A Time Series Approach to Numerical Differentiation

The problem of obtaining the derivative of a set of data arises naturally in many fields. The usual methods for obtaining derivatives are based on abstract formulations of the problem, which do not take errors of observation explicitly into account. For this reason, their performarice when applied to observational data is unpredictable. By introducing random errors into the model, one may derive methods whose performance may be stated in statistical terms. The theory of time series analysis provides useful tools for discussing such a model. A parametric family of models is introduced, and estimation of the parameters is discussed.