Arbeitspapier

Adaptive Testing for Cointegration with Nonstationary Volatility

This paper generalises Boswijk and Zu (2018)'s adaptive unit root test for time series with nonstationary volatility to a multivariate context. Persistent changes in the innovation variance matrix of a vector autoregressive model lead to size distortions in conventional cointegration tests, which may be resolved using the wild bootstrap, as shown by Cavaliere et al. (2010, 2014). We show that it also leads to the possibility of constructing tests with higher power, by taking the time-varying volatilities and correlations into account in the formulation of the likelihood function and the resulting likelihood ratio test statistic. We find that under suitable conditions, adaptation with respect to the volatility process is possible, in the sense that nonparametric volatility matrix estimation does not lead to a loss of asymptotic local power relative to the case where the volatilities are observed. The asymptotic null distribution of the test is nonstandard and depends on the volatility process; we show that various bootstrap implementations may be used to conduct asymptotically valid inference. Monte Carlo simulations show that the resulting test has good size properties, and higher power than existing tests. Two empirical examples illustrate the applicability of the tests.

Language
Englisch

Bibliographic citation
Series: Tinbergen Institute Discussion Paper ; No. TI 2019-043/III

Classification
Wirtschaft
Multiple or Simultaneous Equation Models: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
Hypothesis Testing: General
Subject
Adaptive estimation
Nonparametric volatility estimation
Wild bootstrap

Event
Geistige Schöpfung
(who)
Boswijk, Herman Peter
Zu, Yang
Event
Veröffentlichung
(who)
Tinbergen Institute
(where)
Amsterdam and Rotterdam
(when)
2019

Handle
Last update
10.03.2025, 11:45 AM CET

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Object type

  • Arbeitspapier

Associated

  • Boswijk, Herman Peter
  • Zu, Yang
  • Tinbergen Institute

Time of origin

  • 2019

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