| Probabilistic forecasts play a significant role in a wide variety of economics activities. However, established econometric modeling approaches for probabilistic forecasts may yield unsatisfactory forecasting performance due to model misspecification. In my dissertation, I try to minimize such a risk by introducing a semi-nonparametric modeling approach for probabilistic forecasting. The new approach combines the ARMA memory index modeling approach of Bierens (1988) with the semi-nonparametric estimation method that uses wavelet basis to construct a flexible functional form. With this combination, we are able to avoid imposing restrictive constraints on the specification of critical components of conditional probability functions, i.e., the lag structure and distribution functions of error terms. As a result, it is possible that the new modeling approach will lead to improved forecasting performance if the reduction of modeling bias is significant. To test the usefulness of the new approach, we compare the relative performance between the new modeling approach and traditional forecasting models in both Monte Carlo experiments and real-world applications including business cycle regime forecasting and the forecast of rank performance of stock returns. The experimental and empirical results suggest that the new modeling approach can outperform traditional modeling approaches due to the flexibility of the model specification and the way various nonlinearities in the dependence of conditional probabilities on information variables are captured by ARMA memory indices. |
