Effect of time discretization and finite record length on continuous-time stochastic properties

"Natural processes evolve in continuous time but their observation is inevitably made at discrete time. The observational time series formed are either series of instantaneous values of the natural phenomenon at a certain time step or aggregated quantities during this time step. In addition, the observation period is apparently a finite time period. Both time discretization and finite length may strongly affect the stochastic properties inferred from the data. In particular, time discretization distorts the stochastic properties at small time scales, while the finite length affects the properties at large time scales. Modelling of natural processes is typical made assuming discrete time and parameter estimation is usually done using classical statistical estimators which assume that observations are random samples. All these are inadequate practices and result in inappropriate and biased models. A different modelling strategy is proposed, in which the stochastic model is by definition a continuous-time process and the distortion due to discretization and finite-period observation is explicitly taken into account in model calibration. An additional benefit of the proposed strategy is that it avoids the too artificial, often non-parsimonious, families of discrete time stochastic models (like the ARIMA(p,d,q) models)."