Accurate Estimation of Autocorrelation and Power Spectrum Using Parametric Models

Parametric models such as Autoregressive (AR), Moving Average (MA), or Autoregressive Moving Average (ARMA) enable accurate estimation of autocorrelation and power spectrum. Through automated inference, both model parameters and model structure can be determined directly from data. It is assumed that the ARMASA toolbox is already installed. This toolbox provides multiple functions for estimating model parameters and selecting optimal model structures, facilitating better understanding of data characteristics. The implementation typically involves using functions like armasa for automated model selection and arima for parameter estimation, where algorithms such as maximum likelihood estimation (MLE) or Bayesian information criterion (BIC) are employed for optimal model fitting. Additionally, the models can be used for prediction and simulation to better understand data behavior and trends. When applying these techniques for data analysis, researchers can gain comprehensive insights into datasets, leading to more informed decision-making.