I would like some advise on how I should analyse my time series data.
I have hourly measurements of water temperature data for 5 months across 5 sites.
I have summarized my data in following way
1.Site(5 sites)
2.Day (0-150)
2. Month (June-October, 5 levels)
3. Daily Mean Temperature(Response variable 1)
4. Daily Max Temperature (Response variable 2)
5. daily standard deviation,or some other measure of variation (Response variable 3)
So I have 5 x 5 x 150 = 750 observations
I want to test the following : -
1. Is my response variable significantly different between sites.
2.Is there a monthly interaction? For example in month 1 there all sites have similar response and in month 2 the one site will have significantly higher response than other sites.
I am planning to do a time - series / or a mixed model analysis by specifying an temporal autocorrelation structure.
For fixed effect I want the explanatory variables to be
Option 1- month (as factor) , site(as factor) and interaction of these two.
Option 2 - day (as a continous variable) and site (as factor) and intereaction of these two.
Since this is a time series data I am expecting significant temporal autocorrelation.
So when I do this analysis for mean and max temperature I should add a correlation structure. But I am not sure which variable should I use for correlation - month or Day ?
Also I want to do an anova/ancova on standard deviation of daily temperature, so for this do I still need to add a correlation structure ? Or since it is a deviation, the values become independent ?
Thank you
