IDEAS home Printed from https://ideas.repec.org/a/eee/ecosta/v1y2017icp184-200.html
   My bibliography  Save this article

Functional time series forecasting with dynamic updating: An application to intraday particulate matter concentration

Author

Listed:
  • Shang, Han Lin

Abstract

Environmental data often take the form of a collection of curves observed sequentially over time. An example of this includes daily pollution measurement curves describing the concentration of a particulate matter in ambient air. These curves can be viewed as a time series of functions observed at equally spaced intervals over a dense grid. The nature of high-dimensional data poses challenges from a statistical aspect, due to the so-called “curse of dimensionality”, but it also poses opportunities to analyze a rich source of information to better understand dynamic changes at short time intervals. Statistical methods are introduced and compared for forecasting one-day-ahead intraday concentrations of particulate matter; as new data are sequentially observed, dynamic updating methods are proposed to update point and interval forecasts to achieve better accuracy. These forecasting methods are validated through an empirical study of half-hourly concentrations of airborne particulate matter in Graz, Austria.

Suggested Citation

  • Shang, Han Lin, 2017. "Functional time series forecasting with dynamic updating: An application to intraday particulate matter concentration," Econometrics and Statistics, Elsevier, vol. 1(C), pages 184-200.
    • Handle: RePEc:eee:ecosta:v:1:y:2017:i:c:p:184-200
    DOI: 10.1016/j.ecosta.2016.08.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S2452306216300235
    Download Restriction: Full text for ScienceDirect subscribers only. Contains open access articles
    File URL: https://libkey.io/10.1016/j.ecosta.2016.08.004?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. Müller, Hans-Georg & Sen, Rituparna & Stadtmüller, Ulrich, 2011. "Functional data analysis for volatility," Journal of Econometrics, Elsevier, vol. 165(2), pages 233-245.
    2. Horváth, Lajos & Kokoszka, Piotr & Rice, Gregory, 2014. "Testing stationarity of functional time series," Journal of Econometrics, Elsevier, vol. 179(1), pages 66-82.
    3. Hyndman, Rob J. & Khandakar, Yeasmin, 2008. "Automatic Time Series Forecasting: The forecast Package for R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i03).
    4. André Mas & Besnik Pumo, 2009. "Functional linear regression with derivatives," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(1), pages 19-40.
    5. Shang, Han Lin & Hyndman, Rob.J., 2011. "Nonparametric time series forecasting with dynamic updating," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1310-1324.
    6. Horváth, Lajos & Rice, Gregory & Whipple, Stephen, 2016. "Adaptive bandwidth selection in the long run covariance estimator of functional time series," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 676-693.
    7. Chatfield, Chris, 1993. "Calculating Interval Forecasts: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 143-144, April.
    8. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    9. Philippe C. Besse & Herve Cardot & David B. Stephenson, 2000. "Autoregressive Forecasting of Some Functional Climatic Variations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 673-687, December.
    10. Peter Hall & Céline Vial, 2006. "Assessing the finite dimensionality of functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(4), pages 689-705, September.
    11. Manuel Febrero & Pedro Galeano & Wenceslao González-Manteiga, 2007. "A functional analysis of NOx levels: location and scale estimation and outlier detection," Computational Statistics, Springer, vol. 22(3), pages 411-427, September.
    12. Aneiros-Pérez, Germán & Vieu, Philippe, 2008. "Nonparametric time series prediction: A semi-functional partial linear modeling," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 834-857, May.
    13. Chatfield, Chris, 1993. "Calculating Interval Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 121-135, April.
    14. Vinod, Hrishikesh D. & Lopez-de-Lacalle, Javier, 2009. "Maximum Entropy Bootstrap for Time Series: The meboot R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 29(i05).
    15. André A. P. Santos & Francisco J. Nogales & Esther Ruiz, 2013. "Comparing Univariate and Multivariate Models to Forecast Portfolio Value-at-Risk," Journal of Financial Econometrics, Oxford University Press, vol. 11(2), pages 400-441, March.
    16. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    17. Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4942-4956, June.
    18. Berkes, István & Horváth, Lajos & Rice, Gregory, 2016. "On the asymptotic normality of kernel estimators of the long run covariance of functional time series," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 150-175.
    19. Vinod, H. D., 2004. "Ranking mutual funds using unconventional utility theory and stochastic dominance," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 353-377, June.
    20. Haipeng Shen & Jianhua Z. Huang, 2008. "Interday Forecasting and Intraday Updating of Call Center Arrivals," Manufacturing & Service Operations Management, INFORMS, vol. 10(3), pages 391-410, July.
    21. Frédéric Ferraty & Aldo Goia & Philippe Vieu, 2002. "Functional nonparametric model for time series: a fractal approach for dimension reduction," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 317-344, December.
    22. Alexander Aue & Diogo Dubart Norinho & Siegfried Hörmann, 2015. "On the Prediction of Stationary Functional Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 378-392, March.
