A tutorial and methodological review of linear time series models: Using R and SPSS

Area of Science:

• Psychology
• Behavioral Sciences
• Quantitative Methods

Background:

• Autoregressive (AR) linear models are crucial for time series analysis but underutilized in behavioral sciences due to complexity.
• Conceptual challenges in interpreting autocorrelation and seasonality hinder AR model adoption.

Purpose of the Study:

• To simplify the implementation and interpretation of AR linear models for psychology students and researchers.
• To present time series models as accessible linear regression cases with practical examples.
• To enhance understanding of residual diagnostics and their impact on statistical significance.

Main Methods:

• Step-by-step tutorial using SPSS and R software.
• Illustrates AR estimation with real data, including lagged variables as predictors.
• Focuses on residual diagnostics with figures and statistical tests.
• Compares polynomial and AR models using the confounding test.
• Provides annotated scripts and data for replication.

Main Results:

• Demonstrates how serially correlated residuals can lead to inflated Type I errors (false positives).
• Offers visualizations and decision rules for model building, lag selection, and seasonality detection.
• Highlights practical advantages of AR-only models in psychological research contexts.

Conclusions:

• AR models can be effectively implemented in psychological research with clear guidance.
• Accurate residual diagnostics are essential for valid statistical inference in time series analysis.
• Aligning statistical models with data's temporal structure and theoretical assumptions is paramount.