References
- Anděl, J. (1976), “Autoregressive Series with Random Parameters,” Mathematische Operationsforschung und Statistik, 7, 735–741. DOI: 10.1080/02331887608801334.
- Andersen, T. G., and Varneskov, R. T. (2022), “Testing for Parameter Instability and Structural Change in Persistent Predictive Regressions,” Journal of Econometrics, Forthcoming.
- Andrews, D. W. (1993), “Tests for Parameter Instability and Structural Change with Unknown Change Point,” Econometrica, 61, 821–856. DOI: 10.2307/2951764.
- Astill, S., Harvey, D. I., Leybourne, S. J., Taylor, A., and Zu, Y. (2021), “CUSUM-based Monitoring for Explosive Episodes in Financial Data in the Presence of Time-Varying Volatility,” Journal of Financial Econometrics (forthcoming). DOI: 10.1093/jjfinec/nbab009.
- Aue, A. (2004), “Strong Approximation for RCA(1) Time Series with Applications,” Statistics & Probability Letters, 68, 369–382.
- Aue, A., and Horváth, L. (2011), “Quasi-likelihood Estimation in Stationary and Nonstationary Autoregressive Models with Random Coefficients,” Statistica Sinica, 21, 973–999.
- Aue, A., Horváth, L., and Steinebach, J. (2006), “Estimation in Random Coefficient Autoregressive Models,” Journal of Time Series Analysis, 27, 61–76. DOI: 10.1111/j.1467-9892.2005.00453.x.
- Bai, J., and Perron, P. (1998), “Estimating and Testing Linear Models with Multiple Structural Changes,” Econometrica, 66, 47–78. DOI: 10.2307/2998540.
- Benati, L., and Kapetanios, G. (2003), “Structural Breaks in Inflation Dynamics,” in Computing in Economics and Finance (Vol. 169), pp. 563–587. Society for Computational Economics.
- Berkes, I., Horváth, L., and Ling, S. (2009), “Estimation in Nonstationary Random Coefficient Autoregressive Models,” Journal of Time Series Analysis, 30, 395–416. DOI: 10.1111/j.1467-9892.2009.00615.x.
- Boldea, O., Cornea-Madeira, A., and Hall, A. R. (2019), “Bootstrapping Structural Change Tests,” Journal of Econometrics, 213, 359–397. DOI: 10.1016/j.jeconom.2019.05.019.
- Bollerslev, T., Patton, A. J., and Wang, W. (2016), “Daily House Price Indices: Construction, Modeling, and Longer-Run Predictions,” Journal of Applied Econometrics, 31, 1005–1025. DOI: 10.1002/jae.2471.
- Case, K. E., and Shiller, R. J. (2003), “Is There a Bubble in the Housing Market?” Brookings Papers on Economic Activity, 2003, 299–362. DOI: 10.1353/eca.2004.0004.
- Casini, A., and Perron, P. (2019), “Structural Breaks in Time Series,” in Oxford Research Encyclopedia of Economics and Finance, Oxford: Oxford University Press.
- Cavaliere, G., and Taylor, A. R. (2006), “Testing for a Change in Persistence in the Presence of a Volatility Shift,” Oxford Bulletin of Economics and Statistics, 68, 761–781. DOI: 10.1111/j.1468-0084.2006.00455.x.
- Chan, N. H., Li, D., and Peng, L. (2012), “Toward a Unified Interval Estimation of Autoregressions,” Econometric Theory, 28, 705–717. DOI: 10.1017/S0266466611000727.
- Chan, N. H., Yau, C. Y., and Zhang, R.-M. (2014), “Group Lasso for Structural Break Time Series,” Journal of the American Statistical Association, 109, 590–599. DOI: 10.1080/01621459.2013.866566.
- Csörgő, M., and Horváth, L. (1997), Limit Theorems in Change-Point Analysis (Vol. 18), Hoboken, NJ: Wiley.
- Darling, D. A., and Erdős, P. (1956), “A Limit Theorem for the Maximum of Normalized Sums of Independent Random Variables,” Duke Mathematical Journal, 23, 143–155. DOI: 10.1215/S0012-7094-56-02313-4.
- Diba, B. T., and Grossman, H. I. (1988), “The Theory of Rational Bubbles in Stock Prices,” The Economic Journal, 98, 746–754. DOI: 10.2307/2233912.
- Elliott, G., and Müller, U. K. (2006), “Efficient Tests for General Persistent Time Variation in Regression Coefficients,” The Review of Economic Studies, 73, 907–940. DOI: 10.1111/j.1467-937X.2006.00402.x.
- Engle, R. F. (1982), “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation,” Econometrica, 50, 987–1007. DOI: 10.2307/1912773.
- Giraitis, L., Kapetanios, G., and Yates, T. (2014), “Inference on Stochastic Time-Varying Coefficient Models,” Journal of Econometrics, 179, 46–65. DOI: 10.1016/j.jeconom.2013.10.009.
- Gombay, E., and Horváth, L. (1996), “On the Rate of Approximations for Maximum Likelihood Tests in Change-Point Models,” Journal of Multivariate Analysis, 56, 120–152. DOI: 10.1006/jmva.1996.0007.
