Time Series Analysis Models

Time series analysis models serve as crucial tools for analyzing and forecasting time-dependent data. Among these, the ARMA (Autoregressive Moving Average) model stands as a classical approach widely applied in finance, meteorology, industrial engineering, and other domains.

The core objective of this program is to simulate an ARMA model and investigate how temporal aggregation impacts model characteristics. Temporal aggregation refers to the process of converting high-frequency time series data (e.g., minute-level observations) into lower-frequency data (e.g., hourly or daily aggregates). This transformation may alter the statistical properties of the data, consequently affecting the model's predictive performance.

The program's main workflow includes:

ARMA Model Simulation Generates synthetic time series data conforming to ARMA structure, where parameters for both autoregressive (AR) and moving average (MA) components can be customized. Implementation typically involves using MATLAB's arima() function to define model order (p,q) and coefficients, followed by simulate() function with specified innovation distribution. The simulated data serves as the foundation for subsequent analysis.

Temporal Aggregation Performs downsampling on original data (e.g., converting minute-level readings to hourly averages) to examine whether aggregated data still satisfies ARMA assumptions. Aggregation methods may include statistical operations like mean, sum, or maximum values, implemented through resample() or retime() functions with appropriate aggregation rules.

Model Comparison Fits ARMA models separately to pre-aggregation and post-aggregation data, comparing changes in parameter estimates. Uses estimation functions like estimate() with maximum likelihood optimization to quantify potential bias or information loss introduced by aggregation. Diagnostic checks through functions such as infer() for residuals and aicbic() for model selection criteria.

This analysis provides insights into time series behavior across different temporal scales, with applications in data compression optimization and long-term forecasting enhancement scenarios.