Computing and using residuals in time series models

The most often used approaches to obtaining and using residuals in applied work with time series models, are unified and documented with both partially-known and new features. Specifically, three different types of residuals, namely "conditional residuals", "unconditional residuals" and "innovations", are considered with regard to (i) their precise definitions, (ii) their computation in practice after model estimation, (iii) their approximate distributional properties in finite samples, and (iv) potential applications of their properties in model diagnostic checking. The focus is on both conditional and unconditional residuals, whose properties have received very limited attention in the literature. However, innovations are also briefly considered in order to provide a comprehensive description of the various classes of residuals a time series analyst might find in applied work. Theoretical discussion is accompanied by practical examples, illustrating (a)...

• Type: Journal
• Year: 2008
• Where: CSDA
• Authors: José Alberto Mauricio
• Keywords: Approximate Distributional Properties, CSDA 2008, Time Series Models, Unconditional Residuals