A1726
Title: Linear hypothesis test for dynamic factor model
Authors: Rikako Senoo - Waseda University (Japan) [presenting]
Giovanni Motta - Columbia University (United States)
Yan Liu - Waseda University (Japan)
Abstract: A hypothesis testing framework is proposed for the linear structure of latent factors in an approximate factor model. Despite the widespread use of dynamic factor models and dimensional reduction via PCA, formal hypothesis testing for latent factor dynamics remains unexplored. To address this gap, a linear hypothesis testing problem for factor dynamics is considered, where the latent factors follow a VAR(p) process within a general approximate factor model. Estimation proceeds in two steps: latent factors are first estimated via PCA, followed by OLS estimation of the VAR coefficient matrices. Asymptotic normality of the estimated VAR coefficient matrices is derived under two regimes, $\sqrt{N}/T \to 0$ and $\sqrt{N}/T$ does not vanish as $N, T \to \infty$, and a Wald-type statistic for general linear hypotheses is proposed. The statistic is constructed using a rotated OLS estimator and is shown to be asymptotically chi-square distributed. The rotated OLS estimator converges directly to the true VAR coefficient matrices, enabling valid inference on the underlying linear structure and overcoming the rotational indeterminacy inherent in the PCA-based approach. Simulation results demonstrate strong finite-sample performance and are consistent with the theoretical findings. Empirical applications of the proposed methods are also presented.
