Quantile regression using metaheuristic algorithms

This paper demonstrates that metaheuristic algorithms can provide a useful general framework for estimating both linear and nonlinear econometric models. Two metaheuristic algorithms - firefly and accelerated particle swarm optimisation - are employed in the context of several quantile regression models. The algorithms are stable and robust to the choice of starting values and the presence of various complications (e.g., non–differentiability, parameter restrictions, discontinuity, possible multimodality, etc.). Two comparative studies involving an autoregressive model and a conditional scale autoregressive conditional heteroscedasticity model, demonstrate the performance of metaheuristic algorithms relative to existing approaches. In addition, the paper presents an application to consumption behaviour in which the presence of constraints makes existing techniques difficult to implement, but metaheuristic algorithms are straightforward to apply. The findings indicate that marginal propensity to consume is highest in quarter 3 for each of the sample years. However, pre– and post–recession comparisons reveal interesting asymmetries in consumption behaviour.