IDEAS home Printed from https://ideas.repec.org/p/esx/essedp/15988.html
   My bibliography  Save this paper

The Estimation of Continuous Time Models with Mixed Frequency Data

Author

Listed:
  • Chambers, MJ

Abstract

This paper derives exact representations for discrete time mixed frequency data generated by an underlying multivariate continuous time model. Allowance is made for different combinations of stock and flow variables as well as deterministic trends, and the variables themselves may be stationary or nonstationary (and possibly co-integrated). The resulting discrete time representations allow for the information contained in high frequency data to be utilised alongside the low frequency data in the estimation of the parameters of the continuous time model. Monte Carlo simulations explore the finite sample performance of the maximum likelihood estimator of the continuous time system parameters based on mixed frequency data, and a comparison with extant methods of using data only at the lowest frequency is provided. An empirical application demonstrates the methods developed in the paper and it concludes with a discussion of further ways in which the present analysis can be extended and refined.

Suggested Citation

  • Chambers, MJ, 2016. "The Estimation of Continuous Time Models with Mixed Frequency Data," Economics Discussion Papers 15988, University of Essex, Department of Economics.
    • Handle: RePEc:esx:essedp:15988
    as

    Download full text from publisher

    File URL: https://repository.essex.ac.uk/15988/
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Chambers, Marcus J., 2009. "Discrete Time Representations Of Cointegrated Continuous Time Models With Mixed Sample Data," Econometric Theory, Cambridge University Press, vol. 25(4), pages 1030-1049, August.
    2. Claudia Foroni & Massimiliano Marcellino, 2013. "A survey of econometric methods for mixed-frequency data," Working Paper 2013/06, Norges Bank.
    3. Jewitt, Giles & Roderick McCrorie, J., 2005. "Computing estimates of continuous time macroeconometric models on the basis of discrete data," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 397-416, April.
    4. Bergstrom, A.R., 1984. "Continuous time stochastic models and issues of aggregation over time," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 20, pages 1145-1212, Elsevier.
    5. Marcus J. Chambers, 2011. "Cointegration and sampling frequency," Econometrics Journal, Royal Economic Society, vol. 14(2), pages 156-185, July.
    6. Andreou, Elena & Ghysels, Eric & Kourtellos, Andros, 2010. "Regression models with mixed sampling frequencies," Journal of Econometrics, Elsevier, vol. 158(2), pages 246-261, October.
    7. Claudia Foroni & Massimiliano Marcellino, 2014. "Mixed‐Frequency Structural Models: Identification, Estimation, And Policy Analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(7), pages 1118-1144, November.
    8. Chambers, Marcus J. & Thornton, Michael A., 2012. "Discrete Time Representation Of Continuous Time Arma Processes," Econometric Theory, Cambridge University Press, vol. 28(1), pages 219-238, February.
    9. Eric Ghysels & J. Isaac Miller, 2015. "Testing for Cointegration with Temporally Aggregated and Mixed-Frequency Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(6), pages 797-816, November.
    10. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, Decembrie.
    11. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2006. "Predicting volatility: getting the most out of return data sampled at different frequencies," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 59-95.
    12. Eric Ghysels & J. Isaac Miller, 2014. "On the Size Distortion from Linearly Interpolating Low-frequency Series for Cointegration Tests," Advances in Econometrics, in: Essays in Honor of Peter C. B. Phillips, volume 14, pages 93-122, Emerald Group Publishing Limited.
