We now use our identified cointegration relationships to derive short-run dynamic forecasting models for USDDEM and USDJPY using the SEM method discussed above. Using the identified long-run relationship from the previous section, we generated a CVAR and then a PVAR. Compared to the CVAR, the latter systems, have 43 less variables for USDDEM and 42 less for USDJPY.

Given the data-driven nature of the identifiaction procedure, an important test statistic is the ability of the SEM to parsimoniously encompass the PVAR (see Clements and Mizon (1991)). A specific set of equations is taken to represent an acceptable parameterisation of the original VAR, if it contains roughly the same information as the PVAR from which it was derived, given the restrictions imposed. As can be seen in Tables 5 to 6, each of our models easily passes the Clement-Mizon LR test of over-identifying restrictions.

The identified model structures reveals that Δ max and Δ min have an immediate impact on Δ cl, while Δ max and Δ min can be identified as AR(1) processes. This model structure is in line with the identified theoretical relationship embodied in the first cointegration vector which assumes that today’s Close is affected by today’s periodic Maximum and Minimum. Since the Maximum and Minimum series correspond to local Maxima and Minima of the High price and Low price series, it is not surprising that Δ cl does not enter either Δ max or Δ min.

Since the error correction components are highly significant in almost all system equations, it is clear that a single equation reduced form modelling strategy would not have been appropriate. An additional advantage of using a structural equation approach, rather than a single equation reduced form modelling strategy, is that only the first provides us with a closed system that faciliates computation of fully dynamic multi-step ahead forecasts.

The forecasted values of each variable are in this case fed back into the system to provide the basis for the forecasts of subsequent periods. As such, no unfair advantage is given to the model over the random walk.

 

Prof. Ronald MacDonald, Prof. Norbert Fiess

Next: Out-of-Sample Forecasting Results

Summary: Index