Can a least-squares fit be feasible for modelling

When modelling a time series from discrete-time data, a continuous-time parametrization is desirable in some situations. It can have good numerical properties and low computational burden, in particular for fast or nonuniform sampling. In a direct estimation approach, the derivatives are approximated by appropriate differences, leading to a linear regression model. It is shown that standard approximations like Euler backward or Euler forward cannot be used. The precise conditions on the derivative approximation are derived and analysed. It is shown that if the highest order derivative is selected with care, a least-squares estimate will be accurate. The theoretical analysis is complemented by some numerical examples.