System Parameter Estimation using ARMA, AR, MA Models

We can utilize various methods including ARMA, AR, MA models and periodograms for system parameter estimation. The ARMA model combines both autoregressive (AR) and moving average (MA) components, providing a comprehensive approach for time series modeling. In implementation, ARMA models typically require parameter estimation techniques like maximum likelihood estimation or the Yule-Walker equations. The AR model focuses exclusively on the autoregressive component, where current values are expressed as linear combinations of previous values using the ar function in MATLAB or similar libraries. The MA model describes time series through moving averages of error terms, often implemented using algorithms that estimate coefficients through innovation algorithms or state-space representations. Periodograms serve as valuable visualization tools for identifying cyclical patterns in time series data, commonly computed using Fast Fourier Transform (FFT) algorithms in programming languages like Python or MATLAB. This spectral analysis helps determine appropriate model orders and parameters. Therefore, based on specific data characteristics, we can select suitable estimation methods to effectively analyze and interpret system behavior, ensuring optimal model performance through techniques like AIC/BIC criteria for model selection.