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Estimation of latent factors for high-dimensional time series

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  • Lam, Clifford
  • Yao, Qiwei
  • Bathia, Neil

Abstract

This paper deals with the dimension reduction of high-dimensional time series based on common factors. In particular we allow the dimension of time series p to be as large as, or even larger than, the sample size n. The estimation of the factor loading matrix and the factor process itself is carried out via an eigenanalysis of a p £ p non-negative de¯nite 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 p1=2, the estimator of the factor loading matrix is weakly consistent in L2-norm with the convergence rate independent of p. This result exhibits clearly that the `curse' is canceled out by the `blessing' of dimensionality. We also establish the asymptotic properties of the estimation when factors are not strong. The proposed method together with their asymptotic properties are further illustrated in a simulation study. An application to an implied volatility data set, together with a trading strategy derived from the ¯tted factor model, is also reported.

Suggested Citation

  • Lam, Clifford & Yao, Qiwei & Bathia, Neil, 2011. "Estimation of latent factors for high-dimensional time series," LSE Research Online Documents on Economics 31549, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:31549
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    File URL: http://eprints.lse.ac.uk/31549/
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    References listed on IDEAS

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    More about this item

    Keywords

    ISI; convergence in L2-norm; curse and blessing of dimensionality; dimension reduction; eigenanalysis; factor model;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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