Generalized Autoregressive Score models



The following articles, papers, and books are related to the GAS model (alphabetic order per year). For the GAS 2013 JAE main paper, see here. If you find your contribution is missing, please let us know by sending an email to Andre Lucas (a.lucas@vu.nl) Before using any of the code, please read the disclaimer.


    in press

  1. Blasques, Francisco, Andre Lucas and Erkki Silde (in press): "A Stochastic Recurrence Equations Approach for Score Driven Correlation Models", Econometric Reviews.
    Click here to download the working paper version.

  2. Blazsek, Szabolcs, and Luis Antonio Monteros (in press): "Event-study analysis by using dynamic conditional score models", Applied Economics.
    Click here to download the working paper version.

  3. Blazsek, Szabolcs, and Han-Chiang Ho (in press): "Markov regime-switching Beta-t-EGARCH", Applied Economics.
    Click here to download the working paper version.

  4. Blazsek, Szabolcs, and Luis Antonio Monteros (in press): "Dynamic conditional score models of degrees of freedom: filtering with score-driven heavy tails", Applied Economics.
    Click here to download the working paper version.

  5. Billé, Anna Gloria, and Leopoldo Catania (in press): Dynamic Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances", Journal of Applied Econometrics.

  6. Oh, Dong Hwan and Andrew Patton (in press): "Time-varying systemic risk: evidence from a dynamic copula model of CDS spreads", Journal of Business and Economic Statistics.

  7. Opschoor, Anne, Pawel Janus, Andre Lucas, and Dick J. van Dijk (in press): "New HEAVY Models for Fat-Tailed Realized Covariances and Returns", Journal of Business and Economic Statistics.
    Click here to download the working paper version.

  8. Zhao, Lin, and Sweder Van Wijnbergen (in press): "Decision Making in Incomplete Markets with Ambiguity: A case study of a gas field acquisition", Quantitative Finance.
    Click here to download the working paper version.


  9. 2017

  10. Bazzi, Marco, Francisco Blasques, Siem Jan Koopman and Andre Lucas (2017): "Time Varying Transition Probabilities for Markov Regime Switching Models", Journal of Time Series Analysis 38, 458-478.
    Click here to download the working paper version.
    There is also R code accompanying this paper.

  11. Blasques, Francisco, Paolo Gorgi, and Siem Jan Koopman (2017): "Accelerating GARCH and Score-Driven Models: Optimality, Estimation and Forecasting", Tinbergen Institute Discussion Paper, TI 2017-061/III.

  12. Buccheri, Giuseppe, Giacomo Bormetti, Fulvio Corsi, and Fabrizio Lillo (2017): "A Score-driven Conditional Correlation Model for Noisy and Asynchronous Data: An Application to High-frequency Covariance Dynamics", Available at SSRN: https://ssrn.com/abstract=2912438.

  13. Calvori, Francesco, Drew Creal, Siem Jan Koopman and Andre Lucas (2017): "Testing for Parameter Instability in Competing Modeling Frameworks", Journal of Financial Econometrics 15(2), 223-246.
    Click here to download the working paper version.

  14. Delle Monache, Davide and Ivan Petrella (2017): "Adaptive models and heavy tails with an application to inflation forecasting", International Journal of Forecasting 33(2), 482-501.
    Click here to download the working paper version.

  15. Harvey, Andrew, and Ryoko Ito (2017): "Modeling time series with zero observations", Nuffield College working paper, University of Oxford.

  16. Koopman, Siem Jan, and Rutger Lit (2017): "Forecasting football match results in national league competitions using score-driven time series models", Tinbergen Institute Discussion Paper, TI 2017-062/III.

  17. Lin, Qi, and Haiyue Yu (2017): "Option Pricing with Generalized Autoregressive Score Models", Working paper, University of Hong Kong.

  18. Lucas, Andre, Bernd Schwaab and Xin Zhang (2017): "Measuring Credit Risk in a Large Banking System: Econometric Modeling and Empirics", Journal of Applied Econometrics 32(1), 171-191.
    Click here to download the working paper version.

  19. Neves, César, Cristiano Fernandes, and Henrique Hoeltgebaum (2017): "Five different distributions for the Lee–Carter model of mortality forecasting: A comparison using GAS models", Insurance: Mathematics and Economics 75, 48-57.


