Covariance matrix estimation for stationary time series

Covariance Matrix Estimation for Stationary Time Series

We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order of magnitude is derived for spectral radius of sample covariance matrices. We also consider a thresholded covariance matrix estimator that can better characterize sparsity if the true covariance matrix is sparse. As our main tool, we implement Toeplitz [Math. Ann. 70 (1911) 351–376...

Supplement to “ Covariance Matrix Estimation for Stationary Time Series ”

Covariance Matrix Estimation in Time Series

Covariances play a fundamental role in the theory of time series and they are critical quantities that are needed in both spectral and time domain analysis. Estimation of covariance matrices is needed in the construction of confidence regions for unknown parameters, hypothesis testing, principal component analysis, prediction, discriminant analysis among others. In this paper we consider both l...

Spectral Estimation of Stationary Time Series: Recent Developments

Spectral analysis considers the problem of determining (the art of recovering) the spectral content (i.e., the distribution of power over frequency) of a stationary time series from a finite set of measurements, by means of either nonparametric or parametric techniques. This paper introduces the spectral analysis problem, motivates the definition of power spectral density functions, and reviews...

Parameter Estimation for Periodically Stationary Time Series

The innovations algorithm can be used to obtain parameter estimates for periodically stationary time series models. In this paper we compute the asymptotic distribution for these estimates in the case where the innovations have a finite fourth moment. These asymptotic results are useful to determine which model parameters are significant. In the process, we also develop asymptotics for the Yule...