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Theory and Methods

Functional Estimation and Change Detection for Nonstationary Time Series

Pages 1011-1022 | Received 29 Apr 2020, Accepted 10 Aug 2021, Published online: 27 Sep 2021

References

  • Aït-Sahalia, Y., and Jacod, J. (2014), High-Frequency Financial Econometrics, Princeton, NJ: Princeton University Press.
  • Aït-Sahalia, Y., Mykland, P. A., and Zhang, L. (2011), “Ultra High Frequency Volatility Estimation With Dependent Microstructure Noise,” Journal of Econometrics, 160, 160–175. DOI: 10.1016/j.jeconom.2010.03.028.
  • Andersen, T. G., Archakov, I., Cebiroglu, G., and Hautsch, N. (2021), “Local Mispricing and Microstructural Noise: A Parametric Perspective,” Journal of Econometrics, forthcoming. DOI: 10.1016/j.jeconom.2021.06.006.
  • Aue, A., and Horváth, L. (2013), “Structural Breaks in Time Series,” Journal of Time Series Analysis, 34, 1–16. DOI: 10.1111/j.1467-9892.2012.00819.x.
  • Bauer, P., and Hackl, P. (1978), “The Use of MOSUMS for Quality Control,” Technometrics, 20, 431. DOI: 10.2307/1267643.
  • Berkes, I., Gombay, E., and Horváth, L. (2009), “Testing for Changes in the Covariance Structure of Linear Processes,” Journal of Statistical Planning and Inference, 139, 2044–2063. DOI: 10.1016/j.jspi.2008.09.004.
  • Bickel, P. J., and Ritov, Y. (1988), “Estimating Integrated Squared Density Derivatives: Sharp Best Order of Convergence Estimates,” Sankhya: The Indian Journal of Statistics, Series A, 50, 381–393.
  • Billingsley, P. (1999), Convergence of Probability Measures, New York: Wiley.
  • Carlstein, E. (1986), “The Use of Subseries Values for Estimating the Variance of a General Statistic from a Stationary Sequence,” The Annals of Statistics, 14, 1171–1179. DOI: 10.1214/aos/1176350057.
  • Chu, C.-S. J., Hornik, K., and Kuan, C.-M. (1995), “MOSUM Tests for Parameter Constancy,” Biometrika, 82, 603–617. DOI: 10.1093/biomet/82.3.603.
  • Cui, Y., Levine, M., and Zhou, Z. (2020), “Estimation and Inference of Time-Varying Auto-Covariance under Complex Trend: A Difference-Based Approach,”arXiv: 2003.05006.
  • Dahlhaus, R. (1997), “Fitting Time Series Models to Nonstationary Processes,” Annals of Statistics, 25, 1–37.
  • Dahlhaus, R. (2009), “Local Inference for Locally Stationary Time Series Based on the Empirical Spectral Measure,” Journal of Econometrics, 151, 101–112.
  • Dahlhaus, R., and Polonik, W. (2009), “Empirical Spectral Processes for Locally Stationary Time Series,” Bernoulli, 15, 1–39. DOI: 10.3150/08-BEJ137.
  • Dahlhaus, R., and Richter, S. (2019), “Adaptation for Nonparametric Estimators of Locally Stationary Processes,” arXiv: 1902.10381.
  • Dahlhaus, R., Richter, S., and Wu, W. B. (2019), “Towards a General Theory for Nonlinear Locally Stationary Processes,” Bernoulli, 25, 1013–1044. DOI: 10.3150/17-BEJ1011.
  • Demetrescu, M., and Wied, D. (2018), “Testing for Constant Correlation of Filtered Series Under Structural Change,” Econometrics Journal, 22, 10–33. DOI: 10.1111/ectj.12116.
  • Dette, H., and Gösmann, J. (2020), “A Likelihood Ratio Approach to Sequential Change Point Detection for a General Class of Parameters,” Journal of the American Statistical Association, 115, 1361–1377. DOI: 10.1080/01621459.2019.1630562.
