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Confidence Intervals for Diffusion Index Forecasts with a Large Number of Predictor

Author

Listed:
  • Jushan Bai

    (NYU)

  • Serena Ng

    (University of Michigan)

Abstract
We consider the situation when there is a large number of series, $N$, each with $T$ observations, and each series has some predictive ability for the variable of interest, $y$. A methodology of growing interest is to first estimate common factors from the panel of data by the method of principal components, and then augment an otherwise standard regression or forecasting equation with the estimated factors. In this paper, we show that the least squares estimates obtained from these factor augmented regressions are $\sqrt{T}$ consistent if $\sqrt{T}/N\rightarrow 0$. The factor forecasts for the conditional mean are $\min[\sqrt{T},\sqrt{N}]$ consistent, but the effect of ``estimated regressors' is asymptotically negligible when $T/N$ goes to zero. We present analytical formulas for predication intervals that take into account the sampling variability of the factor estimates. These formulas are valid regardless of the magnitude of $N/T$, and can also be used when the factors are non-stationary. The generality of these results is made possible by a covariance matrix estimator that is robust to weak cross-section correlation and heteroskedasticity in the idiosyncratic errors. We provide a consistency proof for this CS-HAC estimator.

Suggested Citation

  • Jushan Bai & Serena Ng, 2004. "Confidence Intervals for Diffusion Index Forecasts with a Large Number of Predictor," Econometrics 0408006, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpem:0408006
    Note: Type of Document - pdf
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/em/papers/0408/0408006.pdf
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    Citations

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    Cited by:

    1. Massimiliano Marcellino, 2007. "Pooling‐Based Data Interpolation and Backdating," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(1), pages 53-71, January.
    2. Bai, Jushan & Ng, Serena, 2006. "Evaluating latent and observed factors in macroeconomics and finance," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 507-537.
    3. Angelini, Elena & Henry, Jerome & Marcellino, Massimiliano, 2006. "Interpolation and backdating with a large information set," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2693-2724, December.
    4. Kilian, Lutz & Inoue, Atsushi, 2005. "How Useful is Bagging in Forecasting Economic Time Series? A Case Study of US CPI Inflation," CEPR Discussion Papers 5304, C.E.P.R. Discussion Papers.
    5. Antoine A. Djogbenou, 2020. "Comovements in the real activity of developed and emerging economies: A test of global versus specific international factors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(3), pages 344-370, April.
    6. Daniel Kaufmann & Sarah M. Lein, 2012. "Is There a Swiss Price Puzzle?," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 148(I), pages 57-75, March.

    More about this item

    Keywords

    Panel data; common factors; generated regressors; cross- section dependence; robust covariance matrix;
    All these keywords.

    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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