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A Large Confirmatory Dynamic Factor Model for Stock Market Returns in Different Time Zones

Oliver B. Linton, Haihan Tang, Jianbin Wu

Abstract

We propose a confirmatory dynamic factor model for a large number of stocks whose returns are observed daily across multiple time zones. The model has a global factor and a continental factor that both drive the individual stock return series. We propose two estimators of the model: a quasi-maximum likelihood estimator (QML-just-identified), and an improved estimator based on an Expectation Maximization (EM) algorithm (QML-all-res). Our estimators are consistent and asymptotically normal under the large approximate factor model setting. In particular, the asymptotic distributions of QML-all-res are the same as those of the infeasible OLS estimators that treat factors as known and utilize all the restrictions on the parameters of the model. We apply the model to MSCI equity indices of 42 developed and emerging markets, and find that most markets are more integrated when the CBOE Volatility Index (VIX) is high.

A Large Confirmatory Dynamic Factor Model for Stock Market Returns in Different Time Zones

Abstract

We propose a confirmatory dynamic factor model for a large number of stocks whose returns are observed daily across multiple time zones. The model has a global factor and a continental factor that both drive the individual stock return series. We propose two estimators of the model: a quasi-maximum likelihood estimator (QML-just-identified), and an improved estimator based on an Expectation Maximization (EM) algorithm (QML-all-res). Our estimators are consistent and asymptotically normal under the large approximate factor model setting. In particular, the asymptotic distributions of QML-all-res are the same as those of the infeasible OLS estimators that treat factors as known and utilize all the restrictions on the parameters of the model. We apply the model to MSCI equity indices of 42 developed and emerging markets, and find that most markets are more integrated when the CBOE Volatility Index (VIX) is high.
Paper Structure (20 sections, 7 theorems, 35 equations, 2 figures, 11 tables)

This paper contains 20 sections, 7 theorems, 35 equations, 2 figures, 11 tables.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Roadmap and Notation
  4. Model
  5. Setup
  6. The Two-Day Representation
  7. Estimation
  8. The QML Objective Function
  9. QML-Just-Identified
  10. QML-All-Res
  11. QML-Minus
  12. Large Sample Theories
  13. QML-Just-Identified
  14. QML-All-Res
  15. The Estimated Factors
  16. ...and 5 more sections

Key Result

Proposition 1

Suppose that Assumptions assu model--assu estimated within compact hold. When $N,T\to \infty$, with the $196$ particular restrictions imposed on $\hat{\Lambda}$ and $\hat{M}$ as in (main_r1) and (main_r2), we have

Figures (2)

  • Figure 1: Returns and factors
  • Figure 2: Set $T=250$. The black solid line denotes the scaled asymptotic standard deviation of $\hat{\phi}^*$ (or $\hat{\phi}^{ols}$). The red dashed line denotes the scaled asymptotic standard deviation of $\hat{\phi}^{\diamond}$.

Theorems & Definitions (7)

  • Proposition 1
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Lemma 1
  • Corollary 1