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Some Aspects Of Modelling And Forecasting Multivariate Time Series

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  • Gwilym M. Jenkins
  • Athar S. Alavi

Abstract

. The paper describes model structures for representing multivariate time series containing stochastic trends and stochastic seasonal patterns. Methods for identification, fitting and checking these models are described. Two methods of identification are compared: using statistics calculated from (a) the unprewhitened stationary series, obtained by appropriately transforming and differencing the original series, (b) the series after prewhitening them by their univariate models. We see practical merit in using both methods of approach. A brief description is also given of the use of multivariate stochastic models for forecasting but a fuller description is to be given elsewhere, covering more general situations where the series may have to be aligned or phase‐shifted relative to each other to obtain a more parsimonious representation.

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  • Gwilym M. Jenkins & Athar S. Alavi, 1981. "Some Aspects Of Modelling And Forecasting Multivariate Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 2(1), pages 1-47, January.
    • Handle: RePEc:bla:jtsera:v:2:y:1981:i:1:p:1-47
    DOI: 10.1111/j.1467-9892.1981.tb00309.x
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    1. Francisco J. André & Ricardo Martín & Javier J. Pérez, 2001. "Computing Robust Stylized Facts on Comovement," Economic Working Papers at Centro de Estudios Andaluces E2001/03, Centro de Estudios Andaluces.
    2. M. Dolores Robles Fernandez & Rafael Florez De Frutos, 2000. "Time varying term premia and risk: the case of the Spanish interbank money market," Applied Financial Economics, Taylor & Francis Journals, vol. 10(3), pages 243-260.
    3. Rafael Flors de Frutos & Alfredo M. Pereira, 1993. "Testing theories of economic fluctuations and growth in early development. (The case of the Chesapeake tobacco economy)," Documentos de Trabajo del ICAE 9308, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    4. William Mallios, 2012. "Forecasting National Football League Game Outcomes Relative to Betting Spreads," Journal of Gambling Business and Economics, University of Buckingham Press, vol. 6(3), pages 1-16, December.
    5. Andre, Francisco J. & Perez, Javier J. & Martin, Ricardo, 2002. "Computing white stylized facts on comovement," Economics Letters, Elsevier, vol. 76(1), pages 65-71, June.
    6. León Navarro, Manuel & Flores de Frutos, Rafael, 2015. "Residential versus financial wealth effects on consumption from a shock in interest rates," Economic Modelling, Elsevier, vol. 49(C), pages 81-90.
    7. C. Cosculluela-Martínez & R. Ibar-Alonso & G. J. D. Hewings, 2019. "Life Expectancy Index: Age Structure of Population and Environment Evolution," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 142(2), pages 507-522, April.
    8. José Casals & Miguel Jerez & Sonia Sotoca, 2009. "Modelling and forecasting time series sampled at different frequencies," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(4), pages 316-342.
    9. Francisco Andre & Javier Perez, 2005. "Robust stylized facts on comovement for the Spanish economy," Applied Economics, Taylor & Francis Journals, vol. 37(4), pages 453-462.
    10. Rafael Flores de Frutos & Alfredo M. Pereira, 1993. "Public Capital and Aggregate Growth in the United States: Is Public Capital Productive?," Documentos de Trabajo del ICAE 9313, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    11. Carolina Cosculluela-Mart󹑺 & Rafael Flores de Frutos, 2013. "Housing investment in Spain: has it been the main engine of growth?," Applied Economics, Taylor & Francis Journals, vol. 45(14), pages 1835-1843, May.
    12. Lutkepohl, Helmut & Poskitt, D S, 1996. "Specification of Echelon-Form VARMA Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 69-79, January.
    13. Alfredo Garcia Hiernaux & Miguel Jerez & José Casals, 2005. "Unit Roots and Cointegrating Matrix Estimation using Subspace Methods," Documentos de Trabajo del ICAE 0512, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    14. Carolina Cosculluela-Martínez, 2020. "Sustainable Knowledge Investment Increases Employment and GDP in the Spanish Agricultural Sector More Than Other Investments," Sustainability, MDPI, vol. 12(8), pages 1-14, April.
    15. Marie-Christine Duker & David S. Matteson & Ruey S. Tsay & Ines Wilms, 2024. "Vector AutoRegressive Moving Average Models: A Review," Papers 2406.19702, arXiv.org.
    16. D. S. Poskitt & M. O. Salau, 1995. "On The Relationship Between Generalized Least Squares And Gaussian Estimation Of Vector Arma Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(6), pages 617-645, November.
    17. Emre Kahraman & Gazanfer Unal, 2016. "Multiple Wavelet Coherency Analysis and Forecasting of Metal Prices," Papers 1602.01960, arXiv.org.
    18. Dong Wan Shin & Sahadeb Sarkar, 1995. "Estimation Of The Multivariate Autoregressive Moving Average Having Parameter Restrictions And An Application To Rotational Sampling," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(4), pages 431-444, July.
    19. Alfredo García Hiernaux & Miguel Jerez & José Casals, 2005. "Deteccióon de Raíces Unitarias y Cointegración mediante Métodos de Subespacios," Documentos de Trabajo del ICAE 0503, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    20. Dubois, 2005. "Grocer 1.0, an Econometric Toolbox for Scilab: an Econometrician Point of View," Econometrics 0501014, University Library of Munich, Germany.
    21. Robert B. Litterman, 1982. "A use of index models in macroeconomic forecasting," Staff Report 78, Federal Reserve Bank of Minneapolis.
    22. Ronald W. Butler & Marc S. Paolella, 2017. "Autoregressive Lag—Order Selection Using Conditional Saddlepoint Approximations," Econometrics, MDPI, vol. 5(3), pages 1-33, September.
    23. Rafael Flores de Frutos, 1993. "Sobre la Estimación de Primas por Plazo dentro de la Estructura Temporal de Tipos de Interes," Documentos de Trabajo del ICAE 9302, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.

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