I have a time series in which samples were collected approximately monthly over ten years. I have wanted to identify whether a number of bacterial species were seasonally variable and whether they increased or decreased over time. I had been modelling species abundance with linear regression according to the equation
S = a + b*ED +c*DL + d*DDL.
Where S is the abundance of a species.
ED: Number of days elapsed since the beginning of the study.
DL: Day length on the day the samples were collected
DDL: The rate of change in day length, measured here as the day length minus the day length measured thirty days previous.
I then looked at the P values associated with each of these coefficients and the coefficients themselves. If ED was statistically significant, I said there was a long term triend, and if ED's coefficient was positive, that species abundance was increasing. If DL or DDL's coefficients were statistically significant, I said the species' abundance was seasonal. If DL had a statistically significant coefficient, I said the species was most abundant in the summer; if negative, most abundant in the winter. Same pattern for DDL, positive, most abundant in spring, negative most in fall.
A reviewer tells me that "The regression analysis may not be appropriate because day length and day length change are autocorrelated and also covarying." Is this criticism valid? If valid, is there anything I can salvage from this kind of analysis? Is there a better approach? If not, why isn't it valid? I feel like this approach is analogous to building trigonometric models to describe a data set eg y = a + b*t + c*sin(2pi*t/L) + d*cos(2pi*t/L), which people apply to model some time series. Can I just replace the sign and cosine terms with DL and DDL (which are sinusoidal and DDL is basically the derivative of DL) or am I breaking some rule there? Thanks!