Testing for a unit root with nonstationary nonlinear heteroskedasticity

References

• Beare, B. (2018). Unit root testing with unstable volatility. Journal of Time Series Analysis, 39(6):816–835.
   Web of Science ®Google Scholar
• Berk, K. N. (1974). Consistent autoregressive spectral estimates. The Annals of Statistics 2(3):489–502. doi:10.1214/aos/1176342709
   Web of Science ®Google Scholar
• Boswijk, H. P. (2001). Testing for a Unit Root with Near Integrated Volatility. Tinbergen Institute Discussion Paper 2001-077/4.
   Google Scholar
• Boswijk, H. P. (2005). Adaptive Testing for a Unit Root with Nonstationary Volatility. UvA Econometrics Discussion Paper 2005/07.
   Google Scholar
• Cavaliere, G. (2005). Unit root tests under time-varying variances. Econometric Reviews 23(3):259–292. doi:10.1081/ETC-200028215
   Google Scholar
• Cavaliere, G., Taylor, A. M. R. (2007). Testing for unit roots in time series models with non-stationary volatility. Journal of Econometrics 140(2):919–947. doi:10.1016/j.jeconom.2006.07.019
   Web of Science ®Google Scholar
• Cavaliere, G., Taylor, A. M. R. (2008). Bootstrap unit root tests for time series with non-stationary volatility. Econometric Theory 24(01):43–71. doi:10.1017/S0266466608080043
   Google Scholar
• Cavaliere, G., Taylor, A. M. R. (2008). Time-transformed unit root tests for models with non-stationary volatility. Journal of Time Series Analysis 29(2):300–330. doi:10.1111/j.1467-9892.2007.00557.x
   Web of Science ®Google Scholar
• Cavaliere, G., Taylor, A. M. R. (2009). Heteroskedastic time series with a unit root. Econometric Theory 25(5):1228–1276. doi:10.1017/S026646660809049X
   Web of Science ®Google Scholar
• Chang, Y., Park, J. Y., Phillips, P. C. B. (2001). Nonlinear econometric models with cointegrated and deterministically trending regressors. The Econometrics Journal 4(1):1–36. doi:10.1111/1368-423X.00054
   Google Scholar
• Chan, N. H., Terrin, N. (1995). Inference for unstable long-memory processes with applications to fractional unit root autoregressions. The Annals of Statistics 23(5):1662–1683. doi:10.1214/aos/1176324318
   Web of Science ®Google Scholar
• Chan, N., Wang, Q. (2014). Uniform convergence for nonparametric estimators with nonstationary data. Econometric Theory 30(5):1110–1133. doi:10.1017/S026646661400005X
   Web of Science ®Google Scholar
• Chung, H., Park, J. Y. (2007). Nonstationary nonlinear heteroskedasticity in regression. Journal of Econometrics 137(1):230–259. doi:10.1016/j.jeconom.2006.01.002
   Web of Science ®Google Scholar
• Dickey, D. A., Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74:427–431. doi:10.1080/01621459.1979.10482531
   Web of Science ®Google Scholar
• Duffy, J. (2016). A uniform law for convergence to the local times of linear fractional stable motions. The Annals of Applied Probability 26(1):45–72. doi:10.1214/14-AAP1085
   Web of Science ®Google Scholar
• Duffy, J. (2017). Uniform in bandwidth convergence rates, on a maximal domain, in structure nonparametric cointegrating regression. Econometric Theory 33(6):1387–1417. Cdoi:10.1017/S0266466616000451
   Web of Science ®Google Scholar
• Fuller, W. A. (1996). Introduction to Statistical Time Series, 2nd ed. New York: Wiley.
   Google Scholar
• Hamori, S., Tokihisa, A. (1997). Testing for a unit root in the presence of a variance shift. Economics Letters 57(3):245–253. doi:10.1016/S0165-1765(97)00245-0
   Web of Science ®Google Scholar
• Hansen, B. E. (1995). Regression with nonstationary volatility. Econometrica 63(5):1113–1132. doi:10.2307/2171723
   Web of Science ®Google Scholar
• Hansen, B. E., Rahbek, A. (1998). Stationarity and Asymptotics of Multivariate ARCH Time Series with an Application to Robustness of Cointegration Analysis. Preprint, University of Copenhagen.
