A comparative simulation study of AR(1) estimators in short time series

Area of Science:

• Statistics
• Time Series Analysis
• Econometrics

Background:

• Autoregressive (AR) models are crucial for time series analysis.
• Accurate estimation of autocorrelation is vital for model performance.
• Existing estimators vary in their effectiveness, especially with short time series.

Purpose of the Study:

• To compare the performance of various frequentist and Bayesian estimators for AR(1) models.
• To evaluate estimator bias, variability, and statistical power with short time series.
• To assess estimator robustness under model misspecification (ARMA(1,1) data analyzed as AR(1)).

Main Methods:

• Study 1: Compared frequentist r1, C-statistic, OLS, MLE, and Bayesian methods (flat and B_sr priors) using simulated AR(1) data.
• Varied time series lengths (T=10 to 100) and autocorrelation coefficients (-0.9 to 0.9).
• Study 2: Assessed robustness of B_sr and MLE using ARMA(1,1) data analyzed as AR(1).

Main Results:

• Under correct specification, B_sr yielded the lowest bias, while r1 showed the lowest variability.
• B_sr and OLS demonstrated the highest statistical power.
• All estimators performed poorly with very short time series (T=10).
• Under misspecification, bias increased with the moving average parameter; B_sr and MLE showed negligible differences.

Conclusions:

• The B_sr Bayesian method is recommended for minimizing bias in AR(1) estimation with short time series.
• Model misspecification significantly impacts estimator performance.
• Careful consideration of time series length and model structure is essential for reliable estimation.