Covariance Matrix Estimation for Stationary Time Series

Supplement to “ Covariance Matrix Estimation for Stationary Time Series ”

Multivariate mixed normal conditional heteroskedasticity

This paper proposes a new multivariate volatility model where the conditional distribution of a vector time series is given by a mixture of multivariate normal distributions. Each of these distributions is allowed to have a time-varying covariance matrix. The process can be globally covariance-stationary even though some components are not covariance-stationary. Some theoretical properties of t...

Nonparametric estimation of large covariance matrices of longitudinal data

Estimation of an unstructured covariance matrix is difficult because of its positivedefiniteness constraint. This obstacle is removed by regressing each variable on its predecessors, so that estimation of a covariance matrix is shown to be equivalent to that of estimating a sequence of varying-coefficient and varying-order regression models. Our framework is similar to the use of increasing-ord...

Some New Methods for Prediction of Time Series by Wavelets

Extended Abstract. Forecasting is one of the most important purposes of time series analysis. For many years, classical methods were used for this aim. But these methods do not give good performance results for real time series due to non-linearity and non-stationarity of these data sets. On one hand, most of real world time series data display a time-varying second order structure. On th...

Dynamic covariance estimation via positive semidefinite dictionary learning

Time series are among the most prevalent forms of data we encounter in the real world, whether it be a sequence of audio, biomedical, demographic, climate, or financial measurements. Covariance estimation, where we try to estimate the covariance matrix of a time series, is a classic and important problem that can provide us predictive power in many applications. The vast majority of covariance ...