IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v213y2019i2p578-592.html
   My bibliography  Save this article

Saddlepoint approximations for short and long memory time series: A frequency domain approach

Author

Listed:
  • La Vecchia, Davide
  • Ronchetti, Elvezio

Abstract

Saddlepoint techniques provide numerically accurate, small sample approximations to the distribution of estimators and test statistics. Except for a few simple models, these approximations are not available in the framework of stationary time series. We contribute to fill this gap. Under short or long range serial dependence, for Gaussian and non Gaussian processes, we show how to derive and implement saddlepoint approximations for two relevant classes of frequency domain statistics: ratio statistics and Whittle’s estimator. We compare our new approximations to the ones obtained by the standard asymptotic theory and by two widely-applied bootstrap methods. The numerical exercises for Whittle’s estimator show that our approximations yield accuracy’s improvements, while preserving analytical tractability. A real data example concludes the paper.

Suggested Citation

  • La Vecchia, Davide & Ronchetti, Elvezio, 2019. "Saddlepoint approximations for short and long memory time series: A frequency domain approach," Journal of Econometrics, Elsevier, vol. 213(2), pages 578-592.
    • Handle: RePEc:eee:econom:v:213:y:2019:i:2:p:578-592
    DOI: 10.1016/j.jeconom.2018.10.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407619301629
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2018.10.009?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. Ullah, Aman, 2004. "Finite Sample Econometrics," OUP Catalogue, Oxford University Press, number 9780198774488.
    2. Poskitt, D.S. & Grose, Simone D. & Martin, Gael M., 2015. "Higher-order improvements of the sieve bootstrap for fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 188(1), pages 94-110.
    3. Sowell, Fallaw, 1992. "Modeling long-run behavior with the fractional ARIMA model," Journal of Monetary Economics, Elsevier, vol. 29(2), pages 277-302, April.
    4. Gil-Alana, L. A. & Robinson, P. M., 1997. "Testing of unit root and other nonstationary hypotheses in macroeconomic time series," Journal of Econometrics, Elsevier, vol. 80(2), pages 241-268, October.
    5. Kundhi, Gubhinder & Rilstone, Paul, 2013. "Edgeworth And Saddlepoint Expansions For Nonlinear Estimators," Econometric Theory, Cambridge University Press, vol. 29(5), pages 1057-1078, October.
    6. Daniel Janas, 1994. "Edgeworth expansions for spectral mean estimates with applications to Whittle estimates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(4), pages 667-682, December.
    7. Lieberman, Offer & Rousseau, Judith & Zucker, David M., 2000. "Small-Sample Likelihood-Based Inference In The Arfima Model," Econometric Theory, Cambridge University Press, vol. 16(2), pages 231-248, April.
    8. Lieberman, Offer, 1994. "On the Approximation of Saddlepoint Expansions in Statistics," Econometric Theory, Cambridge University Press, vol. 10(5), pages 900-916, December.
    9. Durlauf, Steven N & Phillips, Peter C B, 1988. "Trends versus Random Walks in Time Series Analysis," Econometrica, Econometric Society, vol. 56(6), pages 1333-1354, November.
    10. Heyde, C. C. & Gay, R., 1993. "Smoothed periodogram asymptotics and estimation for processes and fields with possible long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 45(1), pages 169-182, March.
    11. Ulrich K. Müller & Mark W. Watson, 2015. "Low-Frequency Econometrics," NBER Working Papers 21564, National Bureau of Economic Research, Inc.
    12. Andrews, Donald W.K. & Lieberman, Offer, 2005. "Valid Edgeworth Expansions For The Whittle Maximum Likelihood Estimator For Stationary Long-Memory Gaussian Time Series," Econometric Theory, Cambridge University Press, vol. 21(4), pages 710-734, August.
    13. Xiao, Zhijie & Phillips, Peter C. B., 1998. "Higher-order approximations for frequency domain time series regression," Journal of Econometrics, Elsevier, vol. 86(2), pages 297-336, June.
    14. Kim, Young Min & Nordman, Daniel J., 2013. "A frequency domain bootstrap for Whittle estimation under long-range dependence," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 405-420.
    15. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    16. Ai[dieresis]t-Sahalia, Yacine & Yu, Jialin, 2006. "Saddlepoint approximations for continuous-time Markov processes," Journal of Econometrics, Elsevier, vol. 134(2), pages 507-551, October.
    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. Chaonan Jiang & Davide La Vecchia & Elvezio Ronchetti & Olivier Scaillet, 2023. "Saddlepoint Approximations for Spatial Panel Data Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(542), pages 1164-1175, April.
    2. Alfonso García-Pérez, 2022. "On Robustness for Spatio-Temporal Data," Mathematics, MDPI, vol. 10(10), pages 1-17, May.
    3. Ronchetti, Elvezio, 2020. "Accurate and robust inference," Econometrics and Statistics, Elsevier, vol. 14(C), pages 74-88.

