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System identification is a method of identifying or measuring the mathematical model of a system from measurements of the system inputs and outputs. The applications of system identification include any system where the inputs and outputs can be measured and include industrial processes, control systems, economic data, biology and the life sciences, medicine, social systems and many more.
The original model uses an iterative three-stage modeling approach: Model identification and model selection: making sure that the variables are stationary, identifying seasonality in the dependent series (seasonally differencing it if necessary), and using plots of the autocorrelation (ACF) and partial autocorrelation (PACF) functions of the dependent time series to decide which (if any ...
In the context of nonlinear system identification Jin et al. [9] describe grey-box modeling by assuming a model structure a priori and then estimating the model parameters. Parameter estimation is relatively easy if the model form is known but this is rarely the case.
Note that this is the structural form of the model, showing the relations between the Q and P. The reduced form however can be identified easily. Fisher points out that this problem is fundamental to the model, and not a matter of statistical estimation:
The Strejc system identification method allows the estimate of the transfer function of a non-periodic, black box-type system based on its step response and is widely used in all branches of industrial and mechanical engineering. It allows specifically to estimate the order n of the studied system, its time constant and its delay.
There exists a few papers that systematically compare various model checkers on a common case study. The comparison usually discusses the modelling tradeoffs faced when using the input languages of each model checker, as well as the comparison of performances of the tools when verifying correctness properties. One can mention:
The Sargan test is based on the assumption that model parameters are identified via a priori restrictions on the coefficients, and tests the validity of over-identifying restrictions. The test statistic can be computed from residuals from instrumental variables regression by constructing a quadratic form based on the cross-product of the ...
Identifiability of the model in the sense of invertibility of the map is equivalent to being able to learn the model's true parameter if the model can be observed indefinitely long. Indeed, if { X t } ⊆ S is the sequence of observations from the model, then by the strong law of large numbers ,