Time-series Model Identification And Simulations

Based on the Project "Study of Modeling and Identification of a Class of Nonlinear Systems (The National Nature Science Foundation of China)", this thesis studies identification methods for time-series models. Time series output data are a series of data with time sequences and time series models have wide applications in industry and daily life, and its estimation algorithms attract great attention. Therefore, the research on the time-series models is not only significant in theory, but also potentially valuable application. The thesis briefly makes some surveys on time series identification and deeply studies identification of time series models. The results are as follows.1. Based on the model equivalence principle, two identification algorithms of autoregressive moving average (ARMA) model are proposed, an identification algorithm with the equivalent autoregression (AR) model orders increasing and an identification algorithm based on the equivalent moving average (MA) model. The recursive computation formulae are given for parameter estimation. One algorithm is, by means of the partition matrix inversion formula of the data product moment matrix, to discuss how to reasonably choose the orders of the equivalent AR models and to give the recursive algorithm of determining the parameter estimates of the AR models and the value of the cost function. By examining the changing trend of the cost function, the reasonable orders and parameter estimation of the equivalent AR models are determined; further, the ARMA parameter estimates are obtained by solving a set of algebraic equations. The other uses an equivalent MA model to approximate an ARMA model, the principle used is simlilar. The simulation results indicate that the proposed algorithms are effective.2. By means of the interactive estimation theory in the hierarchical identification: using the estimation residual to replace those noise terms in the information vectors, a stochastic-gradient-iterative algorithms and a least-squares-iterative algorithms are presented and the recursive computation formulae are given for the parameter estimation. The parameter estimation errors given by the proposed algorithms consistently converge to zero under the persistent excitation conditions. The simulation results confirms the theoretic findings.3. The multi-innovation least squares (MILS) method and the multi-innovation stochastic gradient (MISG) method for time-series models are derived and proposed. Digital simulation results show that the multi-innovation methods can greatly improve the rate of convergence of the parameter estimation and the accuracy of the parameter estimation, and can overcome the effect of bad data. 4. By means of the identification algorithm with the data filtering for dynamical adjusting models, a two-stage parameter estimation algorithm is presented for ARMA models. The basic idea is that the parameter estimates of the noise model are assumed to be known (that is, unknown parameters are replaced with their corresponding estimates), by filtering the output data by the estimated noise models, the parameter estimation of the AR part can be determined, and then that the noise estimates of the AR part are regarded as the output of the MA part and a two-stage recursive least squares and a two-stage least-squares-iterative algorithms are presented by means of the interactive estimation theory in the hierarchical identification.