Annealing Algorithm Based On Multi-agent Garch Model Parameter Estimation

GARCH (Generalized Autoregressive Conditional heteroscedasticity) class model has become an efficient instrument for describing capital market volatility. But the methods of estimation of parameter of the GARCH models, BHHH and GMM, may become invalid because they usually meet the situation that the middle data fluctuate greatly. Although the maximum likelihood estimation based on Simulated Annealing Algorithm (SAA) or Genetic Algorithm (GA) improves the exactness and robustness, the result is not desired. Therefore, this paper form a new algorithm called Multi-agent Annealing Algorithm (MAA) which is based on Multi-agent of artificial intelligence. The algorithm makes use of the abilities to compete among the agents, to learn from agents' circumstance, and to accept special "ill-conditioned solutions". Then the paper gives a conclusion that MAA converges to the global optimum. Furthermore, we make a numerical experiment to compare MAA with SAA and GA by several classical experimental functions in optimization, which suggests the availability of MAA. Finally, we present a demonstration of Chinese stock which shows obvious bivariate GARCH effect and apply MAA to the estimation, which solve the estimation of parameter of bivariate GARCH model well.