Econometric models are often used to give a quantitative explanation of economic interdependencies. They provide a linear demonstration of the presumed dependencies be-tween the explanatory factors, the exogenous variables, and the dimensions to be explained, the endogenous variables.

A disadvantage of this linear model is that it always reacts to changes in the exogenous variables with a constant modification of the endogenous variables, irrespective of the actual value and nature of those changes.

One solution to this problem is to use a neural network. These can depict extremely complex and, above all, high-grade, non-linear connections between exogenous and endogenous variables.

Neural networks take their shape from a desire to imitate human learning patterns, in all their sophistication.

Thus this type of network consists of a multitude of neurons, corresponding to the nerve cells of the brain and their connectors, the axons.

By successively determining pairs of exogenous and endogenous variables, the network attempts to learn about how they are interconnected. The use of neural networks assumes a more or less consistent connection between exogenous and endogenous variables. If such connections do not exist, neural networks will fail to achieve the desired result.

The neural network we use for modelling and forecasting the yield of ten-year government bonds is based on an input of six exogenous variables. These are the yield of ten-year US bonds, the overnight rate in Germany, the external value of the Deutschmark against the currencies of 18 industrial nations, the inflation rate, the rate of change in the production index and the rate of change of a leading economic indicator

In contrast to the modelling of the functional interrelation of endogenous and exogenous variables, which is based solely on historical data, the quality of the projection of the endogenous variables depends greatly on the correct assessment of trends in the input variables during the forecasting period.

The modelling ability of our neural network with good determination of exogenous variables, when compared with the actual future event, allows a good forecast of the target variables. Therefore, our neural networks are also used to quantify the impact of the predetermined scenario of input variables on the target variables.

On the basis of our assumptions concerning the development of the exogenous variables, the yield of ten-year government bonds is forecast to rise from an average 6.0% in October 1996 to 6.6% in March 1997.

Klaus Ragotzky is an analyst at Bayerische Landesbank in Munich

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