Estimation error for blind Gaussian time series prediction

TL;DR

This paper introduces a new method for predicting Gaussian time series without prior knowledge, using empirical covariance estimates and projection operators, with proven convergence rates.

Contribution

It presents a novel projection-based predictor for blind Gaussian time series prediction and provides theoretical convergence rate analysis.

Findings

Convergence rates for the proposed estimator are established.

The method effectively predicts Gaussian time series without prior model parameters.

The approach leverages empirical covariance and Schur complement decomposition.

Abstract

We tackle the issue of the blind prediction of a Gaussian time series. For this, we construct a projection operator build by plugging an empirical covariance estimation into a Schur complement decomposition of the projector. This operator is then used to compute the predictor. Rates of convergence of the estimates are given.