On Confidence Bands for Time Series Problems in the Time and Frequency Domains

摘要

The construction of (asymptotic) simultaneous confidencebands for some time series problems is studied, typically for the sample au-tocorrelogram and windowed spectral density estimate. The following ap-proaches are explored: (1) To use the close-form results available in the lit-erature; (2) To use the asymptotic independence of the sample quantitiesto derive new procedures; (3) To resort to inequalities. As expected, thebands turn out being wider than those frequently encountered in the litera-ture, based on point-by-point confidence intervals. Numerical values of thenecessary constants are given for selected values of the joint confidence coef-ficient and various numbers of sample quantities. The use of confidence setsof non-uniform width is also brie.y explored. Monte Carlo simulations arepresented, for problems in the time and in the frequency domains