Richard A. Davis
Department of Statistics
Technical reports and papers

  • Davis, R.A., Kluppelberg, C., and Steinkohl, C. (2013). Semiparametric Estimation for Parameters in a Max-Stable Space-Time Process. (In preparation).
  • Samorodnitsky, G., Resnick, R., Towsley, D., Davis, R., Willis, A., and Wan, P. (2014). Nonstandard Regular Variation of In-Degree and Out-Degree in the Preferential Attachment Model. (Submitted).
  • Cho, Y., Davis, R.A., and Ghosh, S. (2014). Asymptotic Properties of the Empirical Spatial Extremogram. (Submitted.) arXiv:1408:0412v1
  • Nascimento, F.F., Gamerman, D., and Davis, R.A. (2013). A Bayesian Semi-parametric Approach to Extreme Regime Identification. (Submitted.)
  • Wang, C., Liu, H., Yao, J-F, Davis, R.A., and Li, W.K. (2014). Self-excited Threshold Poisson Autoregression. JASA 109, 777-787.
  • Davis, R.A., Kluppelberg, C., and Steinkohl, C. (2012). Statistical Inference for Max-Stable Processes in Space and Time. Journal of Royal Statistical Society, Series B 75(5), 791-819.
  • Davis, R.A. and Yau, C-Y (2013). Consistency of Minimum Description Length Model Selection for Piecewise Stationary Time Series Models. (To appear in Electronic Journal of Statistics) 7 381-411.
  • Davis, R.A., Mikosch, T., and Zhao, Y. (2012). Measures of Serial Extremal Dependence and Their Estimation. Stochastic Processes and Their Applications 123, 381-411.
  • Davis, R.A., Kluppelberg, C., and Steinkohl, C. (2013). Max-stable processes for modelling extremes observed in space and time. Journal of Korean Statistical Society, 42(3), 399-414.
  • Davis, R.A. and Hueter, I. (2012). The Convex Hull of Moving Average, Stochastic Volatility and GARCH Pairs. Extremes 14, 487-505.
  • Davis, R.A. and Liu, H. (2014). Theory and Inference for a Class of Nonlinear Models with Application to Time Series of Counts. (To appear in Statistica Sinica.)
  • Davis, R.A., Zang, P., and Zheng, T. (2012). Sparse Vector Autoregressive Modeling (Submitted).
  • Davis, R.A., Pfaffel, O., and Steltzer, R. (2014) Limit theory for the largest eigenvalues of sample covariance matrices with heavy-tails. Stochastic Processes and Their Applications, 124 , 18–50.
  • Davis, R.A. and Wu, Rongning (2011). LAD Estimation with Applications in Time Series Analysis. Encyclopedia of Environmetrics, 2nd Edition A.-H. El-Shaarawi and W. Piegorsch (eds). John Wiley & Sons Ltd, Chichester, UK, pp.1116-1122. DOI:10.1002/9780470057339.vnn088.
  • Davis, R.A. and Yau, C-Y (2011). Likelihood Inference for Discriminating Between Long-Memory and Change-point Models. Journal of Time Series Analysis 33(4), 649-664.
  • Cooley, D., Davis, R.A., and Naveau, P. (2011). Approximating the Conditional Density Given Large Observed Values via a Multivariate Extremes Framework, with Application to Environmental Data. Annals of Applied Statistics, 6, 1406-1429.
  • Davis, R.A. and Liu, Jingchen (2010). Discussion of: A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable? Annals of Applied Statistics 5, 52-55.
  • Andrews, B. and Davis, R.A. (2013). Model Identification for Infinite Variance Autoregressive Processes. Annals of J. of Econometrics 172, 222-234.
  • Davis, R.A., and Song, L. (2012). Noncausal Vector AR Processes with Application to Financial Time Series. (Submitted.)
  • Davis, R.A., and Song, L. (2012). Functional Convergence of Stochastic Integrals with Application to Statistical Inference. Stochastic Processes and Their Applications 122(issue 3), 725-757.
  • Davis, R.A., and Song, L. (2011). Unit Roots in Moving Averages Beyond First Order. Annals of Statistics 39,, 3062-3091.
  • Davis, R.A. (2010). Heavy Tails in Financial Time Series. In: Cont, Rama (editor): Encyclopedia of Quantitative Finance. Wiley, New York.
  • Huang, W., Wang, K., Breidt, F.J., and Davis, R.A. (2011). A Class of Stochastic Volatility Models for Environmental Applications. J. Time Series Analysis 32 364-377.

