The Estimation And Outlier Detection In Functional-coefficient Time Series Model Based On Varieties Of Evolutionary Algorithms

Functional-coefficient time series model, as a new nonlinear time series model, since 1993 proposed by Chen and Tsay, the estimation and outlier detection problems have attracted many scholars’attention in recent years. However, low efficient estimation became an important factor in its development. Successful use of genetic algorithms gains a good solution to the problem of estimation efficiency.Genetic algorithms (GA) are a class of biological evolution law reference evolved from a random search method. It was first proposed by professor J. Holland in 1975, the United States. In recent years, many scholars proposed improvements of simple genetic algorithm (SGA). Improved genetic algorithms include hierarchical genetic algorithm (HGA), CHC algorithm, Messy GA, adaptive genetic algorithm (AGA), based on niche genetic algorithm technology and parallel genetic algorithm.In this paper, we firstly introduces the basic concepts of functional-coefficient time series model. And then lists the basic flow of simple genetic algorithm (SGA) and improved genetic algorithms (HGA, AGA, Messy GA) in the estimation and outlier detection.Finally, we apply these genetic algorithms (SGA, HGA, AGA, Messy GA) to estimate parameters and detect outliers in given functional-coefficient time series model. In detecting outliers, we use the absolute value of diagnostic statistics, square diagnostic statistics and adjusted square diagnostic statistics. Gumbel approximate quantiled under a significant level served as the threshold for the outlier detection, and Monte Carlo simulation determined whether a string sequence outliers existence and location of the way, and the cumulative value of p was assisted outlier type of judgment. Simulation results show that:SGA, HGA, AGA and Messy GA methods can give a good estimate in given functional-coefficient time series model.These four methods have good results for solving single outlier outliers or multiple noncontiguous outliers.At the same time, the multiple continuous 10 outliers and the multiple continuous mixing 10, AO outliers(only one AO) can be successfully solved.