    13. Simos, Theodore, 1996. "Gaussian Estimation of a Continuous Time Dynamic Model with Common Stochastic Trends," Econometric Theory, Cambridge University Press, vol. 12(2), pages 361-373, June.
    14. Claudia Foroni & Massimiliano Marcellino, 2014. "Mixed frequency structural VARs," Working Paper 2014/01, Norges Bank.
    15. Eric Ghysels & Arthur Sinko & Rossen Valkanov, 2007. "MIDAS Regressions: Further Results and New Directions," Econometric Reviews, Taylor & Francis Journals, vol. 26(1), pages 53-90.
    16. Chambers, Marcus J. & Roderick McCrorie, J., 2007. "Frequency domain estimation of temporally aggregated Gaussian cointegrated systems," Journal of Econometrics, Elsevier, vol. 136(1), pages 1-29, January.
    17. Byeongchan Seong & Sung K. Ahn & Peter A. Zadrozny, 2013. "Estimation of vector error correction models with mixed-frequency data," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(2), pages 194-205, March.
    18. Agbeyegbe, Terence D., 1987. "An Exact Discrete Analog to a Closed Linear First-Order Continuous-Time System with Mixed Sample," Econometric Theory, Cambridge University Press, vol. 3(1), pages 143-149, February.
    19. Chambers, Marcus J., 1998. "The estimation of systems of joint differential-difference equations," Journal of Econometrics, Elsevier, vol. 85(1), pages 1-31, July.
    20. J. Isaac Miller, 2010. "Cointegrating regressions with messy regressors and an application to mixed‐frequency series," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(4), pages 255-277, July.
    21. Phillips, P C B, 1991. "Error Correction and Long-Run Equilibrium in Continuous Time," Econometrica, Econometric Society, vol. 59(4), pages 967-980, July.
    22. Zadrozny, Peter, 1988. "Gaussian Likelihood of Continuous-Time ARMAX Models When Data Are Stocks and Flows at Different Frequencies," Econometric Theory, Cambridge University Press, vol. 4(1), pages 108-124, April.
    23. Agbeyegbe, Terence D., 1988. "An exact discrete analog of an open linear non-stationary first-order continuous-time system with mixed sample," Journal of Econometrics, Elsevier, vol. 39(3), pages 237-250, November.
    24. Bergstrom, Albert Rex, 1983. "Gaussian Estimation of Structural Parameters in Higher Order Continuous Time Dynamic Models," Econometrica, Econometric Society, vol. 51(1), pages 117-152, January.
    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. Philipp Gersing & Leopold Soegner & Manfred Deistler, 2022. "Retrieval from Mixed Sampling Frequency: Generic Identifiability in the Unit Root VAR," Papers 2204.05952, arXiv.org, revised Jul 2023.
    2. Chambers, Marcus J., 2020. "Frequency domain estimation of cointegrating vectors with mixed frequency and mixed sample data," Journal of Econometrics, Elsevier, vol. 217(1), pages 140-160.
    3. Yaoyuan Zhang & Dewen Xiong, 2023. "Optimal Strategy of the Dynamic Mean-Variance Problem for Pairs Trading under a Fast Mean-Reverting Stochastic Volatility Model," Mathematics, MDPI, vol. 11(9), pages 1-19, May.
    4. Thornton, Michael A. & Chambers, Marcus J., 2017. "Continuous time ARMA processes: Discrete time representation and likelihood evaluation," Journal of Economic Dynamics and Control, Elsevier, vol. 79(C), pages 48-65.
    5. Chambers, MJ & McCrorie, JR & Thornton, MA, 2017. "Continuous Time Modelling Based on an Exact Discrete Time Representation," Economics Discussion Papers 20497, University of Essex, Department of Economics.
    6. Deistler, Manfred & Koelbl, Lukas & Anderson, Brian D.O., 2017. "Non-identifiability of VMA and VARMA systems in the mixed frequency case," Econometrics and Statistics, Elsevier, vol. 4(C), pages 31-38.
    7. Antoine GODIN & Sakir-Devrim YILMAZ, 2020. "Modelling Small Open Developing Economies in a Financialized World: A Stock-Flow Consistent Prototype Growth Model," Working Paper 5eb7e0e8-560f-4ce6-91a5-5, Agence française de développement.

