Bootstrapping Whittle estimators

Summary Fitting parametric models by optimizing frequency-domain objective functions is an attractive approach of parameter estimation in time series analysis. Whittle estimators are a prominent example this context. Under weak conditions and the assumption that true spectral density underlying process does not necessarily belong to class densities fitted, distribution typically depends on difficult estimate characteristics process. This makes implementation asymptotic results for construction confidence intervals or assessing variability practice. In paper we propose bootstrap method asymptotically valid under assumptions only allow possible model misspecification, but also dependence satisfied wide range stationary stochastic processes. Adaptations procedure developed incorporate different modifications proposed literature, such as, instance, tapered, debiased boundary extended estimators, considered. Simulations demonstrate capabilities its good finite sample performance. A real-life data analysis sunspots presented.