  • Dette, H., and Wu, W. (2019), “Detecting Relevant Changes in the Mean of Nonstationary Processes—A Mass Excess Approach,” The Annals of Statistics, 47, 3578–3608. DOI: 10.1214/19-AOS1811.
  • Dette, H., Wu, W., and Zhou, Z. (2019), “Change Point Analysis of Correlation in Non-Stationary Time Series,” Statistica Sinica, 29, 611–643. DOI: 10.5705/ss.202016.0493.
  • Gao, Z., Shang, Z., Du, P., and Robertson, J. L. (2019), “Variance Change Point Detection Under a Smoothly-Changing Mean Trend with Application to Liver Procurement,” Journal of the American Statistical Association, 114, 773–781. DOI: 10.1080/01621459.2018.1442341.
  • Giraud, C., Roueff, F., and Sanchez-Perez, A. (2015), “Aggregation of Predictors for Nonstationary Sub-Linear Processes and Online Adaptive Forecasting of Time Varying Autoregressive Processes,” The Annals of Statistics, 43, 2412–2450. DOI: 10.1214/15-AOS1345.
  • Górecki, T., Horváth, L., and Kokoszka, P. (2018), “Change Point Detection in Heteroscedastic Time Series,” Econometrics and Statistics, 7, 63–88. DOI: 10.1016/j.ecosta.2017.07.005.
  • Gösmann, J., Kley, T., and Dette, H. (2021), “A New Approach for Open-End Sequential Change Point Monitoring,” Journal of Time Series Analysis, 42, 63–84. DOI: 10.1111/jtsa.12555.
  • Grenier, Y. (1983), “Time-Dependent ARMA Modeling of Nonstationary Signals,” IEEE Transactions on Acoustics, Speech, and Signal Processing, 31, 899–911. DOI: 10.1109/TASSP.1983.1164152.
  • Hall, P., and Marron, J. S. (1987), “Estimation of Integrated Squared Density Derivatives,” Statistics and Probability Letters, 6, 109–115. DOI: 10.1016/0167-7152(87)90083-6.
  • Hansen, P. R., and Lunde, A. (2006), “Realized Variance and Market Microstructure Noise,” Journal of Business & Economic Statistics, 24, 127–161.
  • Horváth, L. (1995), “Detecting Changes in Linear Regressions,” Statistics, 26, 189–208. DOI: 10.1080/02331889508802489.
  • Huang, L. S. and Jianqing, F. A. (1999), “Nonparametric Estimation of Quadratic Regression Functionals,” Bernoulli, 5, 927–949. DOI: 10.2307/3318450.
  • Jacod, J., Li, Y., Mykland, P. A., Podolskij, M., and Vetter, M. (2009), “Microstructure Noise in the Continuous Case: The Pre-Averaging Approach,” Stochastic Processes and their Applications, 119, 2249 – 2276. DOI: 10.1016/j.spa.2008.11.004.
  • Jacod, J., Li, Y., and Zheng, X. (2017), “Statistical Properties of Microstructure Noise,” Econometrica, 85, 1133–1174. DOI: 10.3982/ECTA13085.
  • Jacod, J., and Rosenbaum, M. (2013), “Quarticity and Other Functionals of Volatility: Efficient Estimation,” The Annals of Statistics, 41, 1462–1484. DOI: 10.1214/13-AOS1115.
  • Jacod, J., and Shiryaev, A. N. (2003), Limit Theorems for Stochastic Processes, Volume 288 of Grundlehren der mathematischen Wissenschaften. Berlin: Springer.
  • Juhl, T., and Xiao, Z. (2009), “Tests for Changing Mean With Monotonic Power,” Journal of Econometrics, 148, 14–24. DOI: 10.1016/j.jeconom.2008.08.020.
  • Killick, R., Eckley, I. A., and Jonathan, P. (2013), “A Wavelet-Based Approach for Detecting Changes in Second Order Structure Within Nonstationary Time Series,” Electronic Journal of Statistics, 7, 1167–1183. DOI: 10.1214/13-EJS799.
