Cyclical Trends in Continuous Time Models

Abstract

It is undoubtedly desirable that econometric models capture the dynamic behavior, like trends and cycles, observed in many economic processes. Building models with such capabilities has been an important objective in the continuous time econometrics literature, for instance, the cyclical growth models of Bergstrom (1966); the economy-wide macroeconometric models of, for example, Bergstrom and Wymer (1976); unobserved stochastic trends of Harvey and Stock (1988 and 1993) and Bergstrom (1997); and differential-difference equations of Chambers and McGarry (2002). This paper considers continuous time cyclical trends, which complement the trend-plus-cycle models in the unobserved components literature but could also be incorporated into Bergstrom type systems of differential equations, as were stochastic trends in Bergstrom (1997).

Estimating Continuous-Time Models on the Basis of Discrete Data via an Exact Discrete Analog

“…14 Using the exact discrete model, Bergstrom and Nowman show that if the Brownian motion processes were correlated, the model even with b = c = 0 is unidentified, and make the zero correlation restriction a priori. The lack of correlation between the disturbance processes, although restrictive, is also a feature of the two-factor Cox-Ingersoll-Ross model considered by Chen and Scott (1992) and the cyclical models introduced by Ercolani (2009) in this volume. Now we show using (A.1) that aliasing alone impacts on identification in different ways depending on the values of the parameters.…”