Prediction in locally stationary time series

TL;DR

This paper introduces a new covariance estimator for locally stationary time series that enables consistent prediction without autoregressive modeling or trend elimination, demonstrated through simulations and financial data.

Contribution

It presents a novel covariance estimator and prediction method for non-stationary time series that does not depend on autoregressive models or trend removal.

Findings

Estimator performs well in simulations

Method yields accurate predictions on financial data

Outperforms traditional autoregressive approaches

Abstract

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 non-stationary 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.