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Covariance estimation for multivariate conditionally Gaussian dynamic linear models

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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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    1. A. C. Harvey, 1986. "Analysis and Generalisation of a Multivariate Exponential Smoothing Model," Management Science, INFORMS, vol. 32(3), pages 374-380, March.
    2. Godolphin, E.J. & Triantafyllopoulos, Kostas, 2006. "Decomposition of time series models in state-space form," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2232-2246, May.
    3. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, Decembrie.
    4. Fernandez, F Javier & Harvey, Andrew C, 1990. "Seemingly Unrelated Time Series Equations and a Test for Homogeneity," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 71-81, January.
    5. Ni, Shawn & Sun, Dongchu, 2003. "Noninformative priors and frequentist risks of bayesian estimators of vector-autoregressive models," Journal of Econometrics, Elsevier, vol. 115(1), pages 159-197, July.
    6. Clinton Watkins & Michael McAleer, 2004. "Econometric modelling of non‐ferrous metal prices," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 651-701, December.
    7. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 247-264.
    8. Christian Francq & Antony Gautier, 2004. "Large sample properties of parameter least squares estimates for time‐varying arma models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 765-783, September.
    9. Salvador, Manuel & Gargallo, Pilar, 2004. "Automatic monitoring and intervention in multivariate dynamic linear models," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 401-431, October.
    10. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    11. Pollock, D. S. G., 2003. "Recursive estimation in econometrics," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 37-75, October.
    12. Harald Uhlig, 1997. "Bayesian Vector Autoregressions with Stochastic Volatility," Econometrica, Econometric Society, vol. 65(1), pages 59-74, January.
    13. Litterman, Robert B, 1986. "Forecasting with Bayesian Vector Autoregressions-Five Years of Experience," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(1), pages 25-38, January.
    14. Filippo Moauro & Giovanni Savio, 2005. "Temporal disaggregation using multivariate structural time series models," Econometrics Journal, Royal Economic Society, vol. 8(2), pages 214-234, July.
    15. Triantafyllopoulos, Kostas & Pikoulas, John, 2002. "Multivariate Bayesian Regression Applied to the Problem of Network Security," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 21(8), pages 579-594, December.
    16. Paul L. Anderson & Mark M. Meerschaert, 2005. "Parameter Estimation for Periodically Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 489-518, July.
    17. Toni Gravelle & James Morley, 2005. "A Kalman filter approach to characterizing the Canadian term structure of interest rates," Applied Financial Economics, Taylor & Francis Journals, vol. 15(10), pages 691-705.
    18. Kadiyala, K Rao & Karlsson, Sune, 1997. "Numerical Methods for Estimation and Inference in Bayesian VAR-Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(2), pages 99-132, March-Apr.
    19. Litterman, Robert, 1986. "Forecasting with Bayesian vector autoregressions -- Five years of experience : Robert B. Litterman, Journal of Business and Economic Statistics 4 (1986) 25-38," International Journal of Forecasting, Elsevier, vol. 2(4), pages 497-498.
    20. Barassi, Marco R. & Caporale, Guglielmo Maria & Hall, Stephen G., 2005. "Interest rate linkages: a Kalman filter approach to detecting structural change," Economic Modelling, Elsevier, vol. 22(2), pages 253-284, March.
    21. Triantafyllopoulos, Kostas, 2006. "Multivariate discount weighted regression and local level models," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3702-3720, August.
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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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