Fitting parametric models by optimizing frequency domain objective functions is an attractive approach of parameter estimation in time series analysis. Whittle estimators is a prominent example in this context.
Under weak conditions on the underlying stationary process and the (realistic) assumption that the true spectral density of the underlying process does not necessarily belong to the parametric class of spectral densities fitted, the distribution of Whittle estimators typically depends on difficult to estimate characteristics of the underlying process. This makes the implementation of asymptotic results for the construction of confidence intervals or for assessing the variability of the estimators, difficult in practice. This paper proposes a frequency domain bootstrap method to estimate the distribution of Whittle estimators which is asymptotically valid under assumptions that not only allow for (possible) model misspecification but also for weak dependence structures which are satisfied by a wide range of stationary stochastic processes. Adaptions of the bootstrap procedure developed to incorporate different modifications of Whittle estimators proposed in the literature are also considered.
Simulations demonstrate the capabilities of the bootstrap method proposed and its good finite sample performance.
Joint work with Jens-Peter Kreiss (Technische Universität Braunschweig, Germany)
Personal Website of Efstathios Paparoditis
To participate please join our ZOOM MEETING
Meeting room opens at: May 17, 2021 4.30 pm Vienna
Meeting ID: 948 8784 2058
Password: 904357