Classical time series methods rely on stationarity, an assumption that is rarely satisfied in practice. This thesis investigates statistical inference for time series exhibiting nonstationarity, distinguishing between intrinsic nonstationarity and nonstationarity induced by contamination. For intrinsically nonstationary series, the thesis focuses on multivariate regularly varying processes. It introduces a novel extreme-value extension of local stationarity, termed E-local stationarity, which enables nonparametric estimation of time-varying extremal features with established asymptotic guarantees. For contamination-induced nonstationarity, the thesis develops a robust frequency-domain estimation framework based on the periodogram ordinates, incorporating bounded influence functions to mitigate the effects of low-frequency and periodic contaminations. The proposed methods are theoretically justified and validated through numerical studies on both synthetic and real data.