Research

Journal articles, forthcoming papers, and working papers.

Improved Andrews’ formula for testing changing mean

A truncated-bandwidth rule (an improved Andrews’ formula) that restores size control and monotonic power for the classical CUSUM and QS mean-shift tests.

Structural change

code

Li, W., Zhang, X. and Zu, Y. (2026). Economics Letters 268, 113141.

Sep 1, 2026

Feature screening for high-dimensional structural break predictive regression

A screening procedure that jointly selects active predictors and estimates multiple change points in high-dimensional predictive regressions.

Structural change

working paper

With Qin, Z., Zhang, R. and Zhang, W. Working paper.

Jun 17, 2026

Covariate-augmented CUSUM bubble monitoring procedures

Real-time CUSUM procedures for monitoring the onset of explosive bubbles that gain power by exploiting information in covariates.

Bubble testing

Monitoring

Astill, S., Taylor, A. M. R. and Zu, Y. (2026). Econometric Theory (early access).

Jun 11, 2026

Statistical comparison of forecasts made at different frequencies

A framework and test for comparing the accuracy of forecasts issued at different sampling frequencies.

Forecast evaluation

code

Zhang, R., Zu, Y. and Li, W. (2026). Journal of Business and Economic Statistics 44, 1279–1291.

May 13, 2026

A new heteroskedasticity-robust test for explosive bubbles

A test for explosive bubbles that is robust to heteroskedasticity in the innovations.

Bubble testing

Time-varying volatility

Harvey, D. I., Leybourne, S. J., Taylor, A. M. R. and Zu, Y. (2025). Journal of Time Series Analysis 46, 846–866.

Sep 1, 2025

Testing for explosiveness in financial asset prices using high-frequency volatility

Uses jump-robust high-frequency volatility to build a more powerful test for explosive bubbles, with real-time date-stamping.

Bubble testing

working paper

code

With Boswijk, H. P. and Yu, J. Working paper.

Jun 2, 2025

CUSUM tests for parameter change under heteroskedasticity

CUSUM tests for detecting parameter change that remain valid under heteroskedasticity.

Structural change

working paper

With Astill, S., Cavaliere, G. and Taylor, A. M. R. Working paper.

Jun 1, 2025

Unit root tests for explosive financial bubbles in the presence of deterministic level shifts

Explosive-root (bubble) tests that stay reliable when the price series also contains deterministic level shifts.

Bubble testing

Harvey, D. I., Leybourne, S. J., Tatlow, B. S. and Zu, Y. (2025). Oxford Bulletin of Economics and Statistics 87, 880–898.

Mar 1, 2025

Testing for equal average forecast accuracy in possibly unstable environments

Tests for equal average forecast accuracy that stay valid when relative forecast performance is unstable over time.

Forecast evaluation

code

Harvey, D. I., Leybourne, S. J. and Zu, Y. (2025). Journal of Business and Economic Statistics 43, 643–656.

Jan 1, 2025

Tests for equal forecast accuracy under heteroskedasticity

Diebold-Mariano-type forecast-comparison tests that remain valid under heteroskedastic forecast errors.

Forecast evaluation

code

Harvey, D. I., Leybourne, S. J. and Zu, Y. (2024). Journal of Applied Econometrics 39, 850–869.

Jan 1, 2024

Estimation of the variance function in structural break autoregressive models with non-stationary and explosive segments

Estimates the time-varying variance function in autoregressive models whose segments may be non-stationary or explosive.

Bubble testing

Volatility

code

Harvey, D. I., Leybourne, S. J. and Zu, Y. (2023). Journal of Time Series Analysis 44, 181–205.

Mar 1, 2023

CUSUM-based monitoring for explosive episodes in financial data in the presence of time-varying volatility

A CUSUM procedure that detects explosive episodes in financial data in real time while remaining robust to time-varying volatility.

Bubble testing

Monitoring

Astill, S., Harvey, D. I., Leybourne, S. J., Taylor, A. M. R. and Zu, Y. (2023). Journal of Financial Econometrics 21, 187–227.

Jan 1, 2023

Adaptive testing for cointegration with nonstationary volatility

Adaptive cointegration tests that recover efficiency and stay valid when volatility is nonstationary.

Unit root & cointegration

Nonstationary volatility

code

Boswijk, H. P. and Zu, Y. (2022). Journal of Business and Economic Statistics 40, 744–755.

Jan 1, 2022

Sign-based unit root tests for explosive financial bubbles in the presence of deterministically time-varying volatility

Sign-based, robust unit-root tests for explosive bubbles that are valid under deterministically time-varying volatility.

Bubble testing

Time-varying volatility

Harvey, D. I., Leybourne, S. J. and Zu, Y. (2020). Econometric Theory 36, 122–169.

Jan 1, 2020

Testing explosive bubbles with time-varying volatility

A wild-bootstrap bubble test that remains correctly sized when volatility changes over time.

Bubble testing

Time-varying volatility

code

Harvey, D. I., Leybourne, S. J. and Zu, Y. (2019). Econometric Reviews 38, 1131–1151.

Jan 1, 2019

Adaptive wild bootstrap tests for a unit root with nonstationary volatility

Adaptive wild-bootstrap unit-root tests that are robust and efficient under nonstationary volatility.

Unit root & cointegration

Nonstationary volatility

code

Boswijk, H. P. and Zu, Y. (2018). Econometrics Journal 21, 87–113.

Jan 1, 2018

Consistent nonparametric specification tests for stochastic volatility models based on the return distribution

Nonparametric tests of whether a stochastic-volatility model is correctly specified, based on the implied return distribution.

Volatility

Specification testing

code

Zu, Y. and Boswijk, H. P. (2017). Journal of Empirical Finance 41, 53–75.

Jan 1, 2017

A note on asymptotic normality of the kernel deconvolution density estimator with logarithmic chi-square noise

Establishes asymptotic normality for a kernel deconvolution density estimator under logarithmic chi-square measurement error.

Volatility

Zu, Y. (2015). Econometrics 3, 561–576.

Sep 1, 2015

Nonparametric specification tests for stochastic volatility models based on volatility density

Specification tests for stochastic-volatility models built from the nonparametric density of spot volatility.

Volatility

Specification testing

code

Zu, Y. (2015). Journal of Econometrics 187, 323–344.

Aug 1, 2015

Estimating spot volatility with high-frequency financial data

A kernel estimator of an asset’s instantaneous (spot) volatility from high-frequency prices, with its large-sample theory.

Volatility

code

Zu, Y. and Boswijk, H. P. (2014). Journal of Econometrics 181, 117–135.

Jan 1, 2014

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