Goodness-of-Fit based on Downsampling with Applications to Linear Drift Diffusions

A goodness-of-fit test for continuous-time models is developed that examines if the parameter estimates are consistent with another for different sampling frequencies. The test compares parameter estimates obtained from estimating functions for downsamples of the data. We prove asymptotic results for stationary and ergodic processes, and apply the downsampling test to linear drift diffusions. Simulations indicate that the test is quite powerful in detecting non-Markovian deviations from the linear drift diffusions.