An extended sparse max-linear moving model with application to high-frequency financial data

References

• Box, G. E. P., & Jenkins, G. M. (1970). Time series analysis: Forecasting and control. San Francisco: Holden-Day.
   Google Scholar
• Chamú-Morales, F. (2005). Estimation of max-stable processes using Monte Carlo methods with applications to financial risk assessment ( PhD dissertation). Department of Statistics at the University of North Carolina, Chapel Hill, NC.
   Google Scholar
• Davis, R. A., & Resnick, S. I. (1989). Basic properties and prediction of Max-ARMA processes. Advances in Applied Probability, 21(4), 781–803.
   Web of Science ®Google Scholar
• Deheuvels, P. (1983). Point processes and multivariate extreme values. Journal of Multivariate Analaysis, 13(2), 257–272.
   Web of Science ®Google Scholar
• Fisher, R. A., & Tippett, L. H. C. (1928). Limiting forms of the frequency distribution of the largest and smallest member of a sample. Proceedings of Cambridge Philosophical Society, 24 (2), 180–190.
   Google Scholar
• Gelman, A., Roberts, G. O., & Gilks, W. R. (1996). Efficient metropolis jumping rules. Bayesian Statistics, 5, 599–607.
   Google Scholar
• Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2003). Bayesian data analysis, 2e. Boca Raton, FL: CRC Press.
   Google Scholar
• Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721–741.
   PubMed Web of Science ®Google Scholar
• Gnedenko, B. V. (1943). Sur la distribution limite du terme maximum d'une serie aleatoire [On the limiting distribution of the maximum term in a random series]. Annals of Mathematics, 44(3), 423–453.
   Google Scholar
• Hall, P., Peng, L., & Yao, Q. (2002). Moving-maximum models for extrema of time series. Journal of Statistical Planning Inference, 103(1–2), 51–63.
   Web of Science ®Google Scholar
• Hansen, L. P. (1982). Large sample properties of generalized method of moments estimator. Econometrica, 50(4), 1029–1054.
   Web of Science ®Google Scholar
• Hastings, W. K. (1970). Monte carlo sampling methods using Markov chains and their application. Biometrika, 57(1), 97–109.
   Web of Science ®Google Scholar
• Heffernan, J. E., Tawn, J. A., & Zhang Z,. (2007). Asymptotically (in)dependent multivariate maxima of moving maxima processes. Extremes, 10(1), 57–82.
   Google Scholar
• Kunihama, T., Omori, Y., & Zhang Z,. (2011). Efficient estimation and particle filter for max-stable processes. Journal of Time Series Analysis, 33(1), 61–80.
   Web of Science ®Google Scholar
• Ledford, A. W., & Tawn, J. A. (2003). Diagnostics for dependence within time series extremes. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 65(2), 521–543.
   Web of Science ®Google Scholar
• McNeil, A. J., & Frey R,. (2000). Estimation of tail-related risk measures for heteroscedastic financial time series:An extreme value approach. Journal of Empirical Finance, 7(3-4), 271–300.
   Google Scholar
• Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller E,. (1953). Equations of state calculations by fast computing machines. Journal of Chemical Physics, 21, 1087–1092.
   Web of Science ®Google Scholar
• Pasarica, C., & Gelman, A. (2010). Adaptively scaling the metropolis algorithm using expected squared jumped distance. Statistica Sinica, 20, 343–364.
   Web of Science ®Google Scholar
• Robert, C. P., & Casella, G. (2004). Monte carlo statistical methods, 2e. New York, NY: Spinger Text in Statistics.
   Google Scholar
• Sibuya, M. (1959). Bivariate extreme statistics. Annals of the Institute of Statistical Mathematics, 11(2), 195–210.
   Google Scholar
• Smith, R. L., & Weissman, I. (1996). Characterization and estimation of the multivariate extremal index. ( Tech. Report). Chapel Hill, NC: Department of Statistics at the University of North Carolina.
   Google Scholar
• Tang, R., Shao, J., & Zhang, Z. (2013). Sparse moving maxima models for tail dependence in multivariate financial time series. Journal of Statistical Planning and Inference, 143(5), 882–895.
   Web of Science ®Google Scholar
• Zhang, Z. (2005). A new class of tail-dependent time series models and its applications in financial time series. Advances in Econometrics, 20(B), 323–358.
   Google Scholar
• Zhang, Z., & Huang, J. (2006). Extremal financial risk model and portfolio evaluation. Computational Statistics and Data Analysis, 51(4), 2313–2338.
   Web of Science ®Google Scholar
• Zhang, Z., & Smith, R. L. (2010). On the estimation and application of max-stable processes. Journal of Statistical Planning and Inference, 140, 1135–1153.
   Web of Science ®Google Scholar
• Zhang, Z., & Zhu, B. (2016). Copula structured M4 processes with application to high-frequency financial data. Journal of Econometrics, 194, 231–241.
   Web of Science ®Google Scholar