  • Davis, R.A, Mikosch, T. and Cribben, I. (2012). Towards Estimating Extremal Serial Dependence via the Bootstrapped Extremogram. J. of Econometrics 170, 142-152.
  • Steinkohl, Christina, Davis, Richard A., Kluppelberg, Claudia (2013). Extreme Value Analysis of Multivariate High Frequency Wind Speed Data. Journal of Statistical Theory and Practice 7, 73-94. pdf file
  • Chen, M., Davis, R.A., and Song, L. (2011). Inference for Regression Models with Errors From a Non-invertible MA(1) Process. J. of Forecasting 30, 6--30.
  • Davis, R.A., Hancock, S., and Yao, Y-C (2009). Consistency of Minimum Description Length Model Selection for Piecewise Autoregressions. (Submitted.)

  • Davis, R.A. and Yau, C-Y (2009). Comments on Pairwise Likelihood in Time Series Models. Statistica Sinica, 21, 255-277.

  • Andersen, T. G., Davis, R.A., Kreiss, J.-P., Mikosch, T. editors. (2009). Handbook of Financial Time Series. Springer-Verlag, Berlin.

  • Tadjuidje Kamgaing, J., Ombao, H., and Davis, R.A. (2009). Autoregressive Processes with Data Driven Regime Switching. J. Time Series Analysis 30 505-533.

  • Cooley, D., Davis, R.A., and Naveau, P. (2010). The Pairwise Beta Distribution: A Flexible Parametric. J. Multivariate Analysis 101, 2103-2117.
  • Wu, Rongning and Davis, R.A. (2010). Least Absolute Deviation Estimation for General Autogressive Moving Average Time Series Modes. J. Time Series Analysis 32 no. 4, 98-112.

  • Wang, K., Huang, W., Breidt, F.J., and Davis, R.A. (2008). Application of Heteroskedastic Spatial Models to Computer Experiments. (Submitted.)

  • Brillinger, D.R. and Davis, R.A. (2009). A Conversation with Murray Rosenblatt. Statistical Science 24 116-140. pdf file Link to Statistical Science

  • Davis, R.A. and Mikosch, T. (2009). The Extremogram: a Correlogram for Extreme Events. Bernoulli 4, 977-1009.

  • Brockwell, P.J., Davis, R.A., and Yang, V. (2011). Estimation for Non-negative Levy-driven CARMA Processes. J. Business and Economic Statistics 29, 250-259.

  • Wu, Rongning and Davis, R.A. (2009). A Negative Binomial Model for Time Series of Counts. Biometrika 96, 1-15.

  • Andrews, B., Calder, M. and Davis, R.A. (2007). Maximum Likelihood Estimation for Alpha-Stable Autoregressive Processes. Annals of Statistics 37 1946-1982.

  • Davis, R.A., Lee, T., and Rodriguez-Yam, G. (2008). Break Detection for a Class of Nonlinear Time Series Models. J. of Time Series Analysis, 29, 834-867. pdf file

  • Brockwell, P.J., Davis, R.A., and Yang, V. (2007). Estimation for Non-negative Levy-driven Ornstein-Uhlenbeck Processes. J. Appl. Prob.) 44, 977-989. pdf file

  • Davis, R.A. and Mikosch, T. (2009). Extreme Value Theory for GARCH Processes. In: Andersen, T.G., Davis, R.A., Kreiss, J.-P. and Mikosch, T. (eds.): Handbook of Financial Time Series, 187-200. Springer, New York. pdf file

  • Davis, R.A. and Mikosch, T. (2009). Probabilistic Properties of Stochastic Volatility Models. In: Andersen, T.G., Davis, R.A., Kreiss, J.-P. and Mikosch, T. (eds.): Handbook of Financial Time Series, 255-267. Springer, New York. pdf file

  • Davis, R.A. and Mikosch, T. (2009). Extremes of Stochastic Volatility Models. In: Andersen, T.G., Davis, R.A., Kreiss, J.-P. and Mikosch, T. (eds.): Handbook of Financial Time Series, 355-364. Springer, New York. pdf file

