Essentially, the observed series is ordered by value, extremes are ignored (by omitting the most extreme 15 values at each end) and 40 values are specified at equal intervals over the remaining range.
Most estimation is undertaken in the package GAUSS. However, Vinod (2000) has questioned the numerical accuracy of the non-linear estimation routines in GAUSS. To avoid such problems our estimates are checked in RATS (Doan, 1995). We find the same parameter estimates but smaller standard errors for the estimation in Gauss with problematic models.
Clearly, the validity of this procedure depends on the estimated transition function varying relatively little as lags are dropped from the model. Thus, a conservative variable deletion strategy needs to be employed.
Extensive grid searches were carried out, but the final model derived using the lowest RSS from the grid search was typically poor. This may be due to the large number of redundant parameters included in the general model of (3), so that the initial grid search does not give a reliable guide to the appropriate transition functions with two such functions. Full grid search results are available from the authors upon request.
All the graphics in the paper were created in Givewin (Doornik and Hendry, 2001).
These were removed where the value of the quarterly difference exceeded three standard deviations from its mean. The outliers removed correspond to 1963q1, 1973q1 and 1979q2.
Financial support from the Leverhulme Trust and ESRC grant L138251002 is gratefully acknowledged. We also acknowledge that the GAUSS programs used here derive from programs made available by Timo Teräsvirta. We would like to thank Dick van Dijk, Mike Artis, Ian Garrett, Mehtap Kesriyeli and an anonymous referee for helpful comments and other assistance.