Three types of residuals in time series models (namely ”conditional residuals”, ”unconditional residuals” and ”innovations”) are considered with regard to (i) their precise definitions, (ii) their computation after model estimation, (iii) their approximate distributions in ?nite samples, and (iv) potential applications of their properties in model diagnostic checking. Both partially-known and n...

background: the objective of this study was to determine the residual concentrations of ethion and imidacloprid in cucumbers grown in greenhouse. the effect of some simple processing procedures on both ethion and imidacloprid residues were also studied. methods: ten active greenhouses that produce cucumber were randomly selected. ethion and imidacloprid as the most widely used pesticides were m...

We introduce a formal language to describe origin functions, which permit to study the notions of descendance and residuals in reduction systems. Computation on this formal language are deened using a term rewriting system, which we show to be canonical. This work has application in semantics and debugging.

Phase space reconstruction is investigated as a diagnostic tool for determining the structure of detected nonlinear processes in regression residuals. Empirical evidence supporting this approach is provided using simulations from an Ikeda mapping and the S&P 500. Results in the form of phase portraits (e.g., scatter plots of reconstructed dynamical systems) provide qualitative information to di...