- Hafner, C. M. (2020), “Testing for Bubbles in Cryptocurrencies with Time-Varying Volatility,” Journal of Financial Econometrics, 18, 233–249.
- Harvey, D., Leybourne, S., and Whitehouse, E. (2022), “Real-Time Monitoring of Bubbles and Crashes,” The Sheffield Economic Research Paper Series (SERPS), 2022007.
- Hill, J., Li, D., and Peng, L. (2016), “Uniform Interval Estimation for an AR(1) process with AR Errors,” Statistica Sinica, 26, 119–136.
- Hill, J., and Peng, L. (2014), “Unified Interval Estimation for Random Coefficient Autoregressive Models,” Journal of Time Series Analysis, 35, 282–297. DOI: 10.1111/jtsa.12064.
- Homm, U., and Breitung, J. (2012), “Testing for Speculative Bubbles in Stock Markets: A Comparison of Alternative Methods,” Journal of Financial Econometrics, 10, 198–231. DOI: 10.1093/jjfinec/nbr009.
- Hörmann, S. (2009), “Berry-Esseen Bounds for Econometric Time Series,” ALEA-Latin American Journal of Probability and Mathematical Statistics, 6, 377–397.
- Horváth, L., Li, H., and Liu, Z. (2022), “How to Identify the Different Phases of Stock Market Bubbles Statistically?” Finance Research Letters 46, 102366. DOI: 10.1016/j.frl.2021.102366.
- Horváth, L., Liu, Z., and Lu, S. (2021), “Sequential Monitoring of Changes in Dynamic Linear Models, Applied to the US Housing Market,” Econometric Theory, 38, 209–272. DOI: 10.1017/S0266466621000104.
- Horváth, L., Liu, Z., Rice, G., and Wang, S. (2020), “Sequential Monitoring for Changes from Stationarity to Mild Non-stationarity,” Journal of Econometrics, 215, 209–238. DOI: 10.1016/j.jeconom.2019.08.010.
- Horváth, L., Miller, C., and Rice, G. (2020), “A New Class of Change Point Test Statistics of Rényi Type,” Journal of Business & Economic Statistics, 38, 570–579.
- Horváth, L., and Rice, G. (2021), “Changepoint Detection in Time Series,” Technical Report, University of Utah.
- Horváth, L., and Trapani, L. (2016), “Statistical Inference in a Random Coefficient Panel Model,” Journal of Econometrics, 193, 54–75. DOI: 10.1016/j.jeconom.2016.01.006.
- Horváth, L., and Trapani, L. (2019), “Testing for Randomness in a Random Coefficient Autoregression Model,” Journal of Econometrics, 209, 338–352.
- Hwang, S., Basawa, I., and Kim, T. Y. (2006), “Least Squares Estimation for Critical Random Coefficient First-Order Autoregressive Processes,” Statistics & Probability Letters, 76, 310–317.
- Hwang, S. Y., and Basawa, I. (2005), “Explosive Random-Coefficient AR(1) Processes and Related Asymptotics for Least-Squares Estimation,” Journal of Time Series Analysis, 26, 807–824. DOI: 10.1111/j.1467-9892.2005.00432.x.
- Kejriwal, M., Yu, X., and Perron, P. (2020), “Bootstrap Procedures for Detecting Multiple Persistence Shifts in Heteroskedastic Time Series,” Journal of Time Series Analysis, 41, 676–690. DOI: 10.1111/jtsa.12528.
- Kim, D., and Perron, P. (2009), “Assessing the Relative Power of Structural Break Tests using a Framework Based on the Approximate Bahadur Slope,” Journal of Econometrics, 149, 26–51. DOI: 10.1016/j.jeconom.2008.10.010.
- Koul, H. L., and Schick, A. (1996), “Adaptive Estimation in a Random Coefficient Autoregressive Model,” Annals of Statistics, 24, 1025–1052.
- Kuersteiner, G. M. (2002), “Efficient IV Estimation for Autoregressive Models with Conditional Heteroskedasticity,” Econometric Theory, 18, 547–583. DOI: 10.1017/S0266466602183010.
- Lee, S. (1998), “Coefficient Constancy Test in a Random Coefficient Autoregressive Model,” Journal of Statistical Planning and Inference, 74, 93–101. DOI: 10.1016/S0378-3758(98)00095-0.
- Lee, S., Ha, J., Na, O., and Na, S. (2003), “The CUSUM Test for Parameter Change in Time Series Models,” Scandinavian Journal of Statistics, 30, 781–796. DOI: 10.1111/1467-9469.00364.
- Leybourne, S. J., McCabe, B. P., and Tremayne, A. R. (1996), “Can Economic Time Series be Differenced to Stationarity?” Journal of Business & Economic Statistics, 14, 435–446.
- Li, D., Phillips, P. C., and Gao, J. (2016), “Uniform Consistency of Nonstationary Kernel-Weighted Sample Covariances for Nonparametric Regression,” Econometric Theory, 32, 655–685. DOI: 10.1017/S0266466615000109.