    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. Chambers, MJ & McCrorie, JR & Thornton, MA, 2017. "Continuous Time Modelling Based on an Exact Discrete Time Representation," Economics Discussion Papers 20497, University of Essex, Department of Economics.
    2. Thornton, Michael A. & Chambers, Marcus J., 2017. "Continuous time ARMA processes: Discrete time representation and likelihood evaluation," Journal of Economic Dynamics and Control, Elsevier, vol. 79(C), pages 48-65.
    3. Eric Ghysels & J. Isaac Miller, 2015. "Testing for Cointegration with Temporally Aggregated and Mixed-Frequency Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(6), pages 797-816, November.
    4. Thornton, Michael A. & Chambers, Marcus J., 2016. "The exact discretisation of CARMA models with applications in finance," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 739-761.
    5. J. Isaac Miller, 2019. "Testing Cointegrating Relationships Using Irregular and Non‐Contemporaneous Series with an Application to Paleoclimate Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(6), pages 936-950, November.
    6. Michael A. Thornton & Marcus J. Chambers, 2013. "Temporal aggregation in macroeconomics," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 13, pages 289-310, Edward Elgar Publishing.
    7. Eric Ghysels & J. Isaac Miller, 2014. "On the Size Distortion from Linearly Interpolating Low-frequency Series for Cointegration Tests," Advances in Econometrics, in: Essays in Honor of Peter C. B. Phillips, volume 14, pages 93-122, Emerald Group Publishing Limited.
    8. J. Isaac Miller, 2014. "Mixed-frequency Cointegrating Regressions with Parsimonious Distributed Lag Structures," Journal of Financial Econometrics, Oxford University Press, vol. 12(3), pages 584-614.
    9. Michael A. Thornton & Marcus J. Chambers, 2013. "Continuous-time autoregressive moving average processes in discrete time: representation and embeddability," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(5), pages 552-561, September.
    10. J. Isaac Miller & Xi Wang, 2016. "Implementing Residual-Based KPSS Tests for Cointegration with Data Subject to Temporal Aggregation and Mixed Sampling Frequencies," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(6), pages 810-824, November.
    11. J. Isaac Miller, 2016. "Conditionally Efficient Estimation of Long-Run Relationships Using Mixed-Frequency Time Series," Econometric Reviews, Taylor & Francis Journals, vol. 35(6), pages 1142-1171, June.
    12. Christensen, Bent Jesper & Posch, Olaf & van der Wel, Michel, 2016. "Estimating dynamic equilibrium models using mixed frequency macro and financial data," Journal of Econometrics, Elsevier, vol. 194(1), pages 116-137.
    13. Chambers, Marcus J., 2020. "Frequency domain estimation of cointegrating vectors with mixed frequency and mixed sample data," Journal of Econometrics, Elsevier, vol. 217(1), pages 140-160.
    14. Milena Hoyos, 2020. "Mixed First‐ and Second‐Order Cointegrated Continuous Time Models with Mixed Stock and Flow Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 249-267, March.
    15. Chambers, Marcus J., 1999. "Discrete time representation of stationary and non-stationary continuous time systems," Journal of Economic Dynamics and Control, Elsevier, vol. 23(4), pages 619-639, February.
    16. Santiago Etchegaray Alvarez, 2022. "Proyecciones macroeconómicas con datos en frecuencias mixtas. Modelos ADL-MIDAS, U-MIDAS y TF-MIDAS con aplicaciones para Uruguay," Documentos de trabajo 2022004, Banco Central del Uruguay.
    17. Miller, J. Isaac, 2018. "Simple robust tests for the specification of high-frequency predictors of a low-frequency series," Econometrics and Statistics, Elsevier, vol. 5(C), pages 45-66.
    18. Götz, Thomas B. & Hecq, Alain & Smeekes, Stephan, 2016. "Testing for Granger causality in large mixed-frequency VARs," Journal of Econometrics, Elsevier, vol. 193(2), pages 418-432.
    19. Schumacher, Christian, 2016. "A comparison of MIDAS and bridge equations," International Journal of Forecasting, Elsevier, vol. 32(2), pages 257-270.
    20. J. Roderick McCrorie, 2000. "The Likelihood of a Continuous-time Vector Autoregressive Model," Working Papers 419, Queen Mary University of London, School of Economics and Finance.

    More about this item

    Keywords

    Continuous time; mixed frequency data; exact discrete time models; stock and flow variables.;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

    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:esx:essedp:15988. 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: Essex Economics Web Manager (email available below). General contact details of provider: https://edirc.repec.org/data/edessuk.html .

    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.