Time Series Modeling, Forecasting And Applied Research

Time series analysis is an important approach to solve and analyze dynamic data.The approach is an extension of traditional statistics to analyze random data series. Itis usually applied to find statistical regularities, develop the mathematic model, and fur-ther applied to forecast, adaptive control and so on. Now, time series analysis is widelyemployed in space science, weather forecast, control engineering and communicationsengineering.In this paper, we mainly focused on two problems:(1) Modeling and forecastingof the seasonal ARIMA model;(2)State and parameter estimation based on bayesianfiltering algorithm in nonlinear state space model. The results are as follows:The general ARIMA models are firstly summarized. Then, we develop a seasonalSARIMA model of precipitation time series and found that the model fit the data well.Bayesian filtering algorithms are summarized. A new method based on MarkovChain Monte Carlo is proposed and performs well in state estimation of the nonlinearstate space model.We use new algorithm, particle Markov Chain Monte Carlo (Particle MCMC),to construct a posteriori distribution of the parameter of the nonlinear state-space model.Taken a discrete time population dynamic model as example, we derived the posteriordistribution of four model parameters. Moreover, numerical simulations indicate thatthe true values of the parameters can be accurately estimated using this Particle MCMCalgorithm.