Short-term forecasting of GDP via evolutionary algorithms using survey-based expectations. Oscar Claveria Enric Monte Salvador Torra

Transcription

1 Short-term forecasting of GDP via evolutionary algorithms using survey-based expectations Oscar Claveria Enric Monte Salvador Torra

2 Highlights We present an empirical modelling approach of agents expectations based on symbolic regression (SR) 1. Via genetic programming (GP) we derive two data-driven indicators from survey-based expectations 2. We assess the performance of both indicators in fourteen European countries 3. By means of constrained optimization we find the optimal weights of both indicators to construct a composite index 4. We evaluate the ability of the generated estimates of economic growth to track the evolution of GDP June

3 Symbolic regression o SR is a data-driven approach for model approximation No model is assumed beforehand Finds the most fitting algebraic expression in large datasets o Indicated when model structure is unknown o Solution based on discrete optimization June

4 Evolutionary algorithms o Apply Darwinian principles that imitate aspects of biological evolution (reproduction of the fittest and survival) o Can be classified into genetic algorithms (Holland, 1975) and genetic programming (Cramer, 1985) o GP uses a more general representation scheme tree-structured, variable-length representations suitable for non-linear modelling o GP allows the model structure to vary during the evolution o Koza (1992) implemented GP to find a solution in SR June

5 SR via GP o Initial population bred using genetic operators (reproduction, crossover and mutation) o The structure is evolved and optimized o Solution after a given number of generations Best single individual program The most fitting algebraic expression to the data o Most applications to economics have been in finance (Álvarez-Díaz and Álvarez, 2005; Chen et al., 2008; Larkin and Ryan, 2008) o In economics Acosta-González et al. (2012) used SR for model selection and Kronberger et al. (2011) to estimate inflation June

6 Experimental setup o We design two independent experiments o In both we link survey-based agents expectations from the World Economic Survey (WES) to GDP growth ( ) WES variables economic situation regarding: overall economy capital expenditures private consumption o The first experiment combines six survey indicators with expectations about the future to derive a leading indicator o The second experiment links six survey indicators with perceptions about the present to derive a coincident indicator June

7 Implementation 1. Creation of initial population 3 million individuals 2. Selection of an error metric (fitness function) Evaluation of fitness for each member (RMSE) 3. Selection of a strategy for reproduction Tournament method 4. Determination of the probability of a new generation 5. Application of genetic operators reproduction, crossover and mutation 6. Automatic generation of constants 7. Selection of a stopping criterion max. 150 generations June

8 Assessment of generated indicators o From the first experiment we obtain a leading indicator (blue), from the second a coincident indicator (black) Germany June

9 Assessment of generated indicators o Coincident indicator outperforms the leading indicator o Belgium is the country with the most accurate forecasts o Greece and Ireland show the highest MAE and RMSE o Survey data are available ahead of official data MASE (two-step naïve forecasts as a benchmark) o Germany is the only economy with a lower than one MASE for the leading indicator o Denmark, Greece and Spain the only economies with a higher than one MASE for the coincident indicator June

10 Results RMSE Coincident indicator RMSE June

11 Results MASE Coincident indicator June 2016 MASE

12 Results by sub-periods o We re-compute the MASE differentiating between: pre-crisis ( ) crisis ( ) post-crisis ( ) o We find an improvement in relative forecast accuracy during the crisis o Austria and Ireland are the only countries where agents perceptions are more accurate than the predictions obtained with the baseline model for all three sub-periods o Spain and the UK are the only countries in which there is an improvement in the relative forecast accuracy of both indicators in the post-crisis period with respect to the pre-crisis period June

13 Composite index o We find the relative optimal weights of both indicators by means of constrained optimization (index tracking) o We use a generalized reduced gradient algorithm to minimize the summation of squared forecast errors subject to two constraints: the weights must be equal or larger than zero the sum of both weights cannot exceed one June

14 Composite index relative weights Leading indicator Coincident indicator Leading indicator Coincident indicator Austria Ireland Belgium Italy Denmark Netherlands Finland Portugal France Spain Germany Sweden Greece UK June

15 Composite index o We find that perceptions about the present outweigh expectations about the future o In Denmark, Greece and Ireland, the algorithm yields a null weight to the leading indicator o In Austria, Finland and Germany the leading indicator weighs close to a third The composite index yields more accurate estimates than the coincident indicator in all countries except Spain June

16 Conclusion o We have presented an empirical modelling approach of survey-based agents expectations o Using SR via GP we have generated two data-driven indicators o The coincident indicator outperformed the leading indicator o By means of constrained optimization we computed the optimal weights of both indicators to construct a composite index o Perceptions about the present outweighed expectations about the future o Survey-based indicators Shall we equally weigh expectations about the future and perceptions about the present? June