Chapter 2 Time-varying regression
Time-varying regression is simply a linear regression where time is the explanatory variable:
log(catch)=α+βt+β2t2+⋯+et The error term ( et ) was treated as an independent Normal error ( ∼N(0,σ) ) in Stergiou and Christou (1996). If that is not a reasonable assumption, then it is simple to fit a non-Gausian error model in R.
Order of the time polynomial
The order of the polynomial of t determines how the time axis (x-axis) relates to the overall trend in the data. A 1st order polynomial (βt) will allow a linear relationship only. A 2nd order polynomial(β1t+β2t2) will allow a convex or concave relationship with one peak. 3rd and 4th orders will allow more flexible relationships with more peaks.