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Estimating the number of common trends in large T and N factor models via canonical correlations analysis

Author

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  • Franchi, Massimo
  • Georgiev, Iliyan
  • Paruolo, Paolo

Abstract

Asymptotic results for canonical correlations are derived when the analysis is performed between levels and cumulated levels of N time series of length T, generated by a factor model with s common stochastic trends. For T→∞ and fixed N and s, the largest s squared canonical correlations are shown to converge to a non-degenerate limit distribution while the remaining N−s converge in probability to 0. Furthermore, if s grows at most linearly in N, the largest s squared canonical correlations are shown to converge in probability to 1 as (T,N)seq→∞. This feature allows one to estimate the number of common trends as the integer with largest decrease in adjacent squared canonical correlations. The maximal gap equals 1 in the limit and this criterion is shown to be consistent. A Monte Carlo simulation study illustrates the findings.

Suggested Citation

  • Franchi, Massimo & Georgiev, Iliyan & Paruolo, Paolo, 2026. "Estimating the number of common trends in large T and N factor models via canonical correlations analysis," Econometrics and Statistics, Elsevier, vol. 39(C), pages 81-95.
    • Handle: RePEc:eee:ecosta:v:39:y:2026:i:c:p:81-95
    DOI: 10.1016/j.ecosta.2023.10.001
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    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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