IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v64y2023i5d10.1007_s00362-022-01357-1.html
   My bibliography  Save this article

A general framework for spatial GARCH models

Author

Listed:
  • Philipp Otto

    (Leibniz University Hannover)

  • Wolfgang Schmid

    (European University Viadrina)

Abstract

In time-series analysis, particularly in finance, generalized autoregressive conditional heteroscedasticity (GARCH) models are widely applied statistical tools for modelling volatility clusters (i.e., periods of increased or decreased risk). In contrast, it has not been considered to be of critical importance until now to model spatial dependence in the conditional second moments. Only a few models have been proposed for modelling local clusters of increased risks. In this paper, we introduce a novel spatial GARCH process in a unified spatial and spatiotemporal GARCH framework, which also covers all previously proposed spatial ARCH models, exponential spatial GARCH, and time-series GARCH models. In contrast to previous spatiotemporal and time series models, this spatial GARCH allows for instantaneous spill-overs across all spatial units. For this common modelling framework, estimators are derived based on a non-linear least-squares approach. Eventually, the use of the model is demonstrated by a Monte Carlo simulation study and by an empirical example that focuses on real estate prices from 1995 to 2014 across the postal code areas of Berlin. A spatial autoregressive model is applied to the data to illustrate how locally varying model uncertainties (e.g., due to latent regressors) can be captured by the spatial GARCH-type models.

Suggested Citation

  • Philipp Otto & Wolfgang Schmid, 2023. "A general framework for spatial GARCH models," Statistical Papers, Springer, vol. 64(5), pages 1721-1747, October.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:5:d:10.1007_s00362-022-01357-1
    DOI: 10.1007/s00362-022-01357-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-022-01357-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-022-01357-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bernard Fingleton, 2008. "A Generalized Method of Moments Estimator for a Spatial Panel Model with an Endogenous Spatial Lag and Spatial Moving Average Errors," Spatial Economic Analysis, Taylor & Francis Journals, vol. 3(1), pages 27-44.
    2. Massimiliano Caporin & Paolo Paruolo, 2015. "Proximity-Structured Multivariate Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 34(5), pages 559-593, May.
    3. Bhattacharjee, Arnab & Jensen-Butler, Chris, 2013. "Estimation of the spatial weights matrix under structural constraints," Regional Science and Urban Economics, Elsevier, vol. 43(4), pages 617-634.
    4. Francq, Christian & Wintenberger, Olivier & Zakoïan, Jean-Michel, 2013. "GARCH models without positivity constraints: Exponential or log GARCH?," Journal of Econometrics, Elsevier, vol. 177(1), pages 34-46.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Sondre Hølleland & Hans Arnfinn Karlsen, 2020. "A Stationary Spatio‐Temporal GARCH Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 177-209, March.
    7. 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.
    8. Gopal K. Basak & Arnab Bhattacharjee & Samarjit Das, 2018. "Causal ordering and inference on acyclic networks," Empirical Economics, Springer, vol. 55(1), pages 213-232, August.
    9. 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.
    10. Philipp Otto & Wolfgang Schmid & Robert Garthoff, 2021. "Stochastic properties of spatial and spatiotemporal ARCH models," Statistical Papers, Springer, vol. 62(2), pages 623-638, April.
    11. Süleyman Taşpınar & Osman DoĞan & Jiyoung Chae & Anil K. Bera, 2021. "Bayesian Inference in Spatial Stochastic Volatility Models: An Application to House Price Returns in Chicago," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(5), pages 1243-1272, October.
    12. 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.
    13. repec:dau:papers:123456789/10571 is not listed on IDEAS
    14. J. Elhorst, 2010. "Applied Spatial Econometrics: Raising the Bar," Spatial Economic Analysis, Taylor & Francis Journals, vol. 5(1), pages 9-28.
    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. Osman Dou{g}an & Raffaele Mattera & Philipp Otto & Suleyman Tac{s}p{i}nar, 2024. "A Dynamic Spatiotemporal and Network ARCH Model with Common Factors," Papers 2410.16526, arXiv.org.

