IDEAS home Printed from https://ideas.repec.org/a/spr/waterr/v30y2016i10d10.1007_s11269-016-1367-x.html
   My bibliography  Save this article

Exploring the Regional Variance using ARMA-GARCH Models

Author

Listed:
  • Huantian Xie

    (Linyi University)

  • Dingfang Li

    (Wuhan University)

  • Lihua Xiong

    (Wuhan University)

Abstract

Recently some generalized autoregressive conditional heteroskedasticity (GARCH) models are proposed and applied to various hydrologic variables to capture and remove the ARCH effect, which has been observed frequently in the residuals from linear autoregressive moving average (ARMA) models fitted to hydrologic time series. As a nonlinear phenomenon of variance behavior, the ARCH effect reveals partially nonstationarity and nonlinearity of hydrological processes. This paper deals with the variation of a river basin using the ARMA-GARCH error model, which combines an ARMA model for modelling the mean behavior and a GARCH model for modelling the variance behavior of the residuals from the ARMA model. Based on the heteroscedasticity of hydrological variable series, the time-varying regional variance is proposed to check the variation of a river basin for the first time. As a study case, the method is applied to four deseasonalized daily discharge series from the middle reach of Yangtze River, China. Through the analyses of the conditional variance in different streamflow series, it is concluded that: (1) The ARCH effect exists in all the studied series which means the stream processes is nonstationary in terms of the variance; (2) The variations of time-varying variances are similar for the series from adjacent hydrological stations, and the similarity degree increases from upstream to downstream; (3) The regional variance is time-varying and can be used for further regional research.

Suggested Citation

  • Huantian Xie & Dingfang Li & Lihua Xiong, 2016. "Exploring the Regional Variance using ARMA-GARCH Models," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(10), pages 3507-3518, August.
    • Handle: RePEc:spr:waterr:v:30:y:2016:i:10:d:10.1007_s11269-016-1367-x
    DOI: 10.1007/s11269-016-1367-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11269-016-1367-x
    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/s11269-016-1367-x?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. L. Vasiliades & P. Galiatsatou & A. Loukas, 2015. "Nonstationary Frequency Analysis of Annual Maximum Rainfall Using Climate Covariates," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(2), pages 339-358, January.
    2. Jenq-Tzong Shiau & Hui-Ting Hsu, 2016. "Suitability of ANN-Based Daily Streamflow Extension Models: a Case Study of Gaoping River Basin, Taiwan," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(4), pages 1499-1513, March.
    3. Mustafa Al-Mukhtar & Volkmar Dunger & Broder Merkel, 2014. "Assessing the Impacts of Climate Change on Hydrology of the Upper Reach of the Spree River: Germany," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(10), pages 2731-2749, August.
    4. Runtong Zhang & Zhenji Zhang & Kecheng Liu & Juliang Zhang (ed.), 2015. "Liss 2013," Springer Books, Springer, number 978-3-642-40660-7, September.
    5. Andrew A. Weiss, 1984. "Arma Models With Arch Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 5(2), pages 129-143, March.
    6. Marius-Victor Birsan, 2015. "Trends in Monthly Natural Streamflow in Romania and Linkages to Atmospheric Circulation in the North Atlantic," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(9), pages 3305-3313, July.
    7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    8. Yixuan Wang & Jianzhu Li & Ping Feng & Rong Hu, 2015. "A Time-Dependent Drought Index for Non-Stationary Precipitation Series," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(15), pages 5631-5647, December.
    9. Lihua Xiong & Tao Du & Chong-Yu Xu & Shenglian Guo & Cong Jiang & Christopher Gippel, 2015. "Non-Stationary Annual Maximum Flood Frequency Analysis Using the Norming Constants Method to Consider Non-Stationarity in the Annual Daily Flow Series," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(10), pages 3615-3633, August.
    10. A. I. McLeod & W. K. Li, 1983. "Diagnostic Checking Arma Time Series Models Using Squared‐Residual Autocorrelations," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(4), pages 269-273, July.
    11. A. Yilmaz & B. Perera, 2015. "Spatiotemporal Trend Analysis of Extreme Rainfall Events in Victoria, Australia," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(12), pages 4465-4480, September.
    12. Dingfang Li & Huantian Xie & Lihua Xiong, 2014. "Temporal Change Analysis Based on Data Characteristics and Nonparametric Test," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(1), pages 227-240, January.
    13. Jenq-Tzong Shiau & Hui-Ting Hsu, 2016. "Suitability of ANN-Based Daily Streamflow Extension Models: a Case Study of Gaoping River Basin, Taiwan," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(4), pages 1499-1513, March.
    14. Zhenji Zhang & Zuojun Max Shen & Juliang Zhang & Runtong Zhang (ed.), 2015. "Liss 2014," Springer Books, Springer, edition 127, number 978-3-662-43871-8, September.
    15. 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.
    Full references (including those not matched with items on IDEAS)