  • Davis, R.A. and Mikosch, T. (2008). Extreme Value Theory for Space-Time Processes with Heavy-Tailed Distributions. Stochastic Processes and Their Applications 118 560-584. pdf file

  • Breidt, F.J., Davis, R.A. Hsu, N-J, Rosenblatt, M. (2006). Pile-up Probabilities for the Laplace Likelihood Estimator of a Non-invertible First Order Moving Average IMS Lecture Notes Monograph Series, Vol 52, 1-19. pdf file

  • Brockwell, P.J., Davis, R.A., and Yang, V. (2007). Continuous-time Gaussian Autoregression. Statistica Sinica 17, 63-80. pdf file

  • Andrews, Beth, Davis, R.A., and Breidt, F. Jay (2007). Rank Estimation for All-Pass Time Series Models. Annals of Statistics 35 844-869. pdf file

  • Davis, R.A., Lee, T., and Rodriguez-Yam, G. (2005). Structural Break Estimation for Non-stationary Time Series Signals. Proceedings of IEEE/SP 13th Workshop on Statistical Signal Processing. Bordeaux, France (July 2005). pdf file

  • Davis, R.A., Lee, T., and Rodriguez-Yam, G. (2006). Structural Break Estimation for Nonstationary Time Series Models. J. American Statist. Assoc. 101, 229-239. pdf file

  • Hoeting, J.H., Davis, R.A., Merton, A.A., and Thompson, S.E. (2006). Model Selection for Geostatistical Models. Ecological Applications 16, 87-98. pdf file

  • Rodriguez-Yam, G., Davis, R.A., and Scharf, L. (2004). Efficient Gibbs Sampling of Truncated Multivariate Normal with Application to Constrained Linear Regression. (Submitted). pdf file

  • Davis, R.A. and Rodriguez-Yam, Gabriel. (2005). Estimation for State-Space Models: an Approximate Likelihood Approach. Statistica Sinica 15, 381-406. pdf file

  • Davis, R.A., Dunsmuir, W.T.M., and Streett, S. (2005). Maximum Likelihood Estimation for an Observation Driven Model for Poisson Counts. Methodology and Computing in Applied Probability 7, 149-159. pdf file

  • Andrews, B., Davis, R.A., and Breidt, F. Jay (2006). Maximum Likelihood Estimation for All-Pass Time Series Models. J. Multivariate Analysis. 97 1638-1659. pdf file

  • Davis, R.A., Dunsmuir, W.T.M., and Streett, S. (2003). Observation driven Models for Poisson Counts. Biometrika 90, 777-790. pdf file

  • Rodriguez-Yam, G., Davis, R.A., and Scharf, L. (2002). A Bayesian Model and Gibbs Sampler for Hyperspectral Imaging. Proceedings 2002 IEEE Sensor Array and Multichannel Signal Processing Workshop, Washington, D.C., 105-109. pdf file

  • Brockwell, P.J., Davis, R.A., and Trindade. A. (2004). Asymptotic Properties of Some Subset Vector Autoregressive Process Estimators. journal of Multivariate Analysis 90(2), 327-347. pdf file

  • Basrak, B., Davis, R.A., and Mikosch, T. (2002). A Characterization of Multivariate Regular Variation. Ann. Applied Prob. 12, 908-920. pdf file

  • Basrak, B., Davis, R.A., and Mikosch, T. (2002). Regular Variation of GARCH Processes, Stoch. Process. Appl. 99, 95-115. pdf file

  • Brockwell, P.J. and Davis, R.A. (2001). Discussion of `Non-Gaussian OU based models and some of their uses in financial economics' by O.E. Bardorff-Nielsen and N. Shephard. J. Royal Statistical Society, B, 63.