    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. Philipp Otto & Osman Dou{g}an & Suleyman Tac{s}p{i}nar & Wolfgang Schmid & Anil K. Bera, 2023. "Spatial and Spatiotemporal Volatility Models: A Review," Papers 2308.13061, arXiv.org.
    2. Philipp Otto & Wolfgang Schmid, 2021. "Generalized Spatial and Spatiotemporal ARCH Models," Papers 2106.10477, arXiv.org.
    3. Leopoldo Catania & Anna Gloria Billé, 2017. "Dynamic spatial autoregressive models with autoregressive and heteroskedastic disturbances," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(6), pages 1178-1196, September.
    4. Philipp Otto, 2022. "A Multivariate Spatial and Spatiotemporal ARCH Model," Papers 2204.12472, arXiv.org.
    5. Philipp Otto & Osman Dou{g}an & Suleyman Tac{s}p{i}nar, 2022. "Dynamic Spatiotemporal ARCH Models," Papers 2202.13856, arXiv.org.
    6. Sucarrat, Genaro & Grønneberg, Steffen & Escribano, Alvaro, 2016. "Estimation and inference in univariate and multivariate log-GARCH-X models when the conditional density is unknown," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 582-594.
    7. Christian Francq & Genaro Sucarrat, 2018. "An Exponential Chi-Squared QMLE for Log-GARCH Models Via the ARMA Representation," Journal of Financial Econometrics, Oxford University Press, vol. 16(1), pages 129-154.
    8. Liu, Xiaodong & Lee, Lung-fei, 2010. "GMM estimation of social interaction models with centrality," Journal of Econometrics, Elsevier, vol. 159(1), pages 99-115, November.
    9. Sucarrat, Genaro & Grønneberg, Steffen, 2016. "Models of Financial Return With Time-Varying Zero Probability," MPRA Paper 68931, University Library of Munich, Germany.
    10. Boubacar Maïnassara, Y. & Kadmiri, O. & Saussereau, B., 2022. "Estimation of multivariate asymmetric power GARCH models," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    11. Simon K. C. Cheung & Tommy K. Y. Cheung, 2022. "Mixed membership nearest neighbor model with feature difference," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(8), pages 1578-1594, December.
    12. Jin, Fei & Lee, Lung-fei, 2018. "Irregular N2SLS and LASSO estimation of the matrix exponential spatial specification model," Journal of Econometrics, Elsevier, vol. 206(2), pages 336-358.
    13. Zhu, Ke & Li, Wai Keung, 2013. "A new Pearson-type QMLE for conditionally heteroskedastic models," MPRA Paper 52344, University Library of Munich, Germany.
    14. Sucarrat, Genaro, 2018. "The Log-GARCH Model via ARMA Representations," MPRA Paper 100386, University Library of Munich, Germany.
    15. Wondmagegn Tirkaso & Atakelty Hailu, 2022. "Does neighborhood matter? Spatial proximity and farmers’ technical efficiency," Agricultural Economics, International Association of Agricultural Economists, vol. 53(3), pages 374-386, May.
    16. Arbués, Pelayo & Baños, José F. & Mayor, Matías, 2015. "The spatial productivity of transportation infrastructure," Transportation Research Part A: Policy and Practice, Elsevier, vol. 75(C), pages 166-177.
    17. Paul Elhorst & Solmaria Halleck Vega, 2013. "On spatial econometric models, spillover effects, and W," ERSA conference papers ersa13p222, European Regional Science Association.
    18. Kun Duan & Tapas Mishra & Mamata Parhi & Simon Wolfe, 2019. "How Effective are Policy Interventions in a Spatially-Embedded International Real Estate Market?," The Journal of Real Estate Finance and Economics, Springer, vol. 58(4), pages 596-637, May.
    19. Marbuah, George & Amuakwa-Mensah, Franklin, 2017. "Spatial analysis of emissions in Sweden," Energy Economics, Elsevier, vol. 68(C), pages 383-394.
    20. Olivier Wintenberger, 2013. "Continuous Invertibility and Stable QML Estimation of the EGARCH(1,1) Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 846-867, December.

    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:spr:stpapr:v:64:y:2023:i:5:d:10.1007_s00362-022-01357-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.