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Factor Models in High-Dimensional Time Series: A Time-Domain Approach

  • Marc Hallin
  • Marco Lippi

High-dimensional time series may well be the most common type of dataset in the socalled“big data” revolution, and have entered current practice in many areas, includingmeteorology, genomics, chemometrics, connectomics, complex physics simulations, biologicaland environmental research, finance and econometrics. The analysis of such datasetsposes significant challenges, both from a statistical as from a numerical point of view. Themost successful procedures so far have been based on dimension reduction techniques and,more particularly, on high-dimensional factor models. Those models have been developed,essentially, within time series econometrics, and deserve being better known in other areas.In this paper, we provide an original time-domain presentation of the methodologicalfoundations of those models (dynamic factor models usually are described via a spectralapproach), contrasting such concepts as commonality and idiosyncrasy, factors and commonshocks, dynamic and static principal components. That time-domain approach emphasizesthe fact that, contrary to the static factor models favored by practitioners, the so-called generaldynamic factor model essentially does not impose any constraints on the data-generatingprocess, but follows from a general representation result.

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Paper provided by ULB -- Universite Libre de Bruxelles in its series Working Papers ECARES with number ECARES 2013-15.

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Length: 18 p.
Date of creation: Mar 2013
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Publication status: Published by:
Handle: RePEc:eca:wpaper:2013/142428
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  1. Forni, Mario & Lippi, Marco, 2011. "The general dynamic factor model: One-sided representation results," Journal of Econometrics, Elsevier, vol. 163(1), pages 23-28, July.
  2. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-62, April.
  3. De Mol, Christine & Giannone, Domenico & Reichlin, Lucrezia, 2006. "Forecasting Using a Large Number of Predictors: Is Bayesian Regression a Valid Alternative to Principal Components?," CEPR Discussion Papers 5829, C.E.P.R. Discussion Papers.
  4. Catherine Doz & Domenico Giannone & Lucrezia Reichlin, 2012. "A Quasi–Maximum Likelihood Approach for Large, Approximate Dynamic Factor Models," The Review of Economics and Statistics, MIT Press, vol. 94(4), pages 1014-1024, November.
  5. Chamberlain, Gary & Rothschild, Michael, 1982. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Scholarly Articles 3230355, Harvard University Department of Economics.
  6. Chamberlain, Gary, 1983. "Funds, Factors, and Diversification in Arbitrage Pricing Models," Econometrica, Econometric Society, vol. 51(5), pages 1305-23, September.
  7. Clifford Lam & Qiwei Yao, 2012. "Factor modeling for high-dimensional time series: inference for the number of factors," LSE Research Online Documents on Economics 45684, London School of Economics and Political Science, LSE Library.
  8. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 1999. "The Generalized Dynamic Factor Model: Identification and Estimation," CEPR Discussion Papers 2338, C.E.P.R. Discussion Papers.
  9. Jushan Bai & Serena Ng, 2004. "A PANIC Attack on Unit Roots and Cointegration," Econometrica, Econometric Society, vol. 72(4), pages 1127-1177, 07.
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  11. Mario Forni & Marc Hallin & Marco Lippi & Paolo Zaffaroni, 2011. "One-Sided Representations of Generalized Dynamic Factor Models," Working Papers ECARES ECARES 2011-019, ULB -- Universite Libre de Bruxelles.
  12. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
  13. Doz, Catherine & Giannone, Domenico & Reichlin, Lucrezia, 2007. "A Two-Step Estimator for Large Approximate Dynamic Factor Models Based on Kalman Filtering," CEPR Discussion Papers 6043, C.E.P.R. Discussion Papers.
  14. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, 09.
  15. Alessi, Lucia & Barigozzi, Matteo & Capasso, Marco, 2010. "Improved penalization for determining the number of factors in approximate factor models," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1806-1813, December.
  16. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1113-1141, December.
  17. Thomas J. Sargent & Christopher A. Sims, 1977. "Business cycle modeling without pretending to have too much a priori economic theory," Working Papers 55, Federal Reserve Bank of Minneapolis.
  18. Forni, Mario & Giannone, Domenico & Lippi, Marco & Reichlin, Lucrezia, 2007. "Opening the black box: structural factor models with large cross-sections," Working Paper Series 0712, European Central Bank.
  19. Bai, Jushan, 2004. "Estimating cross-section common stochastic trends in nonstationary panel data," Journal of Econometrics, Elsevier, vol. 122(1), pages 137-183, September.
  20. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
  21. Motta, Giovanni & Hafner, Christian M. & von Sachs, Rainer, 2011. "Locally Stationary Factor Models: Identification And Nonparametric Estimation," Econometric Theory, Cambridge University Press, vol. 27(06), pages 1279-1319, December.
  22. Hallin, Marc & Liska, Roman, 2007. "Determining the Number of Factors in the General Dynamic Factor Model," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 603-617, June.
  23. Amengual, Dante & Watson, Mark W., 2007. "Consistent Estimation of the Number of Dynamic Factors in a Large N and T Panel," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 91-96, January.
  24. Alexei Onatski, 2009. "Testing Hypotheses About the Number of Factors in Large Factor Models," Econometrica, Econometric Society, vol. 77(5), pages 1447-1479, 09.
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