  • Davis, R.A. (2001). Gaussian Processes, Encyclopedia of Environmetrics, Section on Stochastic Modeling and Environmental Change, (D. Brillinger, Editor), Wiley, New York. pdf file

  • Brockwell, P.J. and Davis, R.A. (2000). Describing Data Over Time (with Peter Brockwell). CyberStats:An Introduction to Statistics, CyberGnostics. (CyberStats is a course delivered entirely on the Web)

  • Davis, R.A. and Mikosch, T. (2001). Point Process Convergence of Stochastic Volatility Processes with Application to Sample Autocorrelations. J. Appl. Probab. 38A, 93-104. pdf file

  • Porth, L.S., Boes, D.C., Davis, R.A., King, R., and Troendle, C.A. (2001). Case Study: Using subsampling to determine sample sizes required for streamflow estimation within acceptable error levels, J.~Hydrology 251 110--116

  • Breidt, F.J., Davis, R.A., and Trindade, A. (2001). Least Absolute Deviation Estimation for All-Pass Time Series Models. Annals of Statistics 29, 919-946. pdf file

  • Davis, R.A. and Mikosch T. (2000). The Sample Autocorrelations of Financial Time Series Models, Nonlinear and Nonstationary Signal Processing, (W.J. Fitzgerald, R.L. Smith, A.T. Walden, P. Young, editors), Cambridge University Press, Cambridge, England, 247--274. pdf file

  • Davis, R.A., Dunsmuir, W.T.M., and Wang, Y. (2000). On Autocorrelation in a Poisson Regression Model, Biometrika 87 491--506.

  • Basrak, B., Davis, R.A., and Mikosch, T. (1999). The Sample ACF of a Simple Bilinear Process, Stoch. Process. Appl. 83 1--14.

  • Davis, R.A., Dunsmuir, W.T.M., and Wang, Y. (1999). Modelling Time Series of Count Data, Asymptotics, Nonparametrics, and Time Series} (Subir Ghosh, editor) Marcel-Dekker, New York, 63--114.

  • Davis, R.A. and Mikosch, T. (1999). The Maximum of the Periodogram of a Non-Gaussian Sequence, Annals of Probability 27 522--536.

  • Davis, R.A. and Mikosch, T. (1998). The Sample ACF of Heavy--Tailed Stationary Processes with Applications to ARCH. Ann.~Statist. 26 2049--2080.

  • Davis, R.A. and Mikosch, T. (1998). Gaussian likelihood based inference for non-invertible MA(1) processes with S$/alpha$S noise, (Stoch. Process. Appl. 77 99--122.

  • Calder, M. and Davis, R.A. (1998). Inference for Linear Processes with Stable Noise, A practical Guide to Heavy Tails: Statistical Techniques and Applications (Adler, R., Feldman, R., and Taqqu, M., editors) Birkh/"auser, Boston, 159--176.

  • Breidt, F.J. and Davis, R.A. (1998). Extremes of Stochastic Volatility Models, Annals of Applied Probability 8 664--675.

  • Calder, M. and Davis, R.A. (1997). Introduction to Whittle (1953) ``The Analysis of Multiple Stationary Time Series", Breakthroughs in Statistics, Volume 3 (Kotz and Johnson, editors), Springer-Verlag, 141--148.

  • Davis, R.A. and Dunsmuir, W.T.M. (1997). Least Absolute Deviation Estimation for Regression with ARMA Errors, J. Theoretical Prob 10, 481--497.

  • Davis, R.A. and Wu, W. (1997). Bootstrapping $M$-Estimates in Regression and Autoregression with Infinite Variance, Statistica Sinica 7 1135--1154.

  • Davis, R.A. and Wu, W. (1997). M-estimation for linear regression with infinite variance, Probability and Mathematical Statistics 17, 1--20.

  • Davis, R.A. and Resnick, S.I. (1996). Limit Theory for Bilinear Processes with Heavy Tailed Noise, Annals of Applied Probability 6, 1191--1210.

  • Davis, R.A., Chen, M., and Dunsmuir, W.T.M. (1996). Inference for Seasonal Moving Average Models With a Unit Root, Athens Conference on Applied Probability and Time Series: Volume II: Time Series Analysis in Memory of E.J. Hannan (P.M. Robinson and M.Rosenblatt, editors), Springer-Verlag, 160--176.

  • Davis, R.A. and Dunsmuir, W.T.M. (1996). Maximum likelihood estimation for MA(1) processes with a root on or near the unit circle, Econometric Theory 12 1--29.