  • Li, X., and Zhao, Z. (2013), “Testing for Changes in Autocovariances of Nonparametric Time Series Models,” Journal of Statistical Planning and Inference, 143, 237–250. DOI: 10.1016/j.jspi.2012.07.012.
  • Moulines, E., Priouret, P., and Roueff, F. (2005), “On Recursive Estimation for Time Varying Autoregressive Processes,” The Annals of Statistics, 33, 2610 – 2654. DOI: 10.1214/009053605000000624.
  • Page, E. (1954), “Continuous Inspection Schemes,” Biometrika, 41, 100–115.
  • Page, E. (1955), “A Test for a Change in a Parameter Occurring at an Unknown Point,” Biometrika, 42, 523–527.
  • Pešta, M., and Wendler, M. (2020), “Nuisance-Parameter-Free Changepoint Detection in Non-Stationary Series,” TEST, 29, 379–408. DOI: 10.1007/s11749-019-00659-1.
  • Potiron, Y., and Mykland, P. (2020), “Local Parametric Estimation in High Frequency Data,” Journal of Business & Economic Statistics, 38, 679–692.
  • Preuss, P., Puchstein, R., and Dette, H. (2015), “Detection of Multiple Structural Breaks in Multivariate Time Series,” Journal of the American Statistical Association, 110, 654–668. DOI: 10.1080/01621459.2014.920613.
  • Schick, A., and Wefelmeyer, W. (2004), “Root n Consistent Density Estimators for Sums of Independent Random Variables,” Journal of Nonparametric Statistics, 16, 925–935. DOI: 10.1080/10485250410001713990.
  • Schmidt, S., Wornowizki, M., Fried, R., and Dehling, H. (2020), “An Asymptotic Test for Constancy of the Variance under Short-Range Dependence,” arXiv: 2002.10178.
  • Shao, X., and Zhang, X. (2010), “Testing for Change Points in Time Series,” Journal of the American Statistical Association, 105, 1228–1240. DOI: 10.1198/jasa.2010.tm10103.
  • Steland, A. (2020), “Testing and Estimating Change-Points in the Covariance Matrix of a High-Dimensional Time Series,” Journal of Multivariate Analysis, 177, 104582. DOI: 10.1016/j.jmva.2019.104582.
  • Subba Rao, T. (1970), “The Fitting of Non-Stationary Time-Series Models With Time-Dependent Parameters,” Journal of the Royal Statistical Society, Series B, 32, 312–322.
  • Truquet, L. (2019), “Local Stationarity and Time-Inhomogeneous Markov Chains,” The Annals of Statistics, 47, 2023–2050. DOI: 10.1214/18-AOS1739.
  • Vogt, M., and Dette, H. (2015), “Detecting Gradual Changes in Locally Stationary Processes,” Annals of Statistics, 43, 713–740.
  • Wu, W. B. (2005), “Nonlinear System Theory: Another Look at Dependence,” Proceedings of the National Academy of Sciences, 102, 14150–14154. DOI: 10.1073/pnas.0506715102.
  • Wu, W. B., and Zhou, Z. (2011), “Gaussian Approximations for Non-Stationary Multiple Time Series,” Statistica Sinica, 21, 1397–1413. DOI: 10.5705/ss.2008.223.
  • Zhou, Z. (2013), “Heteroscedasticity and Autocorrelation Robust Structural Change Detection,” Journal of the American Statistical Association, 108, 726–740. DOI: 10.1080/01621459.2013.787184.
  • Zhou, Z., and Wu, W. B. (2009), “Local Linear Quantile Estimation for Nonstationary Time Series,” Annals of Statistics, 37, 2696–2729.

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