    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. Michelacci, Claudio & Zaffaroni, Paolo, 2000. "(Fractional) beta convergence," Journal of Monetary Economics, Elsevier, vol. 45(1), pages 129-153, February.
    2. Luis A. Gil-Alana & Antonio Moreno & Seonghoon Cho, 2012. "The Deaton paradox in a long memory context with structural breaks," Applied Economics, Taylor & Francis Journals, vol. 44(25), pages 3309-3322, September.
    3. Christophe Andr頍 & Luis A. Gil-Alana & Rangan Gupta, 2014. "Testing for persistence in housing price-to-income and price-to-rent ratios in 16 OECD countries," Applied Economics, Taylor & Francis Journals, vol. 46(18), pages 2127-2138, June.
    4. Bertrand Candelon & Luis A. Gil-Alana, 2004. "Fractional integration and business cycle features," Empirical Economics, Springer, vol. 29(2), pages 343-359, May.
    5. Arteche, Josu & Orbe, Jesus, 2016. "A bootstrap approximation for the distribution of the Local Whittle estimator," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 645-660.
    6. Arteche, Josu & Orbe, Jesus, 2017. "A strategy for optimal bandwidth selection in Local Whittle estimation," Econometrics and Statistics, Elsevier, vol. 4(C), pages 3-17.
    7. Peter C. B. Phillips, 2021. "Pitfalls in Bootstrapping Spurious Regression," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 163-217, December.
    8. Guglielmo Maria Caporale & Luis Alberiko Gil-Alana & Pedro Jose Piqueras Martinez, 2024. "Dynamic Factor Models and Fractional Integration—With an Application to US Real Economic Activity," Econometrics, MDPI, vol. 12(4), pages 1-14, December.
    9. Morten Ørregaard Nielsen & Per Houmann Frederiksen, 2005. "Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 405-443.
    10. Peter C. B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-470, December.
    11. Arteche, Josu & Orbe, Jesus, 2009. "Using the bootstrap for finite sample confidence intervals of the log periodogram regression," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 1940-1953, April.
    12. Macaro, Christian, 2008. "The impact of vintage on the persistence of gross domestic product shocks," Economics Letters, Elsevier, vol. 98(3), pages 301-308, March.
    13. Gil-Alana, Luis A. & Mudida, Robert & Zerbo, Eleazar, 2021. "GDP per capita IN SUB-SAHARAN Africa: A time series approach using long memory," International Review of Economics & Finance, Elsevier, vol. 72(C), pages 175-190.
    14. Luis Alberiko Gil-Alaña, 2010. "Tourism in South Africa. Time series persistence and the nature of shocks. Are they transitory or permament?," NCID Working Papers 06/2011, Navarra Center for International Development, University of Navarra.
    15. John Barkoulas & Christopher Baum & Mustafa Caglayan, 1999. "Fractional monetary dynamics," Applied Economics, Taylor & Francis Journals, vol. 31(11), pages 1393-1400.
    16. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2015. "Infant mortality rates: time trends and fractional integration," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(3), pages 589-602, March.
    17. Yong Glasure & Aie-Rie Lee & James Norris, 1999. "Level of economic development and political democracy revisited," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 5(4), pages 466-477, November.
    18. Monika Zimmermann & Florian Ziel, 2024. "Efficient mid-term forecasting of hourly electricity load using generalized additive models," Papers 2405.17070, arXiv.org.
    19. Entorf, Horst, 1997. "Random walks with drifts: Nonsense regression and spurious fixed-effect estimation," Journal of Econometrics, Elsevier, vol. 80(2), pages 287-296, October.
    20. Christian Macaro, 2007. "The Impact of Vintage on the Persistence of Gross Domestic Product Shocks," CEIS Research Paper 101, Tor Vergata University, CEIS.

    More about this item

    Keywords

    Periodogram; Tilted edgeworth expansion; Macroeconomic time series; Relative error; Whittle’s estimator;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    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:econom:v:213:y:2019:i:2:p:578-592. 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: http://www.elsevier.com/locate/jeconom .

    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.