  • Davis, R.A. (1996). Gauss-Newton and $M$-Estimation for ARMA Processes With Infinite Variance, Stoch. Process. Appl. 63 75--95.

  • Chen, C., Davis, R.A., and Brockwell, P.J. (1996). Order determination for multivariate autoregressions using resampling methods, J.~Multivariate Analysis, 57, 175--190.

  • Chen, M., Davis, R.A., and Dunsmuir, W.T.M. (1995). Inference for MA(1) processes with a root on or near the unit circle, Invited paper in Probability and Mathematical Statistics, Issue in Honour of Neyman's 100 Birthday 15 227--242.

  • Donahue, R., Brockwell, P.J., and Davis, R.A. (1995). On permissible correlations for a class of stationary spatial processes, Stat.~and Prob. Letters 22, 49--53.

  • Davis, R.A., Huang, D., and Yao, Y.C. (1995). Testing for a change in the parameter values and order of an autoregressive model, Ann. Statist. 23, 282--304.

  • Davis, R.A. and Hsing, T. (1995). Point process and partial sum convergence for weakly dependent random variables with infinite variance, Ann Probab}, 23, 879--917.

  • Davis, R.A. and Resnick, S.I. (1995). Crossings of max-stable processes, J.~Appl.~Prob. 31, 130--138.

  • Breidt, F.J., and Davis, R.A., and Dunsmuir, W.T.M. (1995). Improved bootstrap forecast intervals for autoregressions, J.~Time Series Anal. 16, 177-200.

  • Davis, R.A., and Yao, Y.C., and Huang, D. (1994). On almost sure convergence of change-point estimators, Change-point Problems (Carlstein, Muller and Siegmund, editors). Institute of Mathematical Sciences, Lecture Notes-Monograph Series, Volume 23, 359--372.

  • Chen, C., Davis, R.A., Brockwell, P.J., and Bai, Z.D.(1993). Order determination for autoregressive processes using resampling methods, Statist.~Sinica 3, 481--500.

  • Davis, R.A. and Resnick, S.I. (1993). Prediction of stationary max-stable processes, Ann. of Applied Prob 3, 497--525.

  • Brockwell, P.J., Davis, R.A., and Salehi, H. (1992). Transfer function models with non-stationary inputs, New Directions in Time Series Analysis, Part I (Brillinger, Caines, Geweke, Parzen, Rosenblatt, and Taqqu, editors). Springer-Verlag, 65--74.

  • Breidt, F.J., Davis, R.A., and Dunsmuir, W.T.M. (1992). On backcasting in linear time series models, New Directions in Time Series Analysis, Part I (Brillinger, Caines, Geweke, Parzen, Rosenblatt, and Taqqu, editors). Springer-Verlag, 25--40.

  • Breidt, F.J. and Davis, R.A. (1992). Time-reversibility, identifiability, and independence of innovations for stationary time series, J. of Time Series Analysis 13, 377--390.

  • Davis, R.A., Knight, K., and Liu, J. (1992). M-estimation for autoregressions with infinite variance, Stochastic Processes and Their Applications 40, 145--180.

  • Davis, R.A. and Rosenblatt, M. (1991). Parameter estimation for some time series models without contiguity, Statistics and Probability Letters 11, 515--521.

  • Breidt, F.J., Davis, R.A., Lii, K.S., and Rosenblatt, M. (1991). Maximum likelihood estimation for noncausal autoregressive processes, J. Multivariate Analysis 36, 175--198.

  • Davis, R.A. and Resnick, S.I. (1991). Extremes of moving averages of random variables with finite endpoint, Ann Probability 19, 312--328.

  • Brockwell, P.J., Davis, R.A., and Salehi, H. (1991). A state-space approach to transfer-function modelling, Statistical Inference in Stochastic Processes (N.U. Prabhu and I.V. Basawa, Editors). Marcel Dekker, 233--248.

  • Breidt, F.J., Davis, R.A., Lii, K.S., and Rosenblatt, M. (1990). Nonminimum phase non-Gaussian autoregressive processes, Proc. Natl. Acad. Sci. Vol. 87, 179-181.

  • Davis, R.A. and Marengo, J. (1990). Limit theory for the sample covariance and correlation matrix function of a class of multivariate linear processes, Stochastic Models 6, 483--498.

