IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1602.02542.html
   My bibliography  Save this paper

Dynamic Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances

Author

Listed:
  • Leopoldo Catania
  • Anna Gloria Bill'e

Abstract

We propose a new class of models specifically tailored for spatio-temporal data analysis. To this end, we generalize the spatial autoregressive model with autoregressive and heteroskedastic disturbances, i.e. SARAR(1,1), by exploiting the recent advancements in Score Driven (SD) models typically used in time series econometrics. In particular, we allow for time-varying spatial autoregressive coefficients as well as time-varying regressor coefficients and cross-sectional standard deviations. We report an extensive Monte Carlo simulation study in order to investigate the finite sample properties of the Maximum Likelihood estimator for the new class of models as well as its flexibility in explaining several dynamic spatial dependence processes. The new proposed class of models are found to be economically preferred by rational investors through an application in portfolio optimization.

Suggested Citation

  • Leopoldo Catania & Anna Gloria Bill'e, 2016. "Dynamic Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances," Papers 1602.02542, arXiv.org, revised Jan 2023.
    • Handle: RePEc:arx:papers:1602.02542
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1602.02542
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ivo Welch & Amit Goyal, 2008. "A Comprehensive Look at The Empirical Performance of Equity Premium Prediction," The Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1455-1508, July.
    2. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107630024, Enero.
    3. Kelejian, Harry H. & Prucha, Ingmar R., 2010. "Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances," Journal of Econometrics, Elsevier, vol. 157(1), pages 53-67, July.
    4. Blasques, Francisco & van Brummelen, Janneke & Koopman, Siem Jan & Lucas, André, 2022. "Maximum likelihood estimation for score-driven models," Journal of Econometrics, Elsevier, vol. 227(2), pages 325-346.
    5. James P. LeSage & R. Kelley Pace, 2014. "The Biggest Myth in Spatial Econometrics," Econometrics, MDPI, vol. 2(4), pages 1-33, December.
    6. Luc Anselin, 2003. "Spatial Externalities, Spatial Multipliers, And Spatial Econometrics," International Regional Science Review, , vol. 26(2), pages 153-166, April.
    7. Asgharian, Hossein & Hess, Wolfgang & Liu, Lu, 2013. "A spatial analysis of international stock market linkages," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4738-4754.
    8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    9. Viviana Fernandez, 2011. "Spatial linkages in international financial markets," Quantitative Finance, Taylor & Francis Journals, vol. 11(2), pages 237-245.
    10. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    11. Tse, Y. K., 2000. "A test for constant correlations in a multivariate GARCH model," Journal of Econometrics, Elsevier, vol. 98(1), pages 107-127, September.
    12. Wenceslao González‐Manteiga & Rosa M. Crujeiras & Nan‐Jung Hsu & Ya‐Mei Chang & Hsin‐Cheng Huang, 2012. "A group lasso approach for non‐stationary spatial–temporal covariance estimation," Environmetrics, John Wiley & Sons, Ltd., vol. 23(1), pages 12-23, February.
    13. Charles F. Manski, 1993. "Identification of Endogenous Social Effects: The Reflection Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(3), pages 531-542.
    14. Badi H. Baltagi & Bernard Fingleton & Alain Pirotte, 2014. "Estimating and Forecasting with a Dynamic Spatial Panel Data Model," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(1), pages 112-138, February.
    15. Kelejian, Harry H. & Piras, Gianfranco, 2014. "Estimation of spatial models with endogenous weighting matrices, and an application to a demand model for cigarettes," Regional Science and Urban Economics, Elsevier, vol. 46(C), pages 140-149.
    16. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    17. Tse, Y K & Tsui, Albert K C, 2002. "A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-Varying Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 351-362, July.
