ARMA Model Time Series Analysis Method

The ARMA model time series analysis method uses parametric models to analyze ordered random vibration response data for modal parameter identification. Parametric models encompass AR (Autoregressive), MA (Moving Average), and ARMA (Autoregressive Moving Average) models, with ARMA providing superior accuracy in capturing time series data relationships. Below is a MATLAB program for estimating ARMA model parameters, which implements the following workflow: 1. Data Preprocessing: Clean and process raw data to ensure accuracy and reliability. This typically involves handling missing values using interpolation functions like fillmissing, removing trends with detrend, and normalizing data via zscore for stable numerical computation. 2. Model Selection: Choose an appropriate ARMA(p,q) model based on data characteristics. The implementation may use information criteria (e.g., AIC/BIC computed with aicbic) or autocorrelation/partial autocorrelation analysis (using autocorr and parcorr functions) to determine optimal p and q orders. 3. Parameter Estimation: Estimate ARMA parameters using methods like maximum likelihood estimation (implemented with armax or estimation functions) or Bayesian estimation. The algorithm numerically optimizes likelihood functions, often employing Kalman filtering for state-space representations. 4. Model Validation: Validate the model by testing residual series for stationarity (e.g., Augmented Dickey-Fuller test with adftest), autocorrelation (using lbqtest for Ljung-Box test), and partial autocorrelation. Residual diagnostics ensure the model adequately captures data patterns. 5. Model Prediction: Forecast future data points using the estimated ARMA model with the predict or forecast function, which propagates the model recursively based on historical data and estimated parameters. This program demonstrates the principles and applications of ARMA modeling, providing valuable reference for research implementation. The code structure emphasizes modularity, with separate functions for each step to facilitate customization and extension.