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:

  1. Site (5 sites)
  2. Day (0-150)
  3. Month (June-October, 5 levels)
  4. Daily Mean Temperature (Response variable 1)
  5. Daily Max Temperature (Response variable 2)
  6. 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:

  1. Are my response variables significantly different between sites.
  2. 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?

Thank you.

  • $\begingroup$ I just don't understand why downvote this one? I hope this site does not allow to down vote the first question for anyone. $\endgroup$ – Deep North Nov 24 '17 at 3:19

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