Abstract
Recently De Luca and Carfora (Statistica e Applicazioni 8:123–134, 2010) have proposed a novel model for binary time series, the Binomial Heterogenous Autoregressive (BHAR) model, successfully applied for the analysis of the quarterly binary time series of U.S. recessions. In this work we want to measure the efficacy of the out-of-sample forecasts of the BHAR model compared to the probit models by Kauppi and Saikkonen (Rev Econ Stat 90:777–791, 2008). Given the substantial indifference of the predictive accuracy between the BHAR and the probit models, a combination of forecasts using the method proposed by Bates and Granger (Oper Res Q 20:451–468, 1969) for probability forecasts is analyzed. We show how the forecasts obtained by the combination between the BHAR model and each of the probit models are superior compared to the forecasts obtained by each single model.
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Notes
We have also computed the same test for different values of \(v\). The general results do not change. However, for \(h=4\) the combination of forecasts seems to suffer from the comparison with the static and the dynamic model when the value of \(v\) increases. This fact can be explained by the presence in the probit models of the variable \(x_{t-4}\) which gives a relevant contribute to the forecasts four period ahead.
References
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De Luca, G., Carfora, A. Predicting U.S. recessions through a combination of probability forecasts. Empir Econ 46, 127–144 (2014). https://doi.org/10.1007/s00181-012-0671-4
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DOI: https://doi.org/10.1007/s00181-012-0671-4