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Articles

On the Least Squares Estimation of Multiple-Threshold-Variable Autoregressive Models

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References

  • Brachner, C., Fasen, V., and Lindner, A. (2009), “Extremes of Autoregressive Threshold Processes,” Advances in Applied Probability, 41, 428–451.
  • Cai, Z. (2002), “Regression Quantiles for Time Series,” Econometric Theory, 18, 169–192.
  • Cai, Z., and Tiwari, R. C. (2000), “Application of a Local Linear Autoregressive Model to BOD Time Series,” Environmetrics, 11, 341–350.
  • Campbell, J. Y., Grossman, S. J., and Wang, J. (1993), “Trading Volume and Serial Correlation in Stock Returns,” The Quarterly Journal of Economics, 108, 905–939.
  • Chan, K.-S. (1989), “A Note on the Geometric Ergodicity of a Markov Chain,” Advances in Applied Probability, 21, 702–704.
  • Chan, K.-S. (1993), “Consistency and Limiting Distribution of the Least Squares Estimator of a Threshold Autoregressive Model,” The Annals of Statistics, 21, 520–533.
  • Chan, K.-S., and Tong, H. (1985), “On the Use of the Deterministic Lyapunov Function for the Ergodicity of Stochastic Difference Equations,” Advances in Applied Probability, 17, 666–678.
  • Chan, K.-S., Tong, H., and Stenseth, N. C. (2009), “Analyzing Short Time Series Data from Periodically Fluctuating Rodent Populations by Threshold Models: A Nearest Block Bootstrap Approach,” Science in China Series A: Mathematics, 52, 1085–1106.
  • Chan, W. S., Wong, A. C. S., and Tong, H. (2004), “Some Nonlinear Threshold Autoregressive Time Series Models for Actuarial Use,” North American Actuarial Journal, 8, 37–61.
  • Chen, C. W. S., So, M. K. P., and Liu, F. C. (2011), “A Review of Threshold Time Series Models in Finance,” Statistics and Its Interface, 4, 167–181.
  • Chen, H., Chong, T. T. L., and Bai, J. (2012), “Theory and Applications of TAR Model with Two Threshold Variables,” Econometric Reviews, 31, 142–170.
  • Cont, R., and Tankov, P. (2004), Financial Modelling with Jump Processes, Boca Raton, FL: Chapman & Hall/CRC.
  • De Gooijer, J. G. (2001), “Cross-validation Criteria for SETAR Model Selection,” Journal of Time Series Analysis, 22, 267–281.
  • Francq, C., and Zakoian, J. M. (2019), “GARCH Models: Structure, Statistical Inference and Financial Applications (2nd ed.), Hoboken, NJ: Wiley.
  • Genest, C., and Rémillard, B. (2004), “Test of Independence and Randomness based on the Empirical Copula Process,” Test, 13, 335–369.
  • Hall, P., Wolff, R. C. L., and Yao, Q. (1999), “Methods for Estimating a Conditional Distribution Function,” Journal of the American Statistical Association, 94, 154–163.
  • Hansen, B. E. (2000), “Sample Splitting and Threshold Estimation,” Econometrica, 68, 575–603.
  • Hansen, B. E. (2011), “Threshold Autoregression in Economics,” Statistics and Its Interface, 4, 123–127.
  • Li, D., and Ling, S. (2012), “On the Least Squares Estimation of Multiple-Regime Threshold Autoregressive Models,” Journal of Econometrics, 167, 240–253.
  • Li, D., Ling, S., Tong, H., and Yang, G. (2019), “On Brownian Motion Approximation of Compound Poisson Processes with Applications to Threshold Models,” Advances in Decision Sciences, 23, 164–191.
  • Li, D., and Tong, H. (2016), “Nested Sub-sample Search Algorithm for Estimation of Threshold Models,” Statistica Sinica, 26, 1543–1554.
  • Llorente, G., Michaely, R., Saar, G., and Wang, J. (2002), “Dynamic Volume-Return Relation of Individual Stocks,” The Review of Financial Studies, 15, 1005–1047.
  • McQuarrie, A., Shumway, R., and Tsai, C.-L. (1997), “The Model Selection Criterion AICu,” Statistics & Probability Letters, 34, 285–292.
  • Meyn, S., and Tweedie, R. L. (2009), Markov Chains and Stochastic Stability, Leiden: Cambridge University Press.
  • Peña, D., and Rodriguez, J. (2005), “Detecting Nonlinearity in Time Series by Model Selection Criteria,” International Journal of Forecasting, 21, 731–748.
  • Pollard, D. (1984), Convergence of Stochastic Processes, New York: Springer.
  • Samia, N. I., Chan, K.-S., and Stenseth, N. C. (2007), “A Generalized Threshold Mixed Model for Analyzing Nonnormal Nonlinear Time Series, with Application to Plague in Kazakhstan,” Biometrika, 94, 101–118.
  • Schumpeter, J. A. (1939), Business Cycles, New York: McGraw-Hill.
  • Seijo, E., and Sen, B. (2011), “A Continuous Mapping Theorem for the Smallest Argmax Functional,” Electronic Journal of Statistics, 5, 421–439.
  • Stenseth, N. C. (2009), “The Importance of TAR-Modelling for Understanding the Structure of Ecological Dynamics: The Hare-Lynx Population Cycles as an Example,” in Exploration of a Nonlinear World: An Appreciation of Howell Tong’s Contributions to Statistics, ed. K.-S. Chan, pp. 365–374, Singapore: World Scientific.
  • Stenseth, N. C., Chan, K.-S., Tong, H., Boonstra, R., Boutin, S., Krebs, C. J., Post, E., O’Donoghue, M., Yoccoz, N. G., Forchhammer, M. C., and Hurrell, J. W. (1999), “Common Dynamic Structure of Canada Lynx Populations Within Three Climatic Regions,” Science, 285, 1071–1073.
  • Tiao, G. C., and Tsay, R. S. (1994), “Some Advances in Non-linear and Adaptive Modelling in Time-Series,” Journal of Forecasting, 13, 109–131.
  • Tong, H. (1978), “On a Threshold Model,” in Pattern Recognition and Signal Processing, ed. C. H. Chen, pp. 575–586, Amsterdam: Sijthoff and Noordhoff.
  • Tong, H. (1990), Non-Linear Time Series: A Dynamical System Approach, New York: Oxford University Press.
  • Tong, H., and Lim, K. S. (1980), “Threshold Autoregression, Limit-Cycles and Cyclical Data,” Journal of the Royal Statistical Society, Series B, 42, 245–292.
  • Wong, C. S., and Li, W. K. (1998), “A Note on the Corrected Akaike Information Criterion for Threshold Autoregressive Models,” Journal of Time Series Analysis, 19, 113–124.
  • Yu, K., and Jones, M. C. (1998), “Local Linear Quantile Regression,” Journal of the American Statistical Association, 93, 228–237.
  • Yu, P., and Phillips, P. C. (2018), “Threshold Regression Asymptotics: From the Compound Poisson Process to Two-Sided Brownian Motion,” Economics Letters, 172, 123–126.

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