  • Davis, R.A. and Resnick, S.I. (1989). Basic properties and prediction of max-ARMA processes, Adv. App. Prob. 21, 781-803.

  • Davis, R.A. and McCormick, W.P. (1989). Estimation for first-order autoregressive processes with positive or bounded innovations, Stochastic Processes and Their Applications 31, 237-250.

  • Boes, D.C., Davis, R.A., and Gupta, S. (1989). Parameter estimation in low order fractionally differenced ARMA processes, Stochastic Hydrol. and Hydraul. 3, 97-110.

  • Davis, R.A. and Resnick, S.I. (1988). Extremes of moving averages of random variables from the domain of attraction of the double exponential distribution, Stochastic Processes Appl. 30, 41-68.

  • Davis, R.A., Mulrow, E., and Resnick, S.I. (1988). Almost sure limit sets of random samples in $R^d$, Adv. Appl. Prob. 20, 573-599.

  • Brockwell, P.J. and Davis, R.A. (1988). Simple consistent estimation of the coefficients of a linear filter, Stochastic Processes and Their Applications, 47-59.

  • Davis, R.A. (1988). Discussion of `Extreme values--theory and technical applications' by G. Lindgren and H. Rootzen. Scandinavian Journal of Statistics 14, 271-274.

  • Brockwell, P.J. and Davis, R.A. (1988). On the applications of innovation representation in time series analysis, Probability and Statistics: Essays in Honor of Franklin A. Graybill (J. N. Srivastava, editor). North Holland, 61-84.

  • Davis, R.A., Mulrow, E. and Resnick, S.I. (1987). The convex hull of a random sample in $R^2$, Stochastic Models 3, 1-28.

  • Yao, Y.C. and Davis, R.A. (1986). The asymptotic behavior of the likelihood ratio statistic for testing a shift in mean in a sequence of independent normal variables. Sankya 48 339-353.
  • Davis, R.A. and Resnick, S.I. (1986). Limit theory for the sample correlation function of moving averages, Dependence in Probability and Statistics (Eberlein and Taqqu, Editors). Birkhauser, 417-426.

  • Davis, R.A. and Resnick, S.I. (1986). Limit theory for the sample covariance and correlation function of moving averages. Ann. Statist. 14, 533-558.
  • Davis, R.A. and Resnick, S.I. (1985). More limit theory for the sample correlation function of moving averages. Stochastic Provesses and Their Applications 20, 257-279.
  • Davis, R.A. and Resnick, S.I. (1985). Limit theory for moving averages of random variables with regularly varying tail probabilities. Annals of Probability 13, 179-197.
  • Davis, R.A., Marengo, J. and Resnick, S.I. (1985). Extremal properties of a class of multivariate moving averages, Proceedings of the $45^{th}$ Session of the International Statistical Institute, Vol. 4 Amsterdam. With discussion. Bull. Inst. Internat. Statist. Vol V, 185-192.

  • Davis, R.A. and Resnick, S.I. (1984). Tail estimates motivated by extreme value theory. Annals of Statistics 12, 1467-1487.
  • Davis, R.A. (1984). On upper and lower extremes in stationary sequences. Statistical Extremes and Applications, Tiago de Oliveira, Ed., 443-460. Reidel Publishing Company.
  • Davis, R.A. (1983). Stable limits for partial sums of dependent random variables. Annals of Probability 11, 262-269.
  • Davis, R.A. (1983). Limit laws for upper and lower extremes from stationary mixing sequences, J. Multivariate Analysis 13, 273-286.

  • Chernick, M.R. and Davis, R.A. (1982). Extremes in autoregressive processes with uniform marginal distributions, Statistics and Probability Letters 1, 85-88

  • Davis, R.A. (1982). Limit laws for the maximum and minimum of stationary sequences, Z. Wahrscheinlichkeitstheorie und verw Gebiete 61, 31-42.

  • Davis, R.A. (1982). Extremes of one-dimensional diffusions. Stochastic Processes and Their Applications 13, 1-9.

  • Davis, R.A. (1982). The rate of convergence in distribution of the maxima, Statistica Neerlandica 36, 31-35.

  • Davis, R.A. (1979). Maxima and minima of stationary processes, Annals of Probability 7, 453-460.
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