    18. Blasques, Francisco & Koopman, Siem Jan & Lucas, Andre & Schaumburg, Julia, 2016. "Spillover dynamics for systemic risk measurement using spatial financial time series models," Journal of Econometrics, Elsevier, vol. 195(2), pages 211-223.
    19. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    20. F. Blasques & S. J. Koopman & A. Lucas, 2015. "Information-theoretic optimality of observation-driven time series models for continuous responses," Biometrika, Biometrika Trust, vol. 102(2), pages 325-343.
    21. Siem Jan Koopman & André Lucas & Marcel Scharth, 2016. "Predicting Time-Varying Parameters with Parameter-Driven and Observation-Driven Models," The Review of Economics and Statistics, MIT Press, vol. 98(1), pages 97-110, March.
    22. Kelejian, Harry H. & Prucha, Ingmar R., 2007. "HAC estimation in a spatial framework," Journal of Econometrics, Elsevier, vol. 140(1), pages 131-154, September.
    23. Timmermann, Allan, 2008. "Reply to the discussion of Elusive Return Predictability," International Journal of Forecasting, Elsevier, vol. 24(1), pages 29-30.
    24. De Lira Salvatierra, Irving & Patton, Andrew J., 2015. "Dynamic copula models and high frequency data," Journal of Empirical Finance, Elsevier, vol. 30(C), pages 120-135.
    25. Bao, Yong & Ullah, Aman, 2007. "Finite sample properties of maximum likelihood estimator in spatial models," Journal of Econometrics, Elsevier, vol. 137(2), pages 396-413, April.
    26. Keiler, Sebastian & Eder, Armin, 2013. "CDS spreads and systemic risk: A spatial econometric approach," Discussion Papers 01/2013, Deutsche Bundesbank.
    27. J. Paul Elhorst, 2014. "Dynamic Spatial Panels: Models, Methods and Inferences," SpringerBriefs in Regional Science, in: Spatial Econometrics, edition 127, chapter 0, pages 95-119, Springer.
    28. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    29. Giuseppe Arbia & Bernard Fingleton, 2008. "New spatial econometric techniques and applications in regional science," Papers in Regional Science, Wiley Blackwell, vol. 87(3), pages 311-317, August.
    30. Matthias Arnold & Sebastian Stahlberg & Dominik Wied, 2013. "Modeling different kinds of spatial dependence in stock returns," Empirical Economics, Springer, vol. 44(2), pages 761-774, April.
    31. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    32. Lung-Fei Lee, 2004. "Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models," Econometrica, Econometric Society, vol. 72(6), pages 1899-1925, November.
    33. Arthur Getis & Jared Aldstadt, 2010. "Constructing the Spatial Weights Matrix Using a Local Statistic," Advances in Spatial Science, in: Luc Anselin & Sergio J. Rey (ed.), Perspectives on Spatial Data Analysis, chapter 0, pages 147-163, Springer.
    34. J. Elhorst, 2010. "Applied Spatial Econometrics: Raising the Bar," Spatial Economic Analysis, Taylor & Francis Journals, vol. 5(1), pages 9-28.
    35. Timmermann, Allan, 2008. "Elusive return predictability," International Journal of Forecasting, Elsevier, vol. 24(1), pages 1-18.
    36. Harry Kelejian, 2008. "A spatial J-test for model specification against a single or a set of non-nested alternatives," Letters in Spatial and Resource Sciences, Springer, vol. 1(1), pages 3-11, April.
    37. Lee, Lung-fei & Yu, Jihai, 2010. "Some recent developments in spatial panel data models," Regional Science and Urban Economics, Elsevier, vol. 40(5), pages 255-271, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Enzo D'Innocenzo & André Lucas & Anne Opschoor & Xingmin Zhang, 2024. "Heterogeneity and dynamics in network models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(1), pages 150-173, January.
    2. Marius C. O. Amba & Julie Gallo, 2022. "Specification and estimation of a periodic spatial panel autoregressive model," Journal of Spatial Econometrics, Springer, vol. 3(1), pages 1-34, December.
    3. Hannes Böhm & Julia Schaumburg & Lena Tonzer, 2022. "Financial Linkages and Sectoral Business Cycle Synchronization: Evidence from Europe," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 70(4), pages 698-734, December.