    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. Chen, Yichao & Pun, Chi Seng, 2019. "A bootstrap-based KPSS test for functional time series," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    2. Francisco Martínez-Álvarez & Amandine Schmutz & Gualberto Asencio-Cortés & Julien Jacques, 2018. "A Novel Hybrid Algorithm to Forecast Functional Time Series Based on Pattern Sequence Similarity with Application to Electricity Demand," Energies, MDPI, vol. 12(1), pages 1-18, December.
    3. Han Lin Shang & Kaiying Ji & Ufuk Beyaztas, 2021. "Granger causality of bivariate stationary curve time series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(4), pages 626-635, July.
    4. Elías, Antonio & Jiménez, Raúl & Shang, Han Lin, 2022. "On projection methods for functional time series forecasting," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    5. Kokoszka, Piotr & Oja, Hanny & Park, Byeong & Sangalli, Laura, 2017. "Special issue on functional data analysis," Econometrics and Statistics, Elsevier, vol. 1(C), pages 99-100.
    6. repec:cte:wsrepe:24606 is not listed 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. Han Lin Shang & Yang Yang & Fearghal Kearney, 2019. "Intraday forecasts of a volatility index: functional time series methods with dynamic updating," Annals of Operations Research, Springer, vol. 282(1), pages 331-354, November.
    2. Han Lin Shang & Yang Yang, 2021. "Forecasting Australian subnational age-specific mortality rates," Journal of Population Research, Springer, vol. 38(1), pages 1-24, March.
    3. Shang, Han Lin & Hyndman, Rob.J., 2011. "Nonparametric time series forecasting with dynamic updating," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1310-1324.
    4. Han Lin Shang & Rob J Hyndman, 2016. "Grouped functional time series forecasting: An application to age-specific mortality rates," Monash Econometrics and Business Statistics Working Papers 4/16, Monash University, Department of Econometrics and Business Statistics.
    5. Yuan Gao & Han Lin Shang, 2017. "Multivariate Functional Time Series Forecasting: Application to Age-Specific Mortality Rates," Risks, MDPI, vol. 5(2), pages 1-18, March.
    6. 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.
    7. Han Lin Shang & Jiguo Cao & Peijun Sang, 2022. "Stopping time detection of wood panel compression: A functional time‐series approach," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1205-1224, November.
    8. Yang, Yang & Shang, Han Lin & Raymer, James, 2024. "Forecasting Australian fertility by age, region, and birthplace," International Journal of Forecasting, Elsevier, vol. 40(2), pages 532-548.
    9. Shang, Han Lin & Haberman, Steven, 2017. "Grouped multivariate and functional time series forecasting:An application to annuity pricing," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 166-179.
    10. Yang, Yang & Yang, Yanrong & Shang, Han Lin, 2022. "Feature extraction for functional time series: Theory and application to NIR spectroscopy data," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    11. Elías, Antonio & Jiménez, Raúl & Shang, Han Lin, 2022. "On projection methods for functional time series forecasting," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    12. Cees Diks & Bram Wouters, 2023. "Noise reduction for functional time series," Papers 2307.02154, arXiv.org.
    13. Chang, Jinyuan & Chen, Cheng & Qiao, Xinghao & Yao, Qiwei, 2023. "An autocovariance-based learning framework for high-dimensional functional time series," LSE Research Online Documents on Economics 117910, London School of Economics and Political Science, LSE Library.
    14. Han Shang, 2014. "A survey of functional principal component analysis," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(2), pages 121-142, April.
    15. Daniel R. Kowal & David S. Matteson & David Ruppert, 2019. "Functional Autoregression for Sparsely Sampled Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(1), pages 97-109, January.
    16. Kosiorowski Daniel & Mielczarek Dominik & Rydlewski Jerzy P. & Snarska Małgorzata, 2018. "Generalized Exponential Smoothing In Prediction Of Hierarchical Time Series," Statistics in Transition New Series, Statistics Poland, vol. 19(2), pages 331-350, June.
    17. Han Lin Shang, 2017. "Reconciling Forecasts of Infant Mortality Rates at National and Sub-National Levels: Grouped Time-Series Methods," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 36(1), pages 55-84, February.
    18. Shang, Han Lin & Kearney, Fearghal, 2022. "Dynamic functional time-series forecasts of foreign exchange implied volatility surfaces," International Journal of Forecasting, Elsevier, vol. 38(3), pages 1025-1049.
    19. Daniel Kosiorowski & Dominik Mielczarek & Jerzy P. Rydlewski & Małgorzata Snarska, 2018. "Generalized Exponential Smoothing In Prediction Of Hierarchical Time Series," Statistics in Transition New Series, Polish Statistical Association, vol. 19(2), pages 331-350, June.
    20. Shang, Han Lin, 2013. "Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 185-198.

    More about this item

    Keywords

    Block moving; Dynamic updating; Functional principal component regression; Functional linear regression; Maximum entropy bootstrap; VAR;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • Q53 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Air Pollution; Water Pollution; Noise; Hazardous Waste; Solid Waste; Recycling

    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:eee:ecosta:v:1:y:2017:i:c:p:184-200. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/econometrics-and-statistics .

    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.