  20. 2016

  21. Ardia, David, Kris Boudt, and Leopoldo Catania (2016): "Generalized Autoregressive Score Models in R: The GAS Package", Available at SSRN: https://ssrn.com/abstract=2825380.

  22. Ardia, David, Kris Boudt, and Leopoldo Catania (2016): "Value-at-Risk Prediction in R with the GAS Package", Available at SSRN: https://ssrn.com/abstract=2825380.

  23. Bartels, M., and F.A. Ziegelmann (2016): "Market risk forecasting for high dimensional portfolios via factor copulas with GAS dynamics", Insurance: Mathematics and Economics, 70, 66-79.

  24. Barunik, J., T. Krehlik, and L. Vacha (2016): "Modeling and forecasting exchange rate volatility in time-frequency domain", European Journal of Operational Research, 251(1), 329-340.

  25. Blasques, Francisco, Siem Jan Koopman, Katarzyna Lasak and Andre Lucas (2016): "In-Sample Confidence Bounds and Out-of-Sample Forecast Bands for Time-Varying Parameters in Observation Driven Models", International Journal of Forecasting, 32(3), 875-887.
    Click here to download the working paper version.

  26. Blasques, Francisco, Siem Jan Koopman, Andre Lucas and Julia Schaumburg (2016): "Spillover Dynamics for Systemic Risk Measurement using Spatial Financial Time Series Models", Journal of Econometrics, 195, 211-223.
    Click here to download the working paper version.

  27. Blazsek, Szabolcs, and Marco Villatoro (2016): "QARMA-Beta-t-EGARCH versus ARMA-GARCH: an application to S&P 500", Applied Economics, 48(12), 1119-1129.

  28. Blazsek, Szabolcs, and Alvaro Escribano (2016): "Score-driven dynamic patent count panel data models", Economics Letters, 149, 116-119.

  29. Boswijk, Peter, and Yang Liu (2016): "Score-driven variance-factor models", working paper available via research site Yang Liu.

  30. Caivano, Michele, Andrew Harvey and Alessandra Luati (2016): Robust time series models with trend and seasonal components, SERIEs, 7, 99-120.

  31. Catania, Leopoldo (2016): "Dynamic Adaptive Mixture Models", eprint arXiv:1603.01308.

  32. Catania, Leopoldo, and Nima Nonejad (2016): "Density Forecasts and the Leverage Effect: Some Evidence from Observation and Parameter-Driven Volatility Models", eprint arXiv:1605.00230.

  33. Delle Monache, Davide, Ivan Petrella and Fabrizio Venditti (2016): "Adaptive state space models with applications to the business cycle and financial stress", CEPR Discussion Paper 11599.

  34. Delle Monache, Davide, Ivan Petrella and Fabrizio Venditti (2016): "Common Faith or Parting Ways? A Time Varying Parameters Factor Analysis of Euro-Area Inflation", Book Series: Advances in Econometrics, 35, 539-565.

  35. Gao, Chun-Ting and Xiao-Hua Zhou (2016): "Forecasting VaR and ES using dynamic conditional score models and skew Student distribution", Economic Modelling, 53, 216-223.

  36. Gorgi, Paolo (2016): "Integer-valued autoregressive models with survival probability driven by a stochastic recurrence equation", Working paper.

  37. Hansen, Pieter Reinhard, Pawel Janus, and Siem Jan Koopman (2016): "Realized Wishart-GARCH: A Score-driven Multi-Asset Volatility Model", Tinbergen Institute Discussion Paper, TI 2016-061/III.

  38. Harvey, Andrew C. and Stephen Thiele (2016): "Testing against Changing Correlation", Journal of Empirical Finance, 38, 575-589.
    Click here to download the working paper version.

  39. Ito, Ryoko (2016a): "Asymptotic Theory for Beta-t-GARCH", Cambridge Working Papers in Economics CWPE1607.

  40. Ito, Ryoko (2016b): "Spline-DCS for Forecasting Trade Volume in High Frequency Financial Data", Cambridge Working Papers in Economics CWPE1606.

  41. Koopman, Siem Jan, Andre Lucas and Marcel Scharth (2016): "Predicting time-varying parameters with parameter-driven and observation-driven models", Review of Economics and Statistics, 98(1), 97-110.
    Click here to download the working paper version.