   Google Scholar
• Kim, T. H., Leybourne, S., Newbold, P. (2002). Unit root tests with a break in innovation variance. Journal of Econometrics 109(2):365–387. doi:10.1016/S0304-4076(02)00118-5
   Web of Science ®Google Scholar
• Kim, T. H., Schmidt, P. (1993). Unit root test with conditional heteroskedasticity. Journal of Econometrics 59(3):287–300. doi:10.1016/0304-4076(93)90027-3
   Web of Science ®Google Scholar
• Ling, S., Li, W. K., McAleer, M. (2003). Estimation and testing for unit root process with GARCH(1,1) errors: Theory and Monte Carlo evidence. Econometric Reviews 22(2):179–202. doi:10.1081/ETC-120020462
   Google Scholar
• Mcleish, D. L. (1975). A maximal inequality and dependent strong laws. The Annals of Probability 3(5):829–839. doi:10.1214/aop/1176996269
   Web of Science ®Google Scholar
• Park, J. Y. (2002). Nonstationary nonlinear heteroskedasticity. Journal of Econometrics 110(2):383–415. doi:10.1016/S0304-4076(02)00100-8
   Web of Science ®Google Scholar
• Park, J. Y., Phillips, P. C. B. (1999). Asymptotics for nonlinear transformation of integrated time series. Econometric Theory 15(03):269–298. doi:10.1017/S0266466699153015
   Google Scholar
• Park, J. Y., Phillips, P. C. B. (2001). Nonlinear regressions with integrated time series. Econometrica 69(1):117–161. doi:10.1111/1468-0262.00180
   Web of Science ®Google Scholar
• Phillips, P. C. B. (1987). Time series regression with a unit root. Econometrica 55(2):277–302. doi:10.2307/1913237
   Web of Science ®Google Scholar
• Phillips, P. C. B., Durlauf, S. N. (1986). Multiple time series with integrated variables. The Review of Economic Studies 53(4):473–495. doi:10.2307/2297602
   Web of Science ®Google Scholar
• Phillips, P. C. B., Solo, V. (1992). Asymptotics for linear processes. The Annals of Statistics 20(2):971–1001. doi:10.1214/aos/1176348666
   Web of Science ®Google Scholar
• Said, S. E., Dickey, D. A. (1984). Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika 71(3):599–607. doi:10.1093/biomet/71.3.599
   Web of Science ®Google Scholar
• Sowell, F. B. (1990). The fractional unit root distribution. Econometrica 58(2):495–505. doi:10.2307/2938213
   Web of Science ®Google Scholar
• Takacs, L. (1995). On the local time of the Brownian motion. The Annals of Applied Probability 5(3):741–756. doi:10.1214/aoap/1177004703
   Web of Science ®Google Scholar
• Wang, Q. (2015). Limit Theorems for Nonlinear Cointegrating Regression. Singapore: World Scientific.
   Google Scholar
• Wang, Q., Chan, N. (2014). Uniform convergence rates for a class of martingales with application in non-linear co-integrating regression. Bernoulli 20(1):207–230. doi:10.3150/12-BEJ482
   Web of Science ®Google Scholar
• Wang, Q., Lin, Y. X., Gulati, C. M. (2003). Asymptotics for general fractionally integrated processes with applications to unit root tests. Econometric Theory 19(01):143–164. doi:10.1017/S0266466603191062
   Google Scholar
• Wang, Q., Phillips, P. C. B. (2009). Structural nonparametric cointegrating regression. Econometrica 77:1901–1948.
   Web of Science ®Google Scholar
• Wang, Q., Wang, R. (2013). Non-parametric cointegrating regression with NNH errors. Econometric Theory 29(1):1–27. doi:10.1017/S0266466612000205
   Web of Science ®Google Scholar
• Wu, W. B. (2006). Unit root testing for functionals of linear processes. Econometric Theory 22(01):1–14. doi:10.1017/S0266466606060014
   Google Scholar
• Xu, K. L. (2008). Bootstrapping autoregression under nonstationary volatility. The Econometrics Journal 11(1):1–26. doi:10.1111/j.1368-423X.2008.00235.x
   Web of Science ®Google Scholar