Model Identification Procedure Research Articles

Automatic model identification using vector sample autocorrelation function

One of the weaknesses of the ESACF approach for model identification by Tsay and Tiao(1984) is the ambiguity which can be caused by the elements which are in triangle but marginally larger than two standard deviation values. To avoid this drawback, a vector sample autocorrelaton function (VSACF) is defined and an automatic model identification procedure using the VSACF is developed. We illustrate this approach with four examples.

Dissolved Oxygen Dynamics of a Stream: Model Discrimination and Estimation of Parameter Variability Using an Extended Kalman Filter

A model identification procedure is presented based on an extended Kaiman filter (EKF) applied to the oxygen mass balance equation of a stream. The procedure is used with data from a small Danish stream to discriminate among eight mathematical models of the photosynthesis-light (P-I) response of macrophytes in the stream. Each model was tested for adequacy using objective criteria based on the expected behavior of the innovations sequence (the time series of differences between predicted and observed oxygen concentrations) derived from the EKF. Temporal variation of the model parameters was also examined using the EKF. The maximum photosynthetic rate (Pm) varied slowly over the year but was essentially stationary within any three to six day period. The low light efficiency of photosynthesis (Eo) varied from day to day within any short period, but three to six day means of Eo were essentially stationary over the year. The ratio (Ik = Pm/Eo) was highly correlated with both short and long term variations in daily mean light intensity.

A new look at the statistical model identification

The history of the development of statistical hypothesis testing in time series analysis is reviewed briefly and it is pointed out that the hypothesis testing procedure is not adequately defined as the procedure for statistical model identification. The classical maximum likelihood estimation procedure is reviewed and a new estimate minimum information theoretical criterion (AIC) estimate (MAICE) which is designed for the purpose of statistical identification is introduced. When there are several competing models the MAICE is defined by the model and the maximum likelihood estimates of the parameters which give the minimum of AIC defined by AIC = (-2)log-(maximum likelihood) + 2(number of independently adjusted parameters within the model). MAICE provides a versatile procedure for statistical model identification which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure. The practical utility of MAICE in time series analysis is demonstrated with some numerical examples.

A spectral analysis procedure for model identification and parameter evaluation of dynamic systems

A spectral analysis procedure for model identification and parameter evaluation of dynamic systems is given. Assuming the process can be represented as a linear system, an algorithm is given for converting the frequency response to spectra from which the poles and zeros of the process can be identified. The characteristics of the Lorentzian peaks which appear in the spectra can be used to evaluate the location of the poles and zeros in the complex plane as well as the gain and time delay of the dynamic system. Included are several illustrative examples with the fast Fourier transform being used to compute the required spectra.