  42. Lange, Rutger Jan, Andre Lucas, and Arjen H. Siegmann (2016): "Systemic Risk Signaling using Scores", in M. Billio, L. Pelizzon, R. Savona (eds.) Systemic Risk Tomography: Signals, Measurements and Transmission Channels. ISTE-Elsevier.
    See also the working paper version:
    Lange, Rutger-Jan, Andre Lucas, and Arjen H. Siegmann (2016): "Score-Driven Systemic Risk Signaling for European Sovereign Bond Yields and CDS Spreads", Tinbergen Institute Discussion Paper, TI 2016-064/IV.

  43. Lucas, Andre, Anne Opschoor (2016): "Fractional Integration and Fat Tails for Realized Covariance Kernels and Returns", TI Discussion paper 16-069/IV.

  44. Lucas, Andre, Anne Opschoor, Julia Schaumburg (2016): "Accounting for Missing Values in Score-Driven Time-Varying Parameter Models", Economics Letters, 148, 96-98.
    Click here to download the working paper version, Tinbergen Institute Discussion Paper, TI 2016-067/IV.

  45. Lucas, Andre, Bernd Schwaab, and Julia Schaumburg (2016): "Bank business models at zero interest rates", Tinbergen Institute Discussion Paper, TI 2016-066/IV.

  46. Quaedvlieg, Rogier and Peter C. Schotman (2016): "Score-Driven Nelson Siegel: Hedging Long-Term Liabilities", Working Paper.

  47. Sucarrat, Genaro and Steffen Grønneberg (2016): "Models of Financial Return With Time-Varying Zero Probability", MPRA Paper 68931, University Library of Munich, Germany.

  48. Zhang, Xin and Bernd Schwaab (2016): "Tail risk in government bond markets and ECB unconventional policies", working paper.


  49. 2015

  50. Avdulaj, Krenar and Jozef Barunik (2015): "Are benefits from oil-stocks diversification gone? New evidence from a dynamic copula and high frequency data", Energy Economics, 51, 31-44.

  51. Azam, Kazim, and Andre Lucas (2015): "Mixed Density based Copula Likelihood", Tinbergen Institute Discussion Paper, TI 15-003/III.

  52. Bernardi, Mauro and Leopoldo Catania (2015a): "Switching-GAS Copula Models for Systemic Risk Assessment", working papers series.

  53. Bernardi, Mauro and Leopoldo Catania (2015b): "Comparison of Value-at-Risk models: the MCS package", working papers series.

  54. Blasques, Francisco, Siem Jan Koopman and Andre Lucas (2015): "Information Theoretic Optimality of Observation Driven Time Series Models for Continuous Responses", Biometrika, 102(2), 325-343.
    Click here to download the working paper version.

  55. Blazsek, Szabolcs, and Marco Villatoro (2015): "Is Beta-t-EGARCH(1,1) superior to GARCH(1,1)?", Applied Economics, 47(17), 1764-1774.

  56. Caivano, Michele and Andrew Harvey (2015): "Time-series models with an EGB2 conditional distribution", Journal of Time Series Analysis, 35(6), 558-571.

  57. Creal, Drew, Siem Jan Koopman, Andre Lucas, and Marcin Zamojski (2015): "Generalized Autoregressive Method of Moments", Tinbergen Institute Discussion Paper, TI 2015-138/III.

  58. De Lira Salvatierra, Irving and Andrew J. Patton (2015): "Dynamic Copula Models and High Frequency Data", Journal of Empirical Finance, 30, 120-135.

  59. Harvey, Andrew and Rutger-Jan Lange (2015a): "Volatility Modeling with a Generalized t-distribution", Cambridge Working Papers in Economics, CWPE 1517.

  60. Harvey, Andrew and Rutger-Jan Lange (2015b): "Modeling the Interactions between Volatility and Returns", Cambridge Working Papers in Economics, CWPE 1518.

  61. Koopman, Siem Jan, Rutger Lit and Andre Lucas (2015): "Intraday Stock Price Dependence using Dynamic Discrete Copula Distributions", Tinbergen Institute Discussion Paper, TI 15-037/III.

  62. Laurent, Sebastien, Christelle Lecourt and Franz C. Palm (2015): "Testing for jumps in conditionally Gaussian ARMA-GARCH models, a robust approach", Computational Statistics and Data Analysis, forthcoming.

  63. Lucas, Andre and Xin Zhang (2015): "Score Driven Exponentially Weighted Moving Average and Value-at-Risk Forecasting", International Journal of Forecasting, 32, 293-302.
    Click here to download the working paper version.


