Prediction in Locally Stationary Time Series

We develop an estimator for the high-dimensional covariance matrix of a locally stationary process with a smoothly varying trend and use this statistic to derive consistent predictors in nonstationary time series. In contrast to the currently available methods for this problem the predictor developed here does not rely on fitting an autoregressive model and does not require a vanishing trend. The finite sample properties of the new methodology are illustrated by means of a simulation study and a financial indices study.for this article are available online.

Automated summary

We propose an estimator for the high-dimensional covariance matrix of a locally stationary process with a smoothly varying trend. This estimator is used to derive consistent predictors for nonstationary time series. Unlike existing methods, our predictor does not rely on fitting an autoregressive model nor require a vanishing trend. Simulations and a study on financial indices demonstrate the finite sample properties of our methodology.