Skip to main content


  • Javier Hidalgo (a1) and Pedro C. L. Souza (a2)

We examine a test for weak stationarity against alternatives that covers both local-stationarity and break point models. A key feature of the test is that its asymptotic distribution is a functional of the standard Brownian bridge sheet in [0,1]2, so that it does not depend on any unknown quantity. The test has nontrivial power against local alternatives converging to the null hypothesis at a T−1/2 rate, where T is the sample size. We also examine an easy-to-implement bootstrap analogue and present the finite sample performance in a Monte Carlo experiment. Finally, we implement the methodology to assess the stability of inflation dynamics in the United States and on a set of neuroscience tremor data.

Corresponding author
*Address correspondence to Javier Hidalgo, Economics Department, London School of Economics, London WC2A 2AE, UK; e-mail:
Hide All

We thank the Associate Editor and two referees for very helpful comments. Any remaining errors are our sole responsibility.

Hide All
Anderson, T.W. & Walker, A.M. (1964) On the asymptotic distribution of the autocorrelations of a sample from a linear stochastic process. Annals of Mathematical Statistics 35, 12961303.
Aue, A. & Horvarth, L. (2013) Structural breaks in time series. Journal of Time Series Analysis 34, 116.
Bickel, P.J. & Wichura, M.J. (1971) Convergence criteria for multiparameter stochastic processes and its applications. Annals of Mathematical Statistics 42, 16561670.
Bandyopadhy, A.Y., Jentsch, C., & Subba Rao, S. (2017) Spectral domain test for stationarity of spatio-temporal data. Journal of Time Series Analysis 38, 326351.
Brillinger, D.R. (1981) Time Series, Data Analysis and Theory. Holden-Day.
Brockwell, P.J. & Davis, R.A. (1991) Time Series: Theory and Methods. Springer-Verlag.
Dahlhaus, R. (1996) On the Kulback-Leibler information divergence of locally stationary processes. Stochastic Processes and its Applications 62, 139168.
Dahlhaus, R. (1997) Fitting time series models to nonstationary processes. Annals of Statistics 25, 137.
Dahlhaus, R. (2009) Local inference for locally stationary time series based on the empirical spectral measure. Journal of Econometrics 151, 101112.
Dahlhaus, R. & Polonik, W. (2009) Empirical spectral processes for locally stationary time series. Bernoulli 15, 139.
Dalla, V., Giraitis, L., & Hidalgo, J. (2005) Consistent estimation of the memory parameter for nonlinear time series. Journal of Time Series Analysis 27, 211255.
Davis, R.A., Huang, D., & Yao, Y. (1995) Testing for a change in the parameter values and order of an autoregressive model. Annals of Statistics 23, 282304.
Delgado, M.A., Hidalgo, J., & Velasco, C. (2005) Distribution free goodness-of-fit tests for linear processes. Annals of Statistics 33, 25682609.
Dette, H., Preuss, P., & Vetter, M. (2011) A measure of stationarity in locally stationary processes with applications to testing. Journal of the American Statistical Association 106(495), 11131124.
Dwivedi, Y. & Subba Rao, S. (2011) A test for second-order stationarity of a time series based on the discrete Fourier transform. Journal of Time Series Analysis 32, 6891.
Fragkeskou, M. & Paparoditis, E. (2016) Inference for the fourth-order innovation cumulant in linear time series. Journal of Time Series Analysis 37, 240266.
Giacomini, R., Politis, D.N., & White, H. (2013) A warp-speed method for conducting Monte Carlo experiments involving bootstrap estimators. Econometric Theory 29, 567589.
Grenander, U. & Rosenblatt, M. (1957) Statistical Analysis of Stationary Time Series. Wiley.
Hannan, E.J. (1970) Multiple Time Series. Wiley.
Härdle, W. & Mammen, E. (1993) Comparing nonparametric versus parametric regression fits. Annals of Statistics 21, 19261947.
Hidalgo, J. (2007) Specification testing for regression models with dependent data. Journal of Econometrics 143, 143163.
Hidalgo, J. & Seo, M. (2015) Specification with lattice processes. Econometric Theory 31, 294336.
Ibragimov, I.A. & Rozanov, Y.A. (1978) Gaussian Random Processes. Springer-Verlag.
Jentsch, C. & Subba Rao, S. (2015) A test for second order stationarity of a multivariate time series. Journal of Econometrics 185, 124161.
Lucas, R.E. (1976) Econometric policy evaluation: A critique. In Brunner, K. & Meltzer, A. (eds.), Carnegie-Rochester Conference Series on Public Policy, Vol. 1, pp. 1946. North Holland Publishing Company.
Paparoditis, E. (2009) Testing temporal constancy of the spectral structure of a time series. Bernoulli 15, 11901221.
Perron, P. (2006) Dealing with structural breaks. In Hassani, H., Mills, T. C., & Patterson, K. (eds.), Pelgrave Handbook of Econometrics, Vol. 1, Econometric Theory, pp. 278352. Palgrave Macmillan UK.
Picard, D. (1985) Testing and estimating change points in time series. Advances in Time Series Analysis 17, 841867.
Preuss, P., Vetter, M., & Dette, H. (2013) A test for stationarity based on empirical processes. Bernoulli 19, 27152749.
Priestley, M.B. (1965) Evolutionary spectra and non-stationary processes. Journal of the Royal Statistical Society, Series B 62, 204237.
von Sachs, R. & Neumann, M.H. (2000) A wavelet-based test for stationarity. Journal of Time Series Analysis 21(5), 597613.
Welch, P.D. (1967) The use of fast Fourier Transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms. IEEE Transaction of Audio and Electroacoustic 15, 7073.
Whittle, P. (1963) Prediction and Regulation. Van Nostrand.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 23 *
Loading metrics...

Abstract views

Total abstract views: 86 *
Loading metrics...

* Views captured on Cambridge Core between 20th July 2018 - 16th August 2018. This data will be updated every 24 hours.