Covariance estimation for multivariate conditionally Gaussian dynamic linear models

TL;DR

This paper introduces an online Bayesian method for estimating covariance matrices in multivariate time series, improving forecasting accuracy and confidence interval computation.

Contribution

It presents a novel non-iterative Bayesian algorithm for covariance estimation in multivariate conditionally Gaussian dynamic linear models, with empirical validation.

Findings

The estimator converges to true covariance values in simulated data.

It approximates Monte Carlo gold standard estimates effectively.

The method is demonstrated on real metal exchange data.

Abstract

In multivariate time series, the estimation of the covariance matrix of the observation innovations plays an important role in forecasting as it enables the computation of the standardized forecast error vectors as well as it enables the computation of confidence bounds of the forecasts. We develop an on-line, non-iterative Bayesian algorithm for estimation and forecasting. It is empirically found that, for a range of simulated time series, the proposed covariance estimator has good performance converging to the true values of the unknown observation covariance matrix. Over a simulated time series, the new method approximates the correct estimates, produced by a non-sequential Monte Carlo simulation procedure, which is used here as the gold standard. The special, but important, vector autoregressive (VAR) and time-varying VAR models are illustrated by considering London metal exchange data consisting of spot prices of aluminium, copper, lead and zinc.