A definition of extended memory is provided, generalizing the ideas of long memory and persistence, based on the properties of forecasts over long horizons. Specification of nonlinear models with variables having extended memory is considered in terms of the balance of an equation and it is suggested that many more types of misspecification can occur than with usual situations and could produce important specification errors. Tests of linearity and standard methods of nonlinear modeling are briefly considered and advice is given on circumstances in which they can be used.

There occurs on some occasions a difficulty in deciding the direction of causality between two related variables and also whether or not feedback is occurring. Testable definitions of causality and feedback are proposed and illustrated by use of simple two-variable models. The important problem of apparent instantaneous causality is discussed and it is suggested that the problem often arises due to slowness in recording information or because a sufficiently wide class of possible causal variables has not been used. It can be shown that the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation. Measures of causal lag and causal strength can then be constructed. A generalisation of this result with the partial cross spectrum is suggested.

In recent years, a number of power spectra have been estimated from economic data and the majority have been found to be of a similar shape. A number of implications of this shape are discussed, particular attention being paid to the reality of business cycles, stability and control problems, and model building.

Journal Article Spectral Analysis of the Term Structure of Interest Rates Get access C. W. J. Granger, C. W. J. Granger University of Nottingham Search for other works by this author on: Oxford Academic Google Scholar H. J. B. Rees H. J. B. Rees University of Nottingham Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 35, Issue 1, January 1968, Pages 67–76, https://doi.org/10.2307/2974408 Published: 01 January 1968