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Estimation of latent factors for high-dimensional time series


  • Clifford Lam
  • Qiwei Yao
  • Neil Bathia


This paper deals with the dimension reduction of high-dimensional time series based on a lower-dimensional factor process. In particular, we allow the dimension of time series N to be as large as, or even larger than, the length of observed time series T. The estimation of the factor loading matrix and the factor process itself is carried out via an eigenanalysis of a N×N non-negative definite matrix. We show that when all the factors are strong in the sense that the norm of each column in the factor loading matrix is of the order N-super-1/2, the estimator of the factor loading matrix is weakly consistent in L 2 -norm with the convergence rate independent of N. Thus the curse is cancelled out by the blessing of dimensionality. We also establish the asymptotic properties of the estimators when factors are not strong. The proposed method together with the asymptotic properties are illustrated in a simulation study. An application to an implied volatility data set, with a trading strategy derived from the fitted factor model, is also reported. Copyright 2011, Oxford University Press.

Suggested Citation

  • Clifford Lam & Qiwei Yao & Neil Bathia, 2011. "Estimation of latent factors for high-dimensional time series," Biometrika, Biometrika Trust, vol. 98(4), pages 901-918.
  • Handle: RePEc:oup:biomet:v:98:y:2011:i:4:p:901-918

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    References listed on IDEAS

    1. Cressie, Noel & Davidson, Jennifer L., 1998. "Image analysis with partially ordered markov models," Computational Statistics & Data Analysis, Elsevier, vol. 29(1), pages 1-26, November.
    2. Ming Gao Gu & Hong-Tu Zhu, 2001. "Maximum likelihood estimation for spatial models by Markov chain Monte Carlo stochastic approximation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 339-355.
    3. Francesco Bartolucci, 2002. "A recursive algorithm for Markov random fields," Biometrika, Biometrika Trust, vol. 89(3), pages 724-730, August.
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    Cited by:

    1. Banerjee, Anindya & Marcellino, Massimiliano & Masten, Igor, 2014. "Forecasting with factor-augmented error correction models," International Journal of Forecasting, Elsevier, vol. 30(3), pages 589-612.
    2. Chang, Jinyuan & Guo, Bin & Yao, Qiwei, 2015. "High dimensional stochastic regression with latent factors, endogeneity and nonlinearity," LSE Research Online Documents on Economics 61886, London School of Economics and Political Science, LSE Library.
    3. Chen, Songxi, 2012. "Two Sample Tests for High Dimensional Covariance Matrices," MPRA Paper 46026, University Library of Munich, Germany.
    4. 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, September.
    5. Liu, Xialu & Xiao, Han & Chen, Rong, 2016. "Convolutional autoregressive models for functional time series," Journal of Econometrics, Elsevier, vol. 194(2), pages 263-282.
    6. He, Jing & Chen, Song Xi, 2016. "Testing super-diagonal structure in high dimensional covariance matrices," Journal of Econometrics, Elsevier, vol. 194(2), pages 283-297.
    7. repec:bla:jtsera:v:38:y:2017:i:2:p:285-307 is not listed on IDEAS
    8. Poncela, Pilar & Guerrero, Víctor & Islas C., Alejandro & Rodríguez, Julio & Sánchez-Mangas, Rocío, 2014. "Mexico: Combining monthly inflation predictions from surveys," Revista CEPAL, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL), August.
    9. Matteo Barigozzi & Lorenzo Trapani, 2017. "Sequential testing for structural stability in approximate factor models," Papers 1708.02786,
    10. Passemier, Damien & Yao, Jianfeng, 2014. "Estimation of the number of spikes, possibly equal, in the high-dimensional case," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 173-183.
    11. Chang, Jinyuan & Guo, Bin & Yao, Qiwei, 2015. "High dimensional stochastic regression with latent factors, endogeneity and nonlinearity," Journal of Econometrics, Elsevier, vol. 189(2), pages 297-312.

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