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The estimation of continuous time models with mixed frequency data

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  • Chambers, Marcus J.

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 cointegrated). 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, Marcus J., 2016. "The estimation of continuous time models with mixed frequency data," Journal of Econometrics, Elsevier, vol. 193(2), pages 390-404.
    • Handle: RePEc:eee:econom:v:193:y:2016:i:2:p:390-404
    DOI: 10.1016/j.jeconom.2016.04.013
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    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.
    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.
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    Citations

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    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.

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    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

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