed in the error-in-variables frame (see for, example discussion here, https://www.jstor.org/stable/2285991?seq=1 ).
The cited reference includes a time series analysis perspective.
