I would like some advice on how I should analyze my time series data.
I have hourly measurements of water temperature data for 12 months across 5 sites. I have summarized my data in following way:
- Site (5 sites)
- Day (0-150)
- Month (June-October, 5 levels)
- Daily Mean Temperature (Response variable 1)
- Daily Max Temperature (Response variable 2)
- Daily standard deviation, or some other measure of variation (Response variable 3)
So I have 5 x 150 = 750 observations.
I want to test the following:
- Are my response variables significantly different between sites.
- Are there a monthly interaction? For example in month 1 all sites have similar response and in month 2 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 continuous variable) and site (as factor) and interaction 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 I should 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?