Campbell and Shiller (1987) proposed a graphical technique for the present value model, which consists of plotting estimates of the spread and theoretical spread as calculated from the cointegrated vector autoregressive model without imposing the restrictions implied by the present value model. In addition to getting a visual impression of the fit of the model, the purpose is to see if the two spreads are nevertheless similar as measured by correlation, variance ratio, and noise ratio. We extend these techniques to a number of rational expectation models and give a general definition of spread and theoretical spread. The main results are the asymptotic distributions of the variance ratio, noise ratio, and correlation between the estimated spread and theoretical spreads. We derive sup tests for the recursively calculated quantities. Finally, we illustrate the results by two previous studies by Campbell and Shiller (1987) and Engsted (2002).
The Journal of Time Series Econometrics (JTSE) serves as an internationally recognized outlet for important new research in both theoretical and applied classical and Bayesian time series, spatial and panel data econometrics. The scope of the journal includes papers dealing with estimation, testing and other methodological aspects involved in the application of time series and spatial analytic techniques to economic, financial and related data.