Smoothing Spline Semi‐Parametric Non‐Gaussian Structural Vector Autoregressive Models

ABSTRACT We study semiparametric non‐Gaussian structural vector autoregressive (SVAR) models, where the density functions of the structural shocks are left unspecified but are assumed to be non‐Gaussian and mutually independent. This semiparametric framework offers flexibility and robustness to model misspecification regarding the functional form of the shock distributions. We propose a penalized likelihood estimation method grounded in the theory of reproducing kernel Hilbert spaces (RKHS). We derive the joint convergence rates for both the finite‐dimensional parametric component and the infinite‐dimensional functional component. The finite‐sample performance of the estimator is examined through Monte Carlo simulations. The simulations also demonstrate that our method can be adapted for independent component analysis. Finally, we present an empirical application using real data, showing how the proposed approach can be used in non‐Gaussian SVAR models to identify the effects of structural shocks.