Collinearity Issues in Autoregressive Models with Time-Varying Serially Dependent Covariates

Area of Science:

• Statistics
• Econometrics
• Psychometrics

Background:

• First-order autoregressive models are widely used for analyzing univariate time series data.
• Incorporating time-varying covariates is common to explore moderating effects on process dynamics.

Purpose of the Study:

• To demonstrate the implications of serial dependence in time-varying covariates on the estimation of autoregressive and covariate effects.
• To highlight the potential for predictor collinearity arising from serial dependence, a factor often overlooked in current practice.

Main Methods:

• Recapitulation of predictor collinearity's impact on estimation precision in ordinary least squares regression.
• Derivation of a formula for predictor collinearity in first-order autoregressive models, considering covariate serial dependence.
• Simulation study to assess implications for various covariate types and small sample sizes.

Main Results:

• Serial dependence in time-varying covariates can induce predictor collinearity, affecting the precision of autoregressive and covariate effect estimates.
• The severity of collinearity, and its impact on interpretation, depends on the covariate's characteristics.
• Effect estimates can be biased in small samples (e.g., 50 time points).

Conclusions:

• Researchers must consider serial dependence in covariates to avoid misleading interpretations of autoregressive models.
• Implications for optimal study design, the appropriate use of time as a predictor, and the selection of related model variants are discussed.