This paper introduces a network model for analyzing time-varying dependencies in multivariate time series using hidden semi-Markov models. The model incorporates temporal heterogeneity by utilizing regime-dependent parameters governed by a latent finite-state semi-Markov chain and accommodates non-Gaussian features of empirical data through nonparanormal distributions. A Lasso-type penalty is employed to enforce sparsity in the network, ensuring the identification of only the most significant connections. Estimation is performed using an Expectation-Maximization algorithm, which does not assume restrictive assumptions on the states’ sojourn distributions. The empirical analysis focuses on daily returns of the 25 largest S&P 500 companies by market capitalization.