    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. Wentao Xu & Cong Jiang & Lei Yan & Lingqi Li & Shuonan Liu, 2018. "An Adaptive Metropolis-Hastings Optimization Algorithm of Bayesian Estimation in Non-Stationary Flood Frequency Analysis," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(4), pages 1343-1366, March.
    2. Yixuan Wang & Jianzhu Li & Ping Feng & Rong Hu, 2015. "A Time-Dependent Drought Index for Non-Stationary Precipitation Series," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(15), pages 5631-5647, December.
    3. Ntebogang Dinah Moroke, 2015. "An Optimal Generalized Autoregressive Conditional Heteroscedasticity Model for Forecasting the South African Inflation Volatility," Journal of Economics and Behavioral Studies, AMH International, vol. 7(4), pages 134-149.
    4. Jin Lee, 2000. "One-Sided Testing for ARCH Effect Using Wavelets," Econometric Society World Congress 2000 Contributed Papers 1214, Econometric Society.
    5. Guy Melard, 1994. "Modèles linéaires et non linéaires," ULB Institutional Repository 2013/13804, ULB -- Universite Libre de Bruxelles.
    6. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654, January.
    7. Yiming Hu & Zhongmin Liang & Vijay P. Singh & Xuebin Zhang & Jun Wang & Binquan Li & Huimin Wang, 2018. "Concept of Equivalent Reliability for Estimating the Design Flood under Non-stationary Conditions," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(3), pages 997-1011, February.
    8. Duchesne, Pierre, 2004. "On robust testing for conditional heteroscedasticity in time series models," Computational Statistics & Data Analysis, Elsevier, vol. 46(2), pages 227-256, June.
    9. Alagidede, Paul & Panagiotidis, Theodore, 2009. "Modelling stock returns in Africa's emerging equity markets," International Review of Financial Analysis, Elsevier, vol. 18(1-2), pages 1-11, March.
    10. Eleni Constantinou & Robert Georgiades & Avo Kazandjian & George Kouretas, 2005. "Mean and variance causality between the Cyprus Stock Exchange and major equity markets," Working Papers 0501, University of Crete, Department of Economics.
    11. Theodore Panagiotidis, 2010. "Market efficiency and the Euro: the case of the Athens stock exchange," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 37(3), pages 237-251, July.
    12. Suripto & Supriyanto, 2021. "The Effect of the COVID-19 Pandemic on Stock Prices with the Event Window Approach: A Case Study of State Gas Companies, in the Energy Sector," International Journal of Energy Economics and Policy, Econjournals, vol. 11(3), pages 155-162.
    13. Aloui, Chaker & Hammoudeh, Shawkat & Hamida, Hela ben, 2015. "Global factors driving structural changes in the co-movement between sharia stocks and sukuk in the Gulf Cooperation Council countries," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 311-329.
    14. Pan, Ming-Shiun & Chan, Kam C. & Fok, Chi-Wing, 1995. "The distribution of currency futures price changes: A two-piece mixture of normals approach," International Review of Economics & Finance, Elsevier, vol. 4(1), pages 69-78.
    15. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107034723.
    16. van Dijk, Dick & Franses, Philip Hans & Lucas, Andre, 1999. "Testing for ARCH in the Presence of Additive Outliers," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 539-562, Sept.-Oct.
    17. Cheung, Yin-Wong & Ng, Lilian K., 1996. "A causality-in-variance test and its application to financial market prices," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 33-48.
    18. Y. Liu & B. Wang & H. Zhan & Y. Fan & Y. Zha & Y. Hao, 2017. "Simulation of Nonstationary Spring Discharge Using Time Series Models," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(15), pages 4875-4890, December.
    19. Shields, Kalvinder K, 1997. "Threshold Modelling of Stock Return Volatility on Eastern European Markets," Economic Change and Restructuring, Springer, vol. 30(2-3), pages 107-125.
    20. Wang, Lu, 2021. "Time-varying conditional beta, return spillovers, and dynamic bank diversification strategies," The Quarterly Review of Economics and Finance, Elsevier, vol. 79(C), pages 272-280.

    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:waterr:v:30:y:2016:i:10:d:10.1007_s11269-016-1367-x. 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.