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Covariance estimation for multivariate conditionally Gaussian dynamic linear models

Author

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  • K. Triantafyllopoulos

    (Department of Probability and Statistics, University of Sheffield, Sheffield, UK)

Abstract

In multivariate time series, estimation of the covariance matrix of observation innovations plays an important role in forecasting as it enables computation of standardized forecast error vectors as well as the computation of confidence bounds of forecasts. We develop an online, 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. Copyright © 2007 John Wiley & Sons, Ltd.

Suggested Citation

  • K. Triantafyllopoulos, 2007. "Covariance estimation for multivariate conditionally Gaussian dynamic linear models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(8), pages 551-569.
    • Handle: RePEc:jof:jforec:v:26:y:2007:i:8:p:551-569
    DOI: 10.1002/for.1039
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    References listed on IDEAS

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    Cited by:

    1. Wenjie Zhao & Raquel Prado, 2020. "Efficient Bayesian PARCOR approaches for dynamic modeling of multivariate time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 759-784, November.
    2. K. Triantafyllopoulos, 2011. "Time-varying vector autoregressive models with stochastic volatility," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(2), pages 369-382, September.
    3. Sui, Yuelei & Holan, Scott H. & Yang, Wen-Hsi, 2023. "Bayesian circular lattice filters for computationally efficient estimation of multivariate time-varying autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    4. Sotiris Bersimis & Kostas Triantafyllopoulos, 2020. "Dynamic Non-parametric Monitoring of Air-Pollution," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1457-1479, December.
    5. Ya-Ling Huang & Chin-Tsai Lin, 2011. "Developing an interval forecasting method to predict undulated demand," Quality & Quantity: International Journal of Methodology, Springer, vol. 45(3), pages 513-524, April.

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