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Local Gaussian copula inference with structural breaks: testing dependence predictability

Alexander Mayer, Tatsushi Oka, Dominik Wied

Abstract

We propose a score test for dependence predictability in conditional copulas that is robust to temporal instabilities. Our semiparametric procedure accommodates flexible dynamics in the marginal processes and remains agnostic about the copula family by leveraging distributional regression techniques together with a local Gaussian representation of the copula link function. We derive the limiting distribution of our test statistic and propose a resampling scheme based on recent results for the moving block bootstrap of multi-stage estimators. Monte Carlo simulations and an empirical application illustrate the finite-sample performance of our methods.

Local Gaussian copula inference with structural breaks: testing dependence predictability

Abstract

We propose a score test for dependence predictability in conditional copulas that is robust to temporal instabilities. Our semiparametric procedure accommodates flexible dynamics in the marginal processes and remains agnostic about the copula family by leveraging distributional regression techniques together with a local Gaussian representation of the copula link function. We derive the limiting distribution of our test statistic and propose a resampling scheme based on recent results for the moving block bootstrap of multi-stage estimators. Monte Carlo simulations and an empirical application illustrate the finite-sample performance of our methods.
Paper Structure (19 sections, 5 theorems, 130 equations, 1 figure, 2 tables)

This paper contains 19 sections, 5 theorems, 130 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Model and testing problem
  3. Test statistic and bootstrap
  4. Asymptotic properties
  5. Further assumptions
  6. Asymptotics of the restricted estimator
  7. Asymptotics of the test statistic
  8. Monte Carlo simulations
  9. Empirical application
  10. Concluding remarks
  11. Proof of Lemma 1
  12. Proof of Lemma 1 (1)
  13. Proof of Lemma 1 (2)
  14. Proof of Lemma 1 (3)
  15. Proof of Lemma 2
  16. ...and 4 more sections

Key Result

Proposition 1

Suppose $H_0$ is true.

Figures (1)

  • Figure 1: The plots are based on daily CRSP return data from January 2000 to December 2019. Empirical ranks of standardized returns of three financial companies ($r_t$) and the market return ($r_{m,t}$) with 68% Gaussian ellipses and Spearman’s rho superimposed (top row) and conditional quantile dependence curves (bottom row). Blue points/curves correspond to observations with $r_{m,t-1}<0$ (bear, $-$) while orange points/curves correspond to observations with $r_{m,t-1}>0$ (bull, $+$). In the bottom row, solid lines show lower-tail dependence $C(q,q)/q$, $q \in [0.1,0.5]$, and dashed lines show upper-tail dependence $(1-2q+C(q,q))/(1-q)$, $q \in [0.5,0.9]$ (e.g. patton2013copula).

Theorems & Definitions (6)

  • Proposition 1
  • Lemma 1
  • Lemma 2
  • Proposition 2
  • Definition 1: Bracketing Number
  • Lemma B.1