  64. 2014

  65. Andres, P. (2014): "Maximum likelihood estimates for positive valued dynamic score models; The Dysco package", Computational Statistics and Data Analysis, 76, 34-43.

  66. Blasques, Francisco (2014): GAS workshop slides, 2014 International Symposium on Forecasting, Rotterdam.

  67. Blasques, Francisco, Siem Jan Koopman and Andre Lucas (2014a): "Stationarity and Ergodicity of Univariate Generalized Autoregressive Score Processes", Electronic Journal of Statistics, 8, 1088-1112.

  68. Blasques, Francisco, Siem Jan Koopman and Andre Lucas (2014b): "Optimal Formulations for Nonlinear Autoregressive Processes", Tinbergen Institute Discussion Paper, TI 14-103/III.

  69. Blasques, Francisco, Siem Jan Koopman and Andre Lucas (2014c): "Maximum Likelihood Estimation for correctly Specified Generalized Autoregressive Score Models:Feedback Effects, Contraction Conditions and Asymptotic Properties", Tinbergen Institute Discussion Paper, TI 14-074/III.

  70. Blasques, Francisco, Siem Jan Koopman and Andre Lucas (2014e): "Maximum Likelihood Estimation for Generalized Autoregressive Score Models", Tinbergen Institute Discussion Paper, TI 14-029/III.

  71. Calvori, Francesco, Drew Creal, Siem Jan Koopman and Andre Lucas (2014): "Testing for Parameter Instability in Competing Modeling Frameworks", Duisenberg school of finance - Tinbergen Institute Discussion Paper, TI 14-010/IV/DSF71.

  72. Chen, Hua, Richard D. MacMinn and Tao Sun (2014): "Mortality Dependence and Longevity Bond Pricing: A Dynamic Factor Copula Mortality Model with the GAS Structure", working papers series.

  73. Creal, Drew D., Bernd Schwaab, Siem Jan Koopman and Andre Lucas (2014): "Observation Driven Mixed-Measurement Dynamic Factor Models with an Application to Credit Risk", Review of Economics and Statistics, 96(5), 898-915.
    You can also download the working paper version or download the online Appendix.
    Computer code : Ox code with macro data.

  74. Delle Monache, Davide and Ivan Petrella (2014): "Adaptive Models and Heavy Tails", Birkbeck working paper, BWPEF 1409.

  75. Harvey, Andrew C. and Alessandra Luati (2014): "Filtering with heavy tails", Journal of the American Statistical Association, 109, 1112-1122.

  76. Harvey, Andrew C. and Genaro Sucarrat (2014): "EGARCH models with fat tails, skewness and leverage", Computational Statistics and Data Analysis, 76, 320-339.

  77. Huang, Zhuo, Tianyi Wang and Xin Zhang (2014): "Generalized Autoregressive Score Model with Realized Measures of Volatility", working papers series.

  78. Janus, Pawel, Andre Lucas, Anne Opschoor, and Dick J. van Dijk (2014): "New HEAVY Models for Fat-Tailed Returns and Realized Covariance Kernels", Tinbergen Institute Discussion Paper, TI 14-073/III.

  79. Janus, Pawel, Siem Jan Koopman and Andre Lucas (2014) "Long Memory Dynamics for Multivariate Dependence under Heavy Tails", Journal of Empirical Finance, 29, 187-206.
    Click here to download the working paper version.

  80. Koopman, Siem Jan (2014): GAS workshop slides, 2014 International Symposium on Forecasting, Rotterdam.

  81. Lucas, Andre, Bernd Schwaab and Xin Zhang (2014): "Conditional euro area sovereign default risk", Journal of Business and Economic Statistics, 32(2), 271-284.
    You can also download the working paper version.

  82. Mao, Xiuping, Esther Ruiz and Helena Veiga (2014a): "Score Driven Asymmetric Stochastic Volatility Models", Universidad Carlos III de Madrid, Statistics and Econometrics Series 18, working paper 14-26.

  83. Massacci, D. (2014): "Tail Risk and the Macroeconomy", Einaudi Institute for Economics and Finance, working paper.


  84. 2013

  85. Avdulaj, Krenar and Jozef Barunik (2013): "Can we still benefit from international diversification? The case of the Czech and German stock markets", Cornell University Library.

