Incorporating Uncertainties into Economic Forecasts: an Application to Forecasting Economic Activity in Croatia Dario Rukelj Ministry of Finance of the Republic of Croatia Barbara Ulloa Central Bank of Chile Young Economists’ Seminar (YES) Dubrovnik Economic Conference June 23, 2010

Uncertainty is the only certainty there is, and knowing how to live with insecurity is the only security... John Allen Paulos

1. INTRODUCTION 2. METHODOLOGY 3. RESULTS 4. CONCLUSION

MOTIVATION FORECASTS OF THE EUROZONE REAL GDP GROWTH

DEALING WITH UNCERTAINTY  Point forecasts  Mode of distribution  Interval forecasts  Consists of an upper and a lower limit  Density forecasts  The whole probability distribution of the forecasts

1. INTRODUCTION 2. METHODOLOGY 3. RESULTS 4. CONCLUSION

STOCHASTIC SIMULATION APPROACH *  Data generating process assumed to be VAR model, estimated in the finite sample:  Forecasts incorporating future uncertainties:  Forecasts incorporating future and parameter uncertainties:  Simulate s in sample values of y  For each of these estimated models, r replications of the forecasts are calculated * Garrat, Pessaran and Shin (2003 and 2006)

SIMULATED SHOCKS  Parametric approach :  Non-parametric approach:  random draws with replacements from the in sample residuals  Unbalanced risks:

CALCULATION  Future uncertainty  Obtain the set of simulated shocks  Generate the forecasts using the simulated shocks  Sort the forecasted values of the variable of interest  Determine probability bands by the deciles  Future and parameter uncertainty  Using initial values for the number of lags determined by the order of the VAR, calculate forecasts ahead using estimated parameters of the initial model, as well as applying a shock to each observation in each period  Re estimate the models with each set of time series obtained in this way  Based on these models forecasts are made like under only future uncertainty

PRESENTATION Probability density 90% 80% 70% 50% 60% Probability Distribution Fanchart

EVALUATION In Sample Fancharts Probability Integral Transform

KOLMOGOROV – SMIRNOV TEST  Kolmogorov – Smirnov test can be used for comparing two distributions  Comparing Probability Integral Transform of outturns with uniform distribution  Let F(a) be the cumulative distribution function of uniform distribution  Cumulative distribution function of empirical distribution is given by: where t is the number of observations of variable b such that  If variable b comes from uniform distribution then D should be small

1. INTRODUCTION 2. METHODOLOGY 3. RESULTS 4. CONCLUSION

Reduced form VECM from Rukelj (2010) considered: where x t is vector of endogenous variables (m, g and y). Rewritten in a VAR form: PORTMANTEAU TEST (H0:Rh=(r1,...,rh)=0) Tested order:10 Adjusted test statistic p-Value:0.151 JARQUE-BERA TEST VariableTest Statisticp-ValueSkewnessKurtosis u u u BENCHMARK MODEL

FUTURE UNCERTAINTY Fanchart – Parametric Approach PIT – Parametric Approach

FUTURE UNCERTAINTY Fanchart – Non Parametric Approach PIT – Non Parametric Approach

FUTURE UNCERTAINTY Fanchart – Skewed Distribution PIT – Skewed Distribution

FUTURE AND PARAMETER UNCERTAINTY Fanchart – Parametric Approach PIT – Parametric Approach

FUTURE AND PARAMETER UNCERTAINTY Fanchart – Non Parametric Approach PIT – Non Parametric Approach

KOLMOGOROV – SMIRNOV TEST RESULTS

1. INTRODUCTION 2. METHODOLOGY 3. RESULTS 4. CONCLUSION

FORECASTING WITH UNCERTAINTY Probability Forecasts for the Real GDP Growth

CONCLUSION  In this paper we have shown how to calculate, present and evaluate density forecasts by stochastic simulation approach  An application of this methodological framework to the chosen benchmark model showed that:  parametric and non-parametric approach yielded similar results  incorporating parameter uncertainty results in a much wider probability bands of the forecasts  evaluation of the density forecasts indicate a better performance when only future, without parameter uncertainties are considered  Future research in this topic should incorporate model uncertainty and additional goodness of fit tests

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