Forecasting business cycles from threshold models: A comparison of bootstrap and Monte Carlo methods

The purpose of the research is to compare forecasting accuracy of bootstrap and Monte Carlo methods when the threshold autoregressive model (TAR) is considered. Our interest is focused on the following research problems: forecasting a threshold variable and the regime, forecasting the endogenous variable using both bootstrap and Monte Carlo approaches, measuring forecasting errors in sample and out of sample. Our proposals for solving this problems are non-standard. Therefore the forecasting accuracy will be compared with a linear AR model. A procedure available in the Gretl package is also one of the results of our work. The problem of interest is to forecast business cycles in the EU body and in selected European countries. Quarterly data from the period 1995-2014 were examined. As the period covered different phases of the business cycle including the recession of 2007-2009 the threshold model seems to be a straightforward  solution. We assumed that simulation-based procedures generate much more effective forecasts of business cycles when a TAR model is used (depending on state of the phase) comparing to direct methods. Simulation-based procedures based on bootstrap and Monte Carlo  approaches allow evaluating forecast accuracy in a much more flexible way then traditional extrapolation.

Keywords: threshold models, bootstrap, Monte Carlo, business cycle, forecast accuracy

Literature

Clements, M.P., Smith, J., A Monte Carlo study of the forecasting performance of empirical SETAR models, University of Warwick, 1997.

Davidson, R., Hinkley, D.V., Bootstrap Methods and Their Application, Cambridge, Cambridge University Press, 1997.

MacKinnon, J.G., Bootstrap inference in econometrics, “Canadian Journal of Economics” 2002 No. 35, pp. 615-645.