- Li, F., Tian, Z., and Qi, P. (2015), “Structural Change Monitoring for Random Coefficient Autoregressive Time Series,” Communications in Statistics-Simulation and Computation, 44, 996–1009. DOI: 10.1080/03610918.2013.800205.
- Li, F., Tian, Z., Qi, P., and Chen, Z. (2015), “Monitoring Parameter Changes in RCA(p) Models,” Journal of the Korean Statistical Society, 44, 111–122. DOI: 10.1016/j.jkss.2014.06.001.
- Linton, O., and Xiao, Z. (2019), “Efficient Estimation of Nonparametric Regression in the Presence of Dynamic Heteroskedasticity,” Journal of Econometrics, 213, 608–631. DOI: 10.1016/j.jeconom.2019.01.016.
- Na, O., Lee, J., and Lee, S. (2010), “Monitoring Parameter Changes for Random Coefficient Autoregressive Models,” Journal of the Korean Statistical Society, 39, 281–288. DOI: 10.1016/j.jkss.2010.03.006.
- Nicholls, D. F., and Quinn, B. G. (2012), Random Coefficient Autoregressive Models: An Introduction: An Introduction (Vol. 11), New York: Springer.
- Perron, P. (1989), “The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis,” Econometrica, 57, 1361–1401. DOI: 10.2307/1913712.
- Perron, P. (2006), “Dealing with Structural Breaks,” Palgrave Handbook of Econometrics, 1, 278–352.
- Perron, P., and Yamamoto, Y. (2022), “Structural Change Tests under Heteroskedasticity: Joint Estimation versus Two-Steps Methods,” Journal of Time Series Analysis, 43, 389–411. DOI: 10.1111/jtsa.12619.
- Perron, P., Yamamoto, Y., and Zhou, J. (2020), “Testing Jointly for Structural Changes in the Error Variance and Coefficients of a Linear Regression Model,” Quantitative Economics, 11, 1019–1057. DOI: 10.3982/QE1332.
- Phillips, P. C., Shi, S., and Yu, J. (2015a), “Testing for Multiple Bubbles: Historical Episodes of Exuberance and Collapse in the S&P 500,” International Economic Review, 56, 1043–1078. DOI: 10.1111/iere.12132.
- Phillips, P. C., Shi, S., and Yu, J. (2015b), “Testing for Multiple Pubbles: Limit Theory of Real-Time Detectors,” International Economic Review, 56, 1079–1134.
- Phillips, P. C., Wu, Y., and Yu, J. (2011), “Explosive Behavior in the 1990s Nasdaq: When did Exuberance Escalate Asset Values?” International Economic Review, 52, 201–226. DOI: 10.1111/j.1468-2354.2010.00625.x.
- Regis, M., Serra, P., and van den Heuvel, E. R. (2022), “Random Autoregressive Models: A Structured Overview,” Econometric Reviews, 41, 207–230. DOI: 10.1080/07474938.2021.1899504.
- Schick, A. (1996), “n -consistent Estimation in a Random Coefficient Autoregressive Model,” Australian & New Zealand Journal of Statistics, 38, 155–160.
- Shiller, R. J. (2008), “Historic Turning Points in Real Estate,” Eastern Economic Journal, 34, 1–13. DOI: 10.1057/palgrave.eej.9050001.
- Trapani, L. (2021), “Testing for Strict Stationarity in a Random Coefficient Autoregressive Model,” Econometric Reviews, 40, 220–256. DOI: 10.1080/07474938.2020.1773667.
- Tsay, R. S. (1987), “Conditional Heteroscedastic Time Series Models,” Journal of the American Statistical Association, 82, 590–604. DOI: 10.1080/01621459.1987.10478471.
- Venkatraman, E. S. (1992), Consistency Results in Multiple Change-Point Problems. Ph. D. thesis, Stanford University.
- Vostrikova, L. Y. (1981), “Detecting Disorder in Multidimensional Random Processes,” Doklady Akademii Nauk, 259, 270–274. Russian Academy of Sciences.
- Wu, W. B. (2005), “Nonlinear System Theory: Another Look at Dependence,” Proceedings of the National Academy of Sciences of the United States of America, 102, 14150–14154. DOI: 10.1073/pnas.0506715102.
- Xu, K.-L. (2015), “Testing for Structural Change under Non-stationary Variances,” The Econometrics Journal, 18, 274–305. DOI: 10.1111/ectj.12049.
- Xu, K.-L., and Phillips, P. C. (2008), “Adaptive Estimation of Autoregressive Models with Time-Varying Variances,” Journal of Econometrics, 142, 265–280. DOI: 10.1016/j.jeconom.2007.06.001.
- Yao, Y.-C. (1988), “Estimating the Number of Change-Points via Schwarz’ Criterion,” Statistics & Probability Letters, 6, 181–189.
- Zhu, K. (2019), “Statistical Inference for Autoregressive Models under Heteroscedasticity of Unknown Form,” Annals of Statistics, 47, 3185–3215.