  86. Caivano, Michele and Andrew Harvey (2013): "Two EGARCH models and one fat tail", CWPE 1326.

  87. Calvori, Francesco, Fabrizio Cipollini and Giampiero M. Gallo (2013): "High-frequency modeling for VWAP based trading strategies: a Generalized Autoregressive Score approach", SIS 2013 Statistical Conference, Advances in Latent Variables - Methods, Models and Applications, Brescia.

  88. Calvori, Francesco, Fabrizio Cipollini and Giampiero M. Gallo (2013): "Go with the Flow: A GAS Model For Predicting Intra-Daily Volume Shares", working papers series.

  89. Creal, Drew D., Siem Jan Koopman and Andre Lucas (2013, available as OPEN ACCESS): "Generalized Autoregressive Score Models with Applications", Journal of Applied Econometrics, 28(5), 777-795.
    Computer code : Matlab code and Ox code.

  90. Goncalves de Matos, Gilson (2013): "GAS Models Applied to Time Series of Streamflow and Wind.", dissertation from Pontificia Universidade Catolica do Rio de Janeiro.

  91. Harvey, Andrew C. (2013): Dynamic Models for Volatility and Heavy Tails: With Applications to Financial and Economic Time Series. Econometric Series Monographs. Cambridge University Press.

  92. Ito, Ryoko (2013): "Modeling Dynamic Diurnal Patterns in High Frequency Financial Data", Cambridge Working Papers in Economics CWPE1315.

  93. Oh, Dong Hwan and Andrew J. Patton (2013): "Time-Varying Systemic Risk: Evidence from a Dynamic Copula Model of CDS Spreads", Duke University Working Paper.

  94. Sucarrat, Genaro (2013): "betategarch: An R Package for the Simulation and Estimation of Beta-skew-t-EGARCH Models", BI Norwegian Business School Working Paper.


  95. 2012

  96. Andres, Philipp and Andrew C. Harvey (2012): "The Dynamic Location/Scale Model: with applications to intra-day financial data", Cambridge Working Papers in Economics CWPE 1240.

  97. Blasques, Francisco, Siem Jan Koopman and Andre Lucas (2012): "Stationarity and Ergodicity of Univariate Generalized Autoregressive Score Processes", Tinbergen Institute Discussion Paper 12-059/4.

  98. Boudt, Kris, Jon Danielsson, Siem Jan Koopman and Andre Lucas (2012): "Regime Switches in the Volatility and Correlation of Financial Institutions", National Bank of Belgium Working Paper No. 227.


  99. 2011

  100. Creal, Drew D., Siem Jan Koopman and Andre Lucas (2011): "A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations", Journal of Business and Economic Statistics, 29, 552-563.

  101. Creal, Drew D., Bernd Schwaab, Siem Jan Koopman and Andre Lucas (2011): "Observation Driven Mixed-Measurement Dynamic Factor Models with an Application to Credit Risk", Tinbergen Institute Discussion Paper 11-042/2/DSF16.
    Final version published in the Review of Economics and Statistics.

  102. Zhang, Xin, Drew D. Creal, Siem Jan Koopman and Andre Lucas (2011): "Modeling Dynamic Volatilities and Correlations under Skewness and Fat Tails", Tinbergen Institute Discussion Paper 11-078/2/DSF22.

  103. Zhang, Xin, Bernd Schwaab and, Andre Lucas (2011): "Conditional Probabilities and Contagion Measures for Euro Area Sovereign Default Risk", Tinbergen Institute Discussion Paper 11-176/2/DSF29.


  104. 2010

  105. Creal, Drew D., Siem Jan Koopman and Andre Lucas (2010): "A dynamic multivariate heavy-tailed model for time-varying volatilities and correlations", Tinbergen Institute Discussion Paper 10-032/2. You can also download the final version as published in the Journal of Business and Economic Statistics.

  106. Harvey, Andrew C. (2010): "Exponential Conditional Volatility Models", Cambridge Working Papers in Economics CWPE 1040.


  107. 2008

  108. Creal, Drew D., Siem Jan Koopman and Andre Lucas (2008): "A General Framework for Observation Driven Time-Varying Parameter Models", Tinbergen Institute Discussion Paper 08-108/4.
    You can also download the final version as published version in the Journal of Applied Econometrics.

  109. Harvey, Andrew C. and Tirthankar Chakravarty (2008): "Beta-t-(E)GARCH", Discussion Paper University of Cambridge CWPE 08340.