Single-index models and the selection of leading indicator variables are normally based on linear regression methods. Moreover, in statistical modeling of the business cycle, it has been well established that cycles are asymmetric. (See, for example, Kaiser and Maravall 1999, Verbrugge 1997, Kim et al. 1996, Sichel 1993.) Therefore, it is doubtful that linear models can adequately describe them.
The original NBER model (classical model) was built solely within a linear framework. With recent developments in nonlinear time series analysis, several authors have begun to examine the forecasting properties of nonlinear models in economics. Probably the largest share of economic applications of nonlinear models can be found in the field of prediction of time series in capital markets (Meese and Rogoff 1983, Lee et al. 1993). In a study more comparable to ours, Jaditz, Riddick and Sayers (1998) use financial variables to forecast industrial production. They estimated a nonlinear, non-parametric nearest-neighbor regression model. Tkacz (2000) also achieved superior results over linear models in forecasting Canadian GDP growth. Tiao and Tsay (1994) show that a simple threshold autoregressive model is superior to an AR(2) representation for GDP growth. Maasoumi, Khotanzad and Abaye (1994) show that the fourteen macroeconomic series in the Nelson and Ploser (1982) study are nonlinear processes rather than unit root processes.
To avoid the aforementioned pitfalls of widely used linear models, in the present research we adopt neural networks to forecast business cycles. The decision to focus on neural networks arises directly from the features of these models as described by Bishop (1995). First, neural networks are data-driven and can "learn" from, and adapt to, underlying relationships. This property makes them an ideal modeling tool for studies in which there exists little prior knowledge about the appropriate functional representation of the relationship under investigation. Second, when properly specified they are universal functional approximates, implying that they can approximate functional forms to any given degree of accuracy. Finally, neural networks are nonlinear, which seems to be the case for many macroeconomic time series.
Another important issue is the prediction of the future value of the reference series. The classical model of leading indicators can only provide a sign for a turning point in aggregate economic activity. It is not possible to exactly define when the turning point will occur, or how strong the following contraction or expansion will be. Therefore, a reliable composite index of leading indicators should possess the following properties (Fritsche and Stephan 2000): (1) the movements in the index should resemble those in the business cycle reference series, (2) the relationship between the reference series and the indicator should be statistically significant, and (3) the forecasting performance should be stable over time.
Our approach differs from previous studies in several ways. First, we try to modify the classical model with the aim of overcoming the deficiencies of the model. Second, our focus is on constructing a multivariate neural network forecasting model. Third, our model is used for monthly forecasts.
We tested our model on data for a small, open, transition economy. This gave us the opportunity to test the properties of the model under extreme conditions:
* Time series can cover only a short time period. In the case of Slovenia, the data cover a period of nine years.
* As in many other transition economies, Slovenia has faced a deep transformation depression. In the process of restructuring its economy, wild swings in time series occur, which may have a significant impact on chosen indicators.
* In the observed period, the economy is in the process of transforming from a former semi-command socialist economy to a market-oriented economy. …