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Testing for cross-quantilogram change

Chia-Min Chang, Yu-Hsiang Cheng, Tzee-Ming Huang

Abstract

For two time series $\{ (Y_t, Z_t^Y) \}_{t}$ and $\{(X_t, Z_t^X)\}_{t}$, the directional dependence of $\{ X_t \}_{t}$ on $\{ Y_t \}_{t}$ while removing the impact of $Z_t^X$ on $X_t$ and the impact of $Z_t^Y$ on $ Y_t$ can be measured by cross-quantilograms. When the two time series are obeserved over two periods of time, it can be of interest to learn whether the cross-quantilograms remain the same for the two periods of time. We propose a test for this purpose, and the cross-quantilograms are estimated using the estimators proposed by Han (2016). The $p$-value of the proposed test is obtained based on a bootstrap approach.

Testing for cross-quantilogram change

Abstract

For two time series and , the directional dependence of on while removing the impact of on and the impact of on can be measured by cross-quantilograms. When the two time series are obeserved over two periods of time, it can be of interest to learn whether the cross-quantilograms remain the same for the two periods of time. We propose a test for this purpose, and the cross-quantilograms are estimated using the estimators proposed by Han (2016). The -value of the proposed test is obtained based on a bootstrap approach.
Paper Structure (5 sections, 8 equations, 2 figures, 2 tables)

This paper contains 5 sections, 8 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Method
  3. Simulation study
  4. A analysis of OVX and XAU dataset
  5. Conclusion

Figures (2)

  • Figure 1: The cross-quantilogram heatmaps of OVX on XAU for the two periods
  • Figure 2: The cross-quantilogram heatmaps of OVX on XAU for the two periods with VIX as a controlling variable