Finite-Sample Properties of Model Specification Tests for Multivariate Dynamic Regression Models

Battle Count: 77

Highly relevant for quantitative trading as it directly addresses the validity of asset pricing models (Fama-French 3-factor and 5-factor) used in factor investing and portfolio construction. The paper demonstrates that conventional tests (GRS, HAR) can produce misleading rejections of factor models due to size distortions from dynamic regressor-error dependence, which is common in financial data. The bootstrap GD test provides more reliable inference for determining whether pricing errors are jointly zero, directly impacting factor model selection, alpha generation strategies, and portfolio evaluation. The empirical application shows that the FF5 model may not be rejected when using the proposed test, even when conventional tests reject it.

Moderate to high complexity. The two-step GD estimator requires: (1) equation-by-equation OLS estimation of an augmented regression with lagged dependent variables and lagged regressors, (2) recovery of VAR coefficients and innovation covariance, (3) construction of the generalized Durbin transformation, and (4) GLS estimation. The bootstrap procedure adds further complexity with VAR fitting, innovation resampling, and full re-estimation in each replication. The Murphy-Topel variance correction requires computing Jacobian blocks and long-run covariance matrices. However, the algorithm is fully specified in Table 1, and standard econometric software can handle the component steps.

The paper specifies R version 4.5.3 for all computations, provides detailed simulation design parameters (VAR coefficients, innovation covariances, sample sizes, number of replications), and states all data and programs are available upon request. Fama-French data is publicly available from Kenneth French's website. The bootstrap algorithm is fully specified in Table 1. However, no GitHub repository is provided.