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High-dimensional censored MIDAS logistic regression for corporate survival forecasting

Wei Miao, Jad Beyhum, Jonas Striaukas, Ingrid Van Keilegom

Abstract

This paper addresses the challenge of forecasting corporate distress, a problem marked by three key statistical hurdles: (i) right censoring, (ii) high-dimensional predictors, and (iii) mixed-frequency data. To overcome these complexities, we introduce a novel high-dimensional censored MIDAS (Mixed Data Sampling) logistic regression. Our approach handles censoring through inverse probability weighting and achieves accurate estimation with numerous mixed-frequency predictors by employing a sparse-group penalty. We establish finite-sample bounds for the estimation error, accounting for censoring, MIDAS approximation error, and heavy tails. For statistical inference, we develop a de-sparsified version of the proposed penalized estimator and establish its asymptotic theory, which enables valid statistical inference in high-dimensional settings with censoring. We show that censoring induces a nonstandard variance structure for the de-sparsified estimator, a feature that, to the best of our knowledge, has not been studied in the existing literature. The superior performance of the method is demonstrated through Monte Carlo simulations. Finally, we present an extensive application of our methodology to predict the financial distress of Chinese-listed firms and to identify covariates that are statistically significant for predicting distress. Our novel procedure is implemented in the R package \texttt{Survivalml}.

High-dimensional censored MIDAS logistic regression for corporate survival forecasting

Abstract

This paper addresses the challenge of forecasting corporate distress, a problem marked by three key statistical hurdles: (i) right censoring, (ii) high-dimensional predictors, and (iii) mixed-frequency data. To overcome these complexities, we introduce a novel high-dimensional censored MIDAS (Mixed Data Sampling) logistic regression. Our approach handles censoring through inverse probability weighting and achieves accurate estimation with numerous mixed-frequency predictors by employing a sparse-group penalty. We establish finite-sample bounds for the estimation error, accounting for censoring, MIDAS approximation error, and heavy tails. For statistical inference, we develop a de-sparsified version of the proposed penalized estimator and establish its asymptotic theory, which enables valid statistical inference in high-dimensional settings with censoring. We show that censoring induces a nonstandard variance structure for the de-sparsified estimator, a feature that, to the best of our knowledge, has not been studied in the existing literature. The superior performance of the method is demonstrated through Monte Carlo simulations. Finally, we present an extensive application of our methodology to predict the financial distress of Chinese-listed firms and to identify covariates that are statistically significant for predicting distress. Our novel procedure is implemented in the R package \texttt{Survivalml}.

Paper Structure

This paper contains 52 sections, 33 theorems, 417 equations, 8 figures, 21 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature review.
  3. Outline.
  4. Notation.
  5. High-dimensional censored MIDAS logistic regression
  6. Logistic regression model
  7. Estimation with mixed-frequency data
  8. Theoretical results
  9. Estimation theory
  10. De-sparsified procedure and inference theory
  11. Simulations
  12. Simulation design
  13. Evaluation metric: ROC curves with censoring
  14. Discussion on the MIDAS-weighted covariates
  15. Prediction simulation results
  16. ...and 37 more sections

Key Result

Theorem 3.1

Let Assumptions as1, as2, asX, aseign and aseff hold. If there exists a sufficiently large constant $\mathcal{K}$ such that $\lambda \geq \mathcal{K}p^{\frac{1}{q}}\sqrt{\log p}/N^{\frac{1}{2} - \frac{1}{q}}$, then, with probability going to $1$, we have and

Figures (8)

  • Figure 1: Firms with different censoring statuses in the empirical dataset.
  • Figure 2: Correlation matrix of the $L = 3$ elements in the first group ($k=1$) of MIDAS-weighted covariates in Scenarios \ref{['s1']} and \ref{['s2']} for $N = 800$. Results are based on $100$ simulation repetitions, and the MIDAS weighting matrix $W$ is described in Section \ref{['est simulation']}.
  • Figure 3: Number of IPO, first-time-to-be ST, and censored firms across different years in the raw dataset.
  • Figure 4: Selected financial variables by sg-LASSO-MIDAS when $s = 6$ years.
  • Figure 5: Selected financial variables by sg-LASSO-MIDAS when $s = 10$ years.
  • ...and 3 more figures

Theorems & Definitions (62)

  • Theorem 3.1
  • Corollary 3.1
  • Lemma 3.1
  • Theorem 3.2
  • Lemma A.1
  • proof
  • Lemma A.2
  • proof
  • Lemma B.1
  • proof
  • ...and 52 more