Fitting Discrete-Time Dynamic Models Having Any Time Interval

Abstract When the desired time interval of a difference equation is not the same as the interval at which the data used to fit the equation were collected (the measurement interval), some kind of interpolation method is necessary before fitting. Linear growth assumptions, which are often used for such interpolations, are almost always inconsistent with the growth function that is estimated and can lead to biased growth projections. A more logical approach is to use the hypothesized functional form of the difference equation as the basis for interpolation. Two interpolation methods based on this approach are presented. With one method, both the interpolation and the parameter estimation steps are implemented simultaneously. The second method implements the interpolation and parameter estimation steps separately and requires repeated model fittings until consistency is obtained between both steps. The procedures are demonstrated using a tree height growth example. Results are compared with an integrated, continuous-time version of the growth model that can be fitted without interpolation. Growth projections obtained with the proposed interpolation methods are closer to the projections obtained with the integrated, continuous-time model than projections obtained with other commonly used interpolation methods. A simple Monte Carlo analysis showed that two common interpolation methods based on linear assumptions produce biased parameter estimates but failed to show any bias in the parameter estimates obtained with the proposed methods. Parameter estimates obtained with the new interpolation methods converge to limiting values as the time interval of the difference equation is shortened. These limiting values can be used as estimates of the parameters of continuous-time versions of the growth model. For. Sci. 39(3):499-519.