    4. Blasques, Francisco & van Brummelen, Janneke & Koopman, Siem Jan & Lucas, André, 2022. "Maximum likelihood estimation for score-driven models," Journal of Econometrics, Elsevier, vol. 227(2), pages 325-346.
    5. Alice Barreca & Rocco Curto & Diana Rolando, 2020. "Urban Vibrancy: An Emerging Factor that Spatially Influences the Real Estate Market," Sustainability, MDPI, vol. 12(1), pages 1-23, January.
    6. Xu, Yuhong & Yang, Zhenlin, 2020. "Specification Tests for Temporal Heterogeneity in Spatial Panel Data Models with Fixed Effects," Regional Science and Urban Economics, Elsevier, vol. 81(C).
    7. Alfredo Cartone & Domenica Panzera & Paolo Postiglione, 2022. "Regional economic disparities, spatial dependence and proximity structures," Regional Science Policy & Practice, Wiley Blackwell, vol. 14(5), pages 1034-1050, October.
    8. Berloco, Claudia & Argiento, Raffaele & Montagna, Silvia, 2023. "Forecasting short-term defaults of firms in a commercial network via Bayesian spatial and spatio-temporal methods," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1065-1077.
    9. Cristiana Fiorelli & Alfredo Cartone & Matteo Foglia, 2021. "Shadow rates and spillovers across the Eurozone: a spatial dynamic panel model," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 48(1), pages 223-245, February.
    10. Francisco (F.) Blasques & Andre (A.) Lucas & Andries van Vlodrop, 2017. "Finite Sample Optimality of Score-Driven Volatility Models," Tinbergen Institute Discussion Papers 17-111/III, Tinbergen Institute.
    11. Tatjana Dahlhaus & Julia Schaumburg & Tatevik Sekhposyan, 2021. "Networking the Yield Curve: Implications for Monetary Policy," Staff Working Papers 21-4, Bank of Canada.
    12. Niko Hauzenberger & Michael Pfarrhofer, 2021. "Bayesian State‐Space Modeling for Analyzing Heterogeneous Network Effects of US Monetary Policy," Scandinavian Journal of Economics, Wiley Blackwell, vol. 123(4), pages 1261-1291, October.
    13. Tim Kutzker & Dominik Wied, 2024. "Testing the correct specification of a system of spatial dependence models for stock returns," Empirical Economics, Springer, vol. 66(5), pages 2083-2103, May.
    14. Kangogo, Moses & Volkov, Vladimir, 2021. "Dynamic effects of network exposure on equity markets," Working Papers 2021-03, University of Tasmania, Tasmanian School of Business and Economics.
    15. Dieter Wang & Julia Schaumburg, 2020. "Smooth marginalized particle filters for dynamic network effect models," Tinbergen Institute Discussion Papers 20-023/III, Tinbergen Institute.
    16. Matteo Foglia & Eliana Angelini, 2019. "The Time-Spatial Dimension of Eurozone Banking Systemic Risk," Risks, MDPI, vol. 7(3), pages 1-25, July.
    17. David Ardia & Kris Boudt & Leopoldo Catania, 2016. "Generalized Autoregressive Score Models in R: The GAS Package," Papers 1609.02354, arXiv.org.
    18. Mardi Dungey & Moses Kangogo & Vladimir Volkov, 2022. "Dynamic effects of network exposure on equity markets," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 12(4), pages 569-629, December.
    19. Anna Gloria Billé & Samantha Leorato, 2017. "Quasi-ML estimation, Marginal Effects and Asymptotics for Spatial Autoregressive Nonlinear Models," BEMPS - Bozen Economics & Management Paper Series BEMPS44, Faculty of Economics and Management at the Free University of Bozen.
    20. Guo, Juncong & Qu, Xi, 2020. "Fixed effects spatial panel data models with time-varying spatial dependence," Economics Letters, Elsevier, vol. 196(C).
    21. Blasques, Francisco & Lucas, André & van Vlodrop, Andries C., 2021. "Finite Sample Optimality of Score-Driven Volatility Models: Some Monte Carlo Evidence," Econometrics and Statistics, Elsevier, vol. 19(C), pages 47-57.
    22. Anna Gloria Billé & Leopoldo Catania, 2018. "Dynamic Spatial Autoregressive Models with Time-varying Spatial Weighting Matrices," BEMPS - Bozen Economics & Management Paper Series BEMPS55, Faculty of Economics and Management at the Free University of Bozen.
    23. F. Blasques & P. Gorgi & S. J. Koopman & J. Sampi, 2023. "Does trade integration imply growth in Latin America? Evidence from a dynamic spatial spillover model," Tinbergen Institute Discussion Papers 23-007/IVI, Tinbergen Institute.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mauro Bernardi & Leopoldo Catania, 2015. "Switching-GAS Copula Models With Application to Systemic Risk," Papers 1504.03733, arXiv.org, revised Jan 2016.
    2. Blasques, Francisco & Koopman, Siem Jan & Lucas, Andre & Schaumburg, Julia, 2016. "Spillover dynamics for systemic risk measurement using spatial financial time series models," Journal of Econometrics, Elsevier, vol. 195(2), pages 211-223.
    3. Bernardi, Mauro & Catania, Leopoldo, 2018. "Portfolio optimisation under flexible dynamic dependence modelling," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 1-18.
    4. Mauro Bernardi & Leopoldo Catania, 2016. "Portfolio Optimisation Under Flexible Dynamic Dependence Modelling," Papers 1601.05199, arXiv.org.
    5. Anna Gloria Billé & Leopoldo Catania, 2018. "Dynamic Spatial Autoregressive Models with Time-varying Spatial Weighting Matrices," BEMPS - Bozen Economics & Management Paper Series BEMPS55, Faculty of Economics and Management at the Free University of Bozen.
    6. Heil, Thomas L.A. & Peter, Franziska J. & Prange, Philipp, 2022. "Measuring 25 years of global equity market co-movement using a time-varying spatial model," Journal of International Money and Finance, Elsevier, vol. 128(C).
    7. Gong, Pu & Weng, Yingliang, 2016. "Value-at-Risk forecasts by a spatiotemporal model in Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 441(C), pages 173-191.
    8. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    9. Leopoldo Catania & Nima Nonejad, 2016. "Density Forecasts and the Leverage Effect: Some Evidence from Observation and Parameter-Driven Volatility Models," Papers 1605.00230, arXiv.org, revised Nov 2016.
    10. Marco Bazzi & Francisco Blasques & Siem Jan Koopman & Andre Lucas, 2017. "Time-Varying Transition Probabilities for Markov Regime Switching Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(3), pages 458-478, May.
    11. Francisco (F.) Blasques & Andre (A.) Lucas & Andries van Vlodrop, 2017. "Finite Sample Optimality of Score-Driven Volatility Models," Tinbergen Institute Discussion Papers 17-111/III, Tinbergen Institute.
    12. Blasques, Francisco & Lucas, André & van Vlodrop, Andries C., 2021. "Finite Sample Optimality of Score-Driven Volatility Models: Some Monte Carlo Evidence," Econometrics and Statistics, Elsevier, vol. 19(C), pages 47-57.
    13. Blasques, Francisco & van Brummelen, Janneke & Koopman, Siem Jan & Lucas, André, 2022. "Maximum likelihood estimation for score-driven models," Journal of Econometrics, Elsevier, vol. 227(2), pages 325-346.
    14. Solmaria Halleck Vega & J. Paul Elhorst, 2015. "The Slx Model," Journal of Regional Science, Wiley Blackwell, vol. 55(3), pages 339-363, June.
    15. Leopoldo Catania, 2016. "Dynamic Adaptive Mixture Models," Papers 1603.01308, arXiv.org, revised Jan 2023.
    16. Paul Elhorst & Solmaria Halleck Vega, 2013. "On spatial econometric models, spillover effects, and W," ERSA conference papers ersa13p222, European Regional Science Association.
    17. Gorgi, Paolo & Koopman, Siem Jan & Li, Mengheng, 2019. "Forecasting economic time series using score-driven dynamic models with mixed-data sampling," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1735-1747.
    18. Seya, Hajime & Yamagata, Yoshiki & Tsutsumi, Morito, 2013. "Automatic selection of a spatial weight matrix in spatial econometrics: Application to a spatial hedonic approach," Regional Science and Urban Economics, Elsevier, vol. 43(3), pages 429-444.
    19. Buccheri, Giuseppe & Corsi, Fulvio & Flandoli, Franco & Livieri, Giulia, 2021. "The continuous-time limit of score-driven volatility models," Journal of Econometrics, Elsevier, vol. 221(2), pages 655-675.
    20. Tobias Eckernkemper & Bastian Gribisch, 2021. "Intraday conditional value at risk: A periodic mixed‐frequency generalized autoregressive score approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(5), pages